JPRS ID: 9987 USSR REPORT EARTH SCIENCES

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JPRS L/9987
17 September 1981
- I~SSR Re or�t
p
- EARTH SCIENCES
(~OUO 7/81)
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JPRS L/9987
17 September 1981
USSR REPORT
EARTH SCIENCES
(FOUO 7/sl)
CONTENTS
OCEA~IOGRAPHY
Generation of Internal Waves by Local Disturbances in a Fluid With
~ Given Variation of Density Over Aepth 1
Interpreting Measurements of Wind Wave Dispersion Characteristics....... 10
Annotation, Abstract From Book `Basic Elements of Underwater Apparatus
and Robots' 20
Nonlinear Model of the Carbon Cycle in the Ocean 27
Return Signal Magnitude During Remote Laser Sounding of Natural Water
, Mediums 32
Spectra of POLIMODE Currents 40
Spatial Variability of the Acoustic Field Reflected From the Ocean
Floor 44
Selected Abstracts of Unpublished Articles on Geology and Geophysics.... 49
Features of Detection of Sea Surface Inhomogeneities by the Radar
Method 51
Radiative Instability of Shear Currents in a Stratified Fluid........... 61
TERRESTRIAL GEOPHYSICS
S and P Wave Attenuation of the Crust and Upper Mantle Beneath the West
Siberian Plate and Siberian Platform 65
Collection of Articles on Dynamic Theory of Seismic Wave Propagation... 83
_ a _ [1z~ - [:SSt~ - 21K S&T FOUO]
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Papers on Mathematical Methods for Interpreting Geophysical
Observations 86
PHYSICS OF ATMOSPHERE
Papers on Rocket Sounding of the Atmosphere 90
Collection of Papers ~n Atmospheric Optics 92
Collection of Papers on Investigation of the Ionosphere and
Magnetosphere by Artificial Modification Methods 94
ARCTIC AND ANTARCTIC RESEARCH
Laser Sounding of the Upper Atmosphere at the Antarctic Station
_ Molodezhna.ya 96
- b -
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OCEANOGRAPHY
UDC 551.466.81
GENERATION OF INTERNAL WAVES BY LOCAL DISTURBANGES IN A FI,UID WZTH GIVEN VARIATION
OF DENSITY OVER DEPTH
Moscow IZVESTIYA AKADEMII NAUK SSSR: FIZIKA ATMOSF~RY I OI~ANA in Rt;ssian Vol 17,
, No 6, Jun 81 pp 625-631
- [Article by I. V. Sturova and V. A. Sukharev, Institute of Hydrodynamics, Siberian
- Department, USSR Academy of Sciences]
[Text] A method is proposed for calculating linear .zntprnal grav-
itational waves occurring in a nanviscous incompr.essible fluid wi.th
arbifixary continuous stable stratification during uniform flow over
a source and runoff of equal intensi~y and during collapse of a
- "spot" by a completely mixed fluid.
Solution of the given problem has now been found only for sc~me special cases of
dense stratification of a fluid (see, for example [1-4J). Primarily retaining the
postulation of the problem used in [4], let us investigate the behavior of internal
= waves for the general case of continuous (stable) variation of density over depth.
1. Let us consider the stead three-dimensional problem of uniform flow around a
point source system at velocity U and runoff of equal intensity located at depth
h from an undisturbed free surface z= 0 ~f a horizontal layer of fluid < x,
yc~m CM81I18HH08 BOIIH9Hil8 ~9~
I'poya x Ap. [6] (10) - - - ~>~m PaaaiiTOe'sonaense (11)
Ec~aMOa, XpxCTO~o~os [~2 - - - ~?a~m - .
E(j~NMOA H j~p. ~8 3~ - O,2STO~Z9 - W~(~~n
Koanee, Haaapoe [9J (14) - ~0,2 - J~a38 CHeiuaaxoe eonaea~re
s56cx '
JIe�Ki+e, Poaes6epr (10](15 !i5 ~0,2 - 11=6 cM � �
Note. The dash in the table means an absence of the required data in the Daper;
the value of ~Ua/g was not calculated for cases of mixed seas.
Key:
1. Literature 9. Mixed seas
2. m/s 10. Grose et al [6]
3. Hertz 11. Developed seas
4. Range of w(or of a) 12. Yefimov and I~ristoforov [7]
5. Remarks 13. Yefimov et al [8]
6. Kpnyayev and Leykin [4] 14. iconyayev and Nazarov [9]
7. Storm waves 15. Leykin and Rozenberg [10]
8. Kiseleva [5]
Let us first consider one of the simplest methods of an indirect check of disper-
- sion relation (1) for wind waves by the frequency spectra of the rise of level
S(w) and by slope spectra SX1(to) and Sx2(w) corresponding to the spatial deriva-
tives a~/ 3x1 and 8~/8x2 in two mutually perpendicular d;.rections oxl and ox2.
Since the space-time spectrum E~(k, w) of a random field a~/ ~(a = 1, 2) is
related to E(k, w) by the relation
~=a (k, ~)=ka=E(k, w),
then
E,(k, c~)=E=~~k, ~)+E_~(~, ~)~k'E~~ w~'
By integrating with respect to k the latter equality in relation to (2), we find
the relationship of the frequency spectra S(w) and Sx(w) = Sxl(~) + SX2(w) in the
form
s=(~)=(~`~gZ)S(~)� (s)
An experimental check of relation (3) permits one to judge whether the dispersion
relation for wind waves is actually fulfilled.
The usual presentation of experimental data of this type consists in finding the
"dispersion relation"
. k=k~(c~)=(S:(w)lS(~) (4)
_ found upon replacement of multiplier W4/g2 by k on the right side of (3). Similar
data from I5, 6] are pres~nted in Figure 1 that show that dispersion relation (4)
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coincides approximatel~~ with (1) in some frequency range near frequency corre-
sponding to the maximum spectrum of sea state, while function w~(k) determined ac-
cording to (4) in the regior~ of smaller scales systematically exceeds the value of
~(k). However, it is impossible to relate this effect to displacement of the real
dispersion surface WC(k): fi r st, deviation of wC(k) from ~(k) may be related to
increasing errors of determining the spectra of SX(W) and S(W) (the spread of ex-
perimental points in this frequency range usually significantly increases and the
mean path of the derived function is represented in Figure 1 for the data of [5])
and second, blurring of the space-time spectrum E(k~w) with respect to an undis-
torted dispersion surface ~(k) also produces a similar effect.
Similar results from the methodical viewpoint were found in [7] upon comparison of
velocity spectra S~,i1(W) and Sw2(w), which were calculated by simultaneous record-
ings of the vertical velocity component at two l~vels in the surface layer, separ-
ated vertically by distance z. Based on the relation for attenuation of wave mo-
tion with depth, which follows from linear theory, one can find
k(c~)=(1/2Qz) ln (S~~(~)IS,~:(~))� (5)
The values of k(w) calculated according to (5) [7] are also presented in Figure 1.
Consideration of function k(w) shows that dispersion relation w2 = gk is fulfilled
in the frequency range w p 1-2.5 rad~s. A systematic deviation of W~(k) from Q(k)
appears with an increase of frequency; as the authors of [7] note, this indicates
that t~e velocity field in th is frequency band is determined to a significant de-
gree by turbulent motion. In terms of the present paper, this means increased
blurring of spertrum E(k, w).
Let us discuss another metho~ of determining the dispersion relation for wind
waves, consisting of simultaneous recording of the surface rise ~~(t) and ~2(t) at
- two points separated by a short distance lp (compared to the length of the waves
being measured) in the main direction of wave propagation. The phase shift func-
tion arctg (-Q (w) /C (w) )(where C(w) and Q(w) are real and imagi.nary parts of
the mutual spectrum) is calculated by means of mutual spectral analysis and the
phase velocity of the spectral components is determined
c(c~)=l,c~/~(c~). (6)
Full-scale data of this type, related to developed seas (8], are presented in Fig-~
ure 2. A systematic excess of experimental function c(w) over the dispersion func-
tion for free waves c= g/w is partly related to the measurement method--it turns
out that cm ~ g/u,~ when the real angular distribution of wave energy is considered.
However, the difference of experimental values of c(w) from calculated values can-
not be explained in this mar;:zer in the range of higher frequencies (w and
the authors of [8] relate the observed effect to the presence of nonlinear harmonics
of the energy-bearing components of wave action among the high-frequency components
of the spectrum.
One should bear in mind in this regard that even this method has the same disad-
vantages (although in a more subtle form) as methods baseu on a check of relations
- (4) and (5). Actually, the proposition of the existence of dispersion relation (1)
is used a priori in the expre ssions that link frequency spectra C(w) and Q(w) to
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c�t~ -
~5 9
3
5
2 , /
~6 ' .
~4 - - 5--
1,2 - --?f
Z ~ 6 8~,pae~c~
Figure 2. Ratio of Phase Velocity c(w) of Spectral Components of Sea States
to Phase Velocity c= g/W of Free Waves (measurements of Yefimov
et al [8]): 1--experimental values; 2-5--calculated values for
- different approximations of the angular distribution of wave
energy s(6 )(2--5 (A ) ti cos29 , 3--s (6 ) ti cos A. 4--5 (g ) ti cos2 (0. 8g )
~a 5--s ce ) ti Cos co. se
spectrum E(k, w). Therefore, the given expression (6) for c(w), like dispersion
relations (4) and (5), can be used only as an indicator of the similarity ~f the
real dispersion relation to (1). Approximate fulfillment of the equality
lpw/~(w) = g/w (with additional consideration of the angular distribution of~wave
energy) denotes the minor nature of the effects of blurring of the dispersion rela-
tion and its similarity to the function Q(k) _(gk)1~2, but if this equality is
violated, the values of c(w) determined according to (6) no longer describe the
real dispersion relation. Specifically, inequality lp(w)/~(w) > g/w can be ex-
plaine~ only by the effects of blurring the dispersion relation with respect to
the undistorted mean proposition c(w) = g/w.
Thus, thA experimental data at our disposal (Figures 1 and 2), related to the case
of sufficiently developed seas (t,~Ua/g ti 1), indicates that dispersion relation (1)
is fulfilled with acceptable accuracy in this case for the energy-bearing compon-
ents (k x km), although analysis of the degree of smallness of the effects of blur-
ring ~w(k) of real dispersion curve w~(k) and its deviation from function (1) is
difficult.
Determination of dispersion characteristics is made difficult for small-scale com-
ponents (k � km) of developed seas by the complexity of conducting measurements in
the presence of pc.~werful energy-bearing components. On the other hand, the design
complexities related to the use of multicomponent wave sensor systems having selec-
tivity by wave number k and direction of wave arri~al 6 under full scale conditions
have already been overcome for measurements in this range of scales [9]. Using
these systems--two-dimensional i.nterference arrays--one can measure the cross-
_ section Ski(w) of the space-time spectrum E(k, W) for a selected wave number ki,
which essentially permits one to determine both the mean position of the dispersion
surface at k= ki and its effective blurring, which can be determined, for example,
for symmetrical spectra Ski(w) as the width of spectrum Ski(~) by the half-power
level.
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C, CM� L'~
Z0~
n
150
4
100
yY� a,~~ 3 ,
50 Z
~ 4 3 Z ~
. f ~ ~
0 10 ZO JO
w, pa8~c-~
Figure 3. Dependence of Phase Velocity of Waves on Frequency c(w) flabora-
tory measurements of Kononkova and Pokazeyev [11])a 1--disper-
sion curve for free waves c= g/w; 2, 3 and 4--dispersion curves
calculated with regard to drift current for values of dynamic
wind velocity u* = 20.8, 63 and 99 cm/s, resp~ctively; the sym-
bols are the experimental values of c(w)= the error~; show the
position of the frequency of the energy-bearing waves wm
The spectra of Ski(w) for components with a= 38 and 56 cm, obtained during measure-
ments in the coastal zone in a slight wind are presented in [9]. The data of [9)
show that the mean position of the dispersion crest for the investigated c-state
components is similar to the calculated value; at the same time some broadening of
the experimental spectra of Ski(w) is noted compared to the calculated spectra,
the final width of which is related to the spatial resolution of th~ arrays used.
Similar measurements for even smaller scale components (a = 6 cm) showed [10] that
the broadening of the frequency spectra of these components of Ski(w) is so great
at Ua > 1-2 m/s that it is generally impossible to determine the..mean position of
the dispersion crest. ~
Thus, the sparse available data [9, 10] qualitatively confirm the concept of blur-
ring of the dispersion relation for the short-wave crest of the spectrum whose
; value increases with an increase of the wave number k of short waves and, accord-
ing to the authors of [9, 10], is related mainly to modulation of the ripple fre-
quency by long waves. However, quantitative analyses of the magnitude of this
- blurring cannot be found.
Let us judge the experimental data on the dispersion characteristics of wind waves
during the initial stages of development (cm/Ua � 1) whicn are usually studied un-
der laboratory conditions. The most widespread method of ineasuring the dispersion
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relation in laboratory basins is the method already considered of determining the
' phase velocity c(w) by means of two separated sensors. '1"he values of c(w) found ~_n
, [11] and determined by this method are presented in Figure 3; a systematic excess
_ of the measured values c(w) over the dispersion function c(w) = g/w for the energy-
bear ing components of sea state (w ~ c.~) is easily explained by the doppler fre-
~ quency shift due to a drift current in the cr~nnel. Similar results for components
F~ith t~ 'L a}n were found by the same method in [12
At the same tzme the values of c(w) decrease more slowly with an increase of fre-
quency for components with w> c,,}n, which follows from linear theory even with re-
gard to drift (see the data of Figure 3 for u* = 63 and 99 cm/s). According to
the authors of [12], who also obtained a similar result, this is related to non-
linear effects--to the presence of harmonics of the main frequency c,~ in the
spectrum. *
However, as noted above, an excess of the measured values of c(w) over the calcu-
lated values with the given measurement method can also be explained by the pres-
ence of blurring of the dispersion relation with respect to the mean position (with
regard to drift). Some data on blurring of the dispersion relata.on for developed
wind waves with cm/Ua � 1 are ~resented in [14], where broadening of the spectra of
Ski(W) measured by interference arrays for sea-state components with a= 3 and 6 cm
in a slight wind (Ua = 3-5 m/s), was noted.
Information on the extent of blurring ~c~ can also be obtained from radiophysics
papers related to investigation of the doppler spectra of radio (acoustic) signals
scattered by a disturbed water surface. From the viewpoint of spatial analysis of
the wave spectrum, the doppler locater is equivalent to a two-dimensional inter-
- ference array, but provides better spatial selectivity and permits one to realize
the advantages of the noncontact method. Special investigations on blurring of the
dispersion relation using doppler equipment have not yet been carried out, although
similar measurements of the spectra of developed wind waves have already been car-
ried out by the method (see, for example, survey [15]). Nevertheless, it it has
been established that observed broadening of scattered doppler spectra of s(w) can-
not be explained by scattering effects, but is related mainly to blurring of the
dispersion relation of wind waves.
This conclusion is formulated more clearly in [16], where "coherent" broadening
(related to the presence of long-wave components) and "noncoherent" broadening (re-
lated to the turbulent nature of wave formation) of the dispersion relation of
= short-wave components (a ~ 1-10 cm) of wind waves during the initial stages of ~
development were determined.
Taking the foregoing into account, the values obtair~ed in [16-18] for the relative
y width of the spectra of s(w), which comprise from 0.1 to 0.8, can be taken as a
somewhat exaggerated estimate of the relative width of the dispersion crest of
*
Since the drift current is not uniform in depth, there is some ambiguity in select-
ing the values of flow velocity up. A value of u~ = 0.6 u* (u* is the dynamic wind
velocity) was selected in [11], which coincides, according to [13], to the drift
current velocity in a thin surface layer.
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short waves ~w/W. The observed increase in the values of ~w/w with an increase of
wave acceleration F and of wind velocity Ua is apparently related to the modulating
~ effect of the long-wave components, the role of which also increases with an in-
- crease of F and Ua.
- Conclusions. The given consideration of experimental data on the dispersion char-
acteristics of wind waves shows that available full-scale data are very sparse and
were obtained by differsnt (mainly indirect) methods, which makes comparison of
their results difficult. Part of these measurements corresponds to the case of
mixed seasj the values of wind velocity Ua or of the frequency of the spectral max-
imum m are not presented in some papers, which does r.ot permit one to estimate
the degree of development of seas. Therefore, it is presently impossible to obtain
quantitative estimates of the shifting of the mean position of the dispersion crest
and of its blurring for different components of developed seas.
Nevertheless the considered experimental data confirm the analyses presented in
[1], according to which the mean position of the dispersion crest for the energy-
bearing components o� developed seas whose phase velocity is similar to wind ve-
locity (c Ua) coincides with the dispersion relation for linear free waves
w2 = gk, while the magnitude of the blurring is small (Ow/w � 1),although it is
difficult to estimate the degree of smallness of blurring effects.
The values of blurring according to laboratory measurement data are comparable for
wind waves during the initial stage of development to the mean value of frequency
(d,,l/w ti 1), which nakes short waves similar to turbulence in their dispersion prop-
- erties. Further experimental investigations are required to determine the disper-
sion characteristics of the short-wave.components of developed seas, which are
strongly dependent on the orbital motion of long-wave components.
Note. After the given article was sent to press, paper [19] was published in which
the results of direct determination of the dispersion relation for developed wind
waves were presented.from data of simultaneous measurements of sea states at sever-
al separate points. The results of this paper, obtained by adaptive methods of
spectral analysis, agree with the conclusions of this article and shaw that the .
mean position of the dispersion crest is well described by the dispersion relation
w2 = gk while the magnitude of blurring of the crest is small for the energy-bear-
ing components nf seas and those similax to them (u.~ ~ W< 2t,~). In the higher fr~
quency range (w ~ 2Wm), tlie mean position of the dispersion crest.deviates from
the curve w2 = gk :and at the same time there is an increase of the blurring of the
crest, which the authors feel is related to nonlinear effects (the contribution of
the harr.ionics of the main frequency, especially discernible in the range of w~ 2t,.f~)
and to the nonpotential nature of wave motion.
BIBLIOGRAPHY
1. Zaslavskiy, M. M., "The Dispersion Characteristics of Wind Waves," IZVESTIYA AN
SSSR, FAO, Vol 17, No 1, 1981.
2. Davis, R. E. and L. A. Regier, "Methods for Estimating Directional Wave Spectra
from Multielement Arrays," JOURNAL OF MARINE RESEARCH, Vol 35, No 3, 1977.
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3. icozubskaya, G. I., and K. V. IGonyayev, "Adaptive Spectral Analysis of Random
Processes and Fields," IZVESTIYA AN SSSR, FAO, Vol 13, No 1, 1977.
4. IC~nyayev, K. V. and I. A. Leykin, "The Three-Dimensional Structure of Storm
Waves at Sea," IZVESTIYA AN SSSR, FAO, Vol 14, No 12, 1978.
5. Kiseleva, O. A., "Experimzntal Investigation of the Two-Dimensional Energy
Spectriun of Marine Wind Seas," MORSICIYE GIDROFIZICHESKIYA ISSLIDOVANIYA, No 3
(59), 1972.
6. Grose, P. L., K. L. Warsh and M. Garstang, "Dispersion Relations and Wave
Shapes," JOURNAL OF GEOPHYSICAL RESEARCH, Vol 77, No 21, 1972.
7. Yefimov, V. V. and G. N. IQiristoforov, "Wave and Turbulent Components of the
Velocity Spectrum in the Upper Layer of the Ocean," IZVESTIYA AN SSSR, FAO,
Vol 7, No 2, 1971.
, 8. Yefimov, V. V., Yu. P. Solov'yev and G. N. IQiristoforov, "Experimental Deter-
mination of the Phase Propagation Velocity of the Spectral Components of
Marine Wind Seas," IZVESTIYA AN SSSR, FAO, Vol 8, No 4, 1972.
o~
9. ICpnyayev, K. V. ~nd A. A. Nazarov, Measuring the Space-Time Structure of
High-Frequency Coanponents of Wind Seas," IZVESTIYA AN SSSR, FAO, Vol 6, No 1,
1970.
10. Leykin, I. A. and A. D. Rozenberq, "Measuring the Angular Spectra of the High~-
Frequency Part of Seas," IZVESTIYA AN SSSR~ FAO, Vol 7, No 1, 1971.
,
11. Kononkova, G. Ye. and K. V. Pokazeyev, Experimental Investigation of the
Dispersion Relation for the Components of the Frequency Spectrum of Wind
, Waves," VESTNIK MGU, SERIYA FIZIKA, ASTRONOMIYA, Vol 19, No 1, 1978.
12. Ramamonjiarisoa, A. and M. Coantic, "Loi experimentale de dispersion des
vagues par le vent sur une faible longueur d'action," C. R. ACAD. SCI. PARIS,
SER. B, Vol 282, 1976.
13. Wu, J., "Wind-Induced Currents," JOZJRNAL OF FLUID MECHANICS, Vol 68, Part 1,
1965.
14. Leyk3n, I. A., "Experimental Investigation of the Space-Time Structure of
Marine Wind Seas in the High-Frequency Part of the Spectrum~" Candidate of
Physicomathematical Sciences Dissertation, Moscow, YO AN SSSR, 1973.
15. Wright, J. W., "Detection of Ocean Waves by Microwave Radar: The Modulation
of Short Gravity-Capillary Waves," BOUNDARY-LAYER METEOROIAGY, Vol 13, Parts
1-4, 1978.
16. Zel'dis, V. I., I. A. Leykin, I. Ye. Ostrovskiy, A. D. Rozenberg and V. G.
Ruskevich, "Investigating the Fluctuation Chazacteristics of Hydroacoustic
Siqnals Scattered by a Disturbed Water Surface," TRUDY 8-Y VSESOYUZNOY
AKUSTICF~SK~DY KO~TFERENTSII, Nbscow, 1973.
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17. Wright, J. W. and W. C. Keller, "Doppler Spectra in Microwave Scattering From
Wind Waves," PHYSICS OF FLUIDS, Vol 14, No 3, 1971.
18. Duncan, J. R., W. C. Keller and J. W. Wright, "Fetch and Wind Speed Dependence
of Doppler Spectra," RF~D20 SCIENCE, Vol 9, No 10, 1974.
19. Yefimov, V. V. and Yu. P. Salov'yev, "The Dispersion Relation and Frequency-
Angular Spectra of Wind Waves," IZ~dESTIYA AN SSSR, FAO, Vol 15, No 11, 1979.
- COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika atmosfery i okeana",
1981
6521
CSO: 1865/210
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UDC 629.127.066
ANNOTATION, ABSTRACTS FROM BOOK 'BASIC ELEMENTS OF UNDERWATER APPARATUS AND ROBOTS'
Moscow ELE*iENTNAYA BAZA PODVODNYKH APPARATOV I ROBOTOV in Russian 1980 (signed to
press 31 Oct 80) pp 2, 141-144
[Annotation of book "Basic Elements of Underwater Apparatus and Robots" edited by
professor V. S. Yastrebov, doctor of technical sciences, USSR Academy of Sciences,
Izdatel'stvo "Nauka", 1,000 copies, 144 pages]
[Text] The present collection contains reports given at the second Plenum of the
section on "Underwater Apparatus and Robots" of the Oceanographic Commission of
the USSR Academy of Sciences. The plenum was devoted to the problems and chal-
lenges of developing the basic elements of these new technical means of ocean re-
search. The concept of basic elements [literally "element base"] includes not
only the actual elements and systems of underwater 3pparatus and robots, but also
the elements of their theory. It should be noted that the theory of underwater
robots is in the very initial stage of development. Maay of the fundamental
issues are being decided at the present time on the basis of theoretical prin-
ciples that relate to manned underwater vehicles.
The articles in this collection consider the state of the basic elements for
these devices and propose some successful solutions. The book is intended for
scientific workers and engineers engaged in designing technical means of de-
veloping the world ocean.
The book was ratified for printing by the Scientific Council on the Theory and
Principles of the Design of Robots and Manipulators of the USSR Academy of
Sciences and the Institute of Oceanology imeni P. P. Shirshov.
UDC 629.127.065
INTERACTIVE SYSTEMS FOR CONTROLLING UNDERWATER ROBOTS
~
(Abstract of article by Popov, Ye. P., and Kuleshov, V. S.]
[Textj This article considers the basic principles of building interactive sys-
tems to control the movements of underwater manipulating robots which function
purposefully in the ocean ~nvi~onment under conditions of high hydrostatic
pressure. The article has one illustration and three bibliographic entries.
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UDC 629.127.066
PURPOSEFUL ;~CHANICS AS A STANDARDIZED APPARATUS FOR THEORETICAL SUBSTANTIATION
OF MANIPULATOR DESIGNS
[Abstract of article by Korenev, G. V.]
[Text] This article reviews the basic principles of purposeful
[tselenapravlennaya) mechanics for manipulators and techniques of using this
know~edge for effective design of systems to control the movement of manipu-
lators operating in an extreme ocean environment. The article has one illustra-
tion for bibliographic entries.
UDC 629.127.066
BASIC ELEMENTS OF THE SOFTWARE OF t1N ALGORITHM TO CONTROL THE MOVEMENTS OF AN
i.TNDERWATER CARRYING ROBOT IN A MARINE ENVIRONMENT STRATIFIED BY DENSITY
[Abstract of article by Chirskov, S. N.J .
[Text] This article reviews the principles of formation of the file structure of
an algorithm to control ths movements of underwater robots. It discusses the
elementary command of the file to accomplish vertical movements by an underwater
robot in a stratified environment. The article has four bibliographic entries.
UDC 629.127.066
EQUATIONS OF THE ~lOVEMENT OF A SOLID flODY IN A MARINE ENV'IRONMENT STRATIFIED BY
DENSITY
[Abstra~t of article by Chirskov, S. N.]
[TextJ This article reviews the principles of the dynamics of motion by a solid
body in a stratified environment. The author investigates the characteristic
phenomena that occur when a solid body moves in a stratified liquid. The article
has two bibliographic entries.
UDC 629.127.066 -
A LINEAR MODEL OF A RESTRICTED UNDERWATER APPAR~,TUS-?~.~SNIPULATOR SYSTEM
[Abstract of article by Krylov, G. K.J
- [Text] This article considers an underwater apparatus, secured in a current by a
line and receiving disturbances from the work of a manipulator. By analysis of
- the dynamics of the apparatus a system of three scalar differential equations was
derived for planar disturbed motion. By excluding the binding reaction, a linear
- system of two heterogeneous differential equations is shown, and zhen they are
represented in generalized form. The system of equ~ttin;,s permits study of the
_ motion of a restricted underwater apparatus. The article has one illustration
and three bibliographic entries.
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UDC 629.127.066
METHOD OF CONSTRUCTION AND STRUCTURE OF AUTONOMOUS SYSTEMS FOR CONTROL OF THE
?~'IO'TTON OF UNDERWATER APPARATUSES
- [Abstract of article by Popov, 0. S.]
[Text] Underwater apparatuses can be highly efficient only when control of their
movement is automated. The distinctive problems are tracking the bottom and hold-
ing the apparatus at an assigned depth. This article proposes a combined method
to synthesi2e autonomous control systems. The method is based on combined use of
the techniques of optimal control and autonomous regulation.
UDC 629.127.066
PRINCIPLES OF CONSTRL'CTION OF SPECIALIZED COMPUTERS FOR POSITIONAL SUPERVISORY
CONTROL OF UNDERWATER MANIPULATORS
[Abstract of article by Vereshchagin, A. F., and Minayev, L. N.]
[Text] Control of contemporary manipulating robots involves the use of new sources
of command data: coordinating handles, light pens, and displays. With tfie com-
puter they coavert supervisory informa.tion into signals to control the actuating
units. This article reviews the theoretical foundation, control algorithms, and
principles of construction of specialized computers which perform these conver-
sions for positional (static) control systems. The job of these systems is to
switc~i the gripping device of the manipulator automatically. The article has
two illustrations and five bibliographic entries.
. UDC 629.127.066
COMBINED CONTROL OF REMOTE-CONTROLLED UNDERWATER APPARATUSES IN THE DYNAMIC
POSITIONING REGIME
[Abstract of article by Lomonosov, Yu. I.]
[Text] This article is devoted to the questions of automatic stabilization of
an underwater apparatus near the work site in the presence of disturbances by
the manipulator that affect the apparatus. The author considers tfie possi-
bility of building devices to measure the disturbances created by the working
manipulator. He demonstrates the possibility of devising a combined system to
stabilize the position of the apparatus relative to the work site when the ap-
paratus has a device to analyze disturbing forces and moments created by the
working manipulator. The article has one illustration and two bibliographic
entries.
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_ UDC 629,127.066
i
~ SO`fE. ~i~c,:t;.i~;!tiS ~'r' ~:~''~YING SYSTEMS TO CONTROL SECOND-GENERATION APPARATUSES AND
- RCs BL?'~ 5
i.~.b~t~~cc of arricle by V~sil`yev, V. A.J
~;extl ihis article considers ~~Yaracteristics of the process of solving problems
related to devising systems [o control underwater apparatuses and rabots. The
aucha~ ~?.v2s a~lock dia~ram of their hierarchy and analyzes the constituent ele-
ments. This analysis makes it possible to propose regimes and methods of ex- .
aminin~ an assigned regfon usisg underwater robots. The article has one illus-
tration :and five hibliographic entries.
_ UDC 629.127.066
DETER~tI:~aTIOh' OF THE DYWA.~IIC CHARACTERISTICS OF A REMOTE-CONTROLLED APPARATUS IN
THE STAGE OF R~UGH DESIGN �
(Abstrsct of article by Stefanov, G. A.]
~'Text] This arLicle reviews the possibility of determining the dynamic charac-
~eristics of a remnte-controlled apparatus based on the cfiaracteristics of tfi e
ar_tuating, rec~iving, and transmitting devices of a television system, the per-
- sistence of the opcr~tor's visual analyzer, and the rate of updating of the
information content of the television image. Based on the persistence of the
~ transmitting tuues, the author derives equations for maximum rates of tfie most
, typical movement of remo[e-controlled underwater apparatuses (forward and
rotating) around the axis of symmetry. These equations are recommended for
rough calculations vhen determining the maximum tolerable speeds of movement.of
; remote-contrulled underwater apparatuses and, therefore, for determining the
parameters of the propelling unit and selecting the electrical drive of the pro-
~ peller aggregates when studying the work regimes of remote-controlled underwater
apparatuses near the bottom, when the operator is making observations or search-
inb for an object using a television communications channel. The article has
three illustrations and four bibliographic entries.
` UDC 629.127.066
?~`fDROACOli5TIC SYSTE.'`1S OF A DEEP-wr~iER COMPLEX
(~stract of article by Lomonosov, Yu. I., and Sychev, V. A.]
[Text] This article presents a classification of the problems solved by the
hydroacoustic s}~stems of a deep-wz~ter complex. The authors review the systems
used to salve [hese problems and give their basic parameters. The article has
four bibliograph~c entries.
~
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UDC 629.127.066
SECTOR SURVEILLASICE SONAR FOR REMOTE--CONTROLLED UNDERWATER APPaRATUSES
(Abstract of article by Zhavoronkov, S. V., Lomonosov, Yu. I., Rimskiy-Korsakc ,
M. A., Stefanov, G. A., and Sychev, V. A.]
[Text] This article gives a description of a sector surveillance sonar unit de-
signed for use in remote controlled underwater apparatuses. The authors set forth
its operating principles and describe the interaction of the primary assemblies of
the unit. The article has one illustration and two bibliographic entries.
UDC 629.127.066
THE POSSIBILITY OF USING THE STEREO METHOD FOR SURVEYING THE BOTTOM WITH A SIDE-
- LOOKING SONAR
[Abstract of article by Lomonosov, Yu. I., and Sychev, V. A.]
~ (Text] This article considers the possibilities of using the stereo method to
obtain an image of the sector of the bottom being investigated with a side-
looking sonar unit. Expressions are given for determining the magnitude of
displacement beyond the topography owing to the conditions of surveying. The
authors consider two alternatives for obtaining a stereo image and analyze the
images obtained using them. The article has five illustrations and four tiibli-
ographic entries.
UDC 62.52
- SOME CHARACTERISTICS OF COI3STRUCTING CONTROL SYSTEMS FOR REMOTE-CONTROLLED
UNDERWATER APPARATUSES
[Abstract of article by Stefanov, G. A.]
[Text] This article reviews the functions of the human operator as an element
of the control system for remote-controlled underwater apparatuses, charac-
teristics of the operator, and the working conditions. Recommendations are
given for reducing the operator's workload and fatigue by means of automatic
elements and computers that make it possible to use internal potential operator
reserves to solve more complex problems that require fast, operational action.
The article has one illustration and 14 bibliographic entries.
_ UDC 52.514.5
COMMAND AND ACTUATING ELEMENTS OF SYSTEMS TO CONTROL THE MOVEMENT OF REMOTE-
CONTROLLED UNDERWATER APPARATUSES AND SOFTWARE FOR OPERATORS
[Abstract of article by Stafanov, G. ~,.j
[Text] This article reviews the development of control systems depending on the
complexity of the problems which the particular remote-controlled underwater
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apparatus is to solve. Th.e broadening range of ~ohs done by sucfi.apparatuses,
the increasing complexity of tfi.eir design and equipment~ and the growing number
of degrees of freedom of th~ apparatus and its manipulating devices Ftave made it
much more difficult to control them. It is suggested that ways to increase the
efficiency of tfie operator's multifunctional activity should be sought not so
mucfi in improvements of data displaq equipment as in identifying new principles
of control wfiich also contain new forms of information. The article considers
a fundamentally new information-controlling biotechnical system that has been de-
veloped. This system involves creating a multistep suspension system for the
operator's console which simulates the spatial movement of the apparatus and
also has a television image. The article has 19 bibliographic entries.
UDC 629.127.066
PRINCIPLES OF CONSTRUCTION OF PASSIVE DIVING SYSTEMS FOR UNDERWATER APPARATUSES
[Abstract of article by Smirnov, A. V., and Yastrebov, V. S.]
~
[Text] Passive diving systems include oil-filled electrical drive systems, con-
trol systems, and systems for electrical power supply. This article presents
the results of the study of their characteristics under conditions of high
~hydrostatic pressure and reviews the interrelationship and mutual dependence of
these systems and of their individual elements within a diving complex. The
authors formulate 10 principles for the construction of passive diving systems.
The article has three illustrations and one bibliographic entry.
UDC 629.127.066
PRINCIPLES OF CONSTRUCTING HYDRAULIC DIVING SYSTEMS FOR UNDERWATER APPARATUSES
[Abstract of article by Smirnov, A. V., and Yastrebov, S.]
[Text] This article presents the results of studies of all the basic elements of
a hydraulic diving system under conditions of high hydrostatic pressure. The
mutual influence of particular elements is also investigated. As a result, the
authors propose basic principles for designing a deep-water hydraulic drive
system. The "Skat" robot, which was designed on the basis of a hydraulic diving
system, is given as an example. The article has three illustrations and two
i bibliographic entries.
' UDC 629.127.066
PHOTOGRAPHIC COMPLEXES OF UNDERWc1TER ROBOT-APPARATUSES rL~TD TZiEIR BASIC ELEMENTS
[Abstract of article by Kalinin, Yu. S.]
[Text] This article considers the working conditions and requirements of photo-
graphic complexes in underwater apparatuses. The autP.or bives different alter-
natives of optical systems and also a number of types of light sources and their
characteristics in a marine environment with different optical properties.
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UDC 629.127.066
ANALYSIS OF THE CHARACTERISTICS OF THE POWER PLANTS OF UNDERWATER APPARATUSES
[Alistract of article by Gorlov, A. A., and Siminskiy, V. V.]
[Text] This article reviews the structural elements of the energy complex of an
underwater apparatus: the engine installation, the onboard energy unit, the
power supply installation, and the ship support system. The authors give a sys-
tem of equations thaC determine the weight and dimension characteristics of the
sources of various types of energy for the general case wfiere they are arranged
in the solid, spfierical body of an underwater apparatus. The article has two
bibliographic entrfes.
UDC 629.129:620.91
SOURCES OF ENERGY FOR DEEP-WATER APPARATUSES
[Abstract of article by Brilliantov, A. N.J
[Text] This article considers storage batteries, fuel cells, thermal energy
systems, and atomic and radioisotope energy sources. Their energy and weight-
dimension characteristics, strong and weak points, feasibility, and promise for
use as energy sources for deep-water apparatuses are ~.omparad. The article has
two illustrations and five bibliographic entries.
UDC 629.1.075 ~
SOME CHARACTERISTICS OF THE MOVEMENT OF A TOWED BODY
[Abstract of article by Yagodzinskiy, V. A.]
[Textj This article investigates change in the resulting hydrodynamic force of
interaction between liquid and a body traveling close to the bottom. The author
establishes the relationship between the magnitude of the Kelvin force that
arises and the dimensions of the dome and distance from the ocean floor when a
carrier of scientific-technical apparatus is towed in the vertical plane. The
article has two illustrations and two bibliographic entries.
COPYRIGHT: Izdatel'stvo "Nauka", 1980
11,176
CSO: 1863/181
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; �
UDC 551.465:551.464.621
NONLINEAR MODEL OF THE CARBON CYCLE IN THE OCEAN
- Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 285, No 1, 1981 (manuscript re-
ceived 24 Jul 80) pp 212-215
/Article by B.A. Kagan and V.A. Ryabchenko, Leningrad Branch, Institute of
Oceanology imeni P.P. Shirshov, LTSSR Academy of Sciences/
/Text/ A model of the carbon cycle in the ocean that claims to be an adequate re-
production of actuality must describe the interrelated changes in temperaturel, the
total carbon content, the destruction and production of organic mat*_er that is the
source of the flow of carbon of organic origin, the behavior of C02 in solution,
gas exchange with the atmosphere, the thickness of the upper quasihomogeneous layer,
and the processes of exchange between that layer and the deep layer, as well as be-
tween the areas where the cold, deep waters are formed and the rest of the ocean.
The existing models ~an analysis can be found in /1,2/) do not satisfy this re-
_ quirement. To some extent, their flaws are overcome in the model discussed below.
As is usual, we will describe the carbon cycle within the framework of a reservoir
model of the ocean. In contrast to the traditional approach, however, we will re-
linquish the unjustified fixation of the upper quasihomogeneous layer's thickness,
the water temperature, and the coefficients of exchange between the upper quasi-
homogeneous and deep layers. We will regard their values, as with the value of the
C02 rlow at the water-air interface, as being subject to determination. We will
divide the ocean into two areas: the area of the forn,ation of the cold, deep wa-
ters and all the rest of the ocean, within the limits of which there occur rising
vertical movements that compensate for the arrival of cold, deep waters from the
areas where they originate. Let the effect of the first of these areas be distrib-
i uted uniformly or~ the second--a local source is replaced by a distributed one.
~ In view of the condition of conservation of mass, the rate of upwelling in the sec-
ond area will then be W/S, where W is the volume flow rate of the source of the
cold, deep waters and S is the actual area of the second area. In this latter
area we will now distinguish two layers--the upper quasihomogeneous layer and the
deep layer--and examine them together with the area of cold, deep water formation
as a system of interconnected reservoirs. We will further make use of the follow-
ing assumptions, which have been accepted_in the theory of the upper quasi-
homogeneous layer (see, for example, /3,4/. We will assume that there is no turbu-
lence in the seasonal thermocline and the deep layer underlying it; that turbulent
flows on the upper quasihomogeneous layer's lower boundary are caused by the in-
volvement of liquid from the seasonal thermocline as the upper quasihomogeneous
layer deepens and are otherwise equal to zero; that the integral dissipation and
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production ~f turbulent energy of inechanical and convective origin are proportional
to each other, it being the case that the dissipation of the mechanical turbulent
energy is concentrated ir. *_he Ekman boundary layer; that the seasonal thermocline
can be approximated by a temperature jump. As a result, we approach the solution
of the nonlinear problem, which includes the equations for the water temperature T
in each of the reservoirs2:
~ ToH-Qso + S w~Ti - To), (1)
' d1 So
~ T,h - T~ ( ~h + tiv) = 4si - qh_o wT~, ~2)
/
d T2~H-h)+T2~dh +w) = 4it+o+wTo, ~3)
- dt ~
_ the equations for the total carbon concentration /C
- ~ ~~o)H-9so + S "'~~~i~ - ~Co))+Qo, ~4)
dt So
~ ~~i~h- ~C~~~dh +w ~ - 9si -qi-o- W~~~~ +8~~ ~5)
dr � dr �
~ ~~z~~H-lt)+~~z~~~h +ti,~1=y~+o+x~~~o~+Qz. ~6)
dt ~ d! ~
the expression for the gas flow qS at the ocean's surface:
4: = Du. ~~p - ] ( 7 )
the condition of conservation of the sea water ions' charges:
K,(H'] +2K,K2 1~M' ~ (8)
Alk= ~H.~z+K,(H`] +K,K2 ~ +Alko + ~H,~ - ~H J,
the relationship between the concentration of carbon dioxide dissolved in the water
/C02/ and / C / :
- . z ~~`~~(c] (9)
[H ) +K~ [H j +K~K2 ~
the expression for the turbulent flows qt~~ of heat and carbon at the lower bound-
ary of the upper quasihomoge:~eous layer:
i
C( ( ( + wl for (-+w > 0,
T.C' _ ~ 1~~- \~C?]~~\ tj / \~h ~
y~'-~ ~10)
0 for + wl ~ 0,
~ dt /
- the expressions for the equivalent flows qh+p of heat and carbon at the upper
boundary of the deep layer, which parametrize the formation process of the so-
called multiple thermocline3:
r / \
0 for (~r + w 1> 0,
_ ,,c _ \ ~ (11)
q,, +o -
- \~~z~/~\d~ +w~ for (dt +w~s 0,
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~ /cll
~ z.~n
~6 T ~ ~~of
:A ; 110
B jz o
T ~ lc,l
~ 1/0
0 zS ~
0
~ ~
~ /p i ~s ~.ro
~ ZO ~
.~0 , ` ~ S : ~Jc
~ v ti
~
_s
f, ~o.
~ / I i! I D Yp Pdl Id I d/ IY
B ~ .
t r ` i ~
O T S~b-O v-/00 Qh 0/ 9h-O
~ ~ ~b�a ~ I00 ~ ~
q~y
o ~ ! ~i�p
~ I P D!I P YIIY Y~lll I IIII a-J00 I
t, na
Figure 1. Annual pattern of the model's basic variables.
and, finally, for determininn the upper quasihomogeneous layer's thickness h: ~
u3 hl
dh + w= 1 -C~qs~ - C~ a h F(h for dy + w > 0, ~12' )
dr (T~ - Tz 8 r c ( dt ~
C2 u; C~ u; dh
h=-- T (1--- T for w~ G. (12")
C~ SaT4si \ C~ BaTh~4si \ dr ~
where D= coefficient of gas exchange with the atmosphere; cp = equilibrium concen-
tration of C02 in the water, which depends on the water's temperature and salinity
and the partial pressure (p~p2) in the atmosphere; /H*/ = hydrogen ion concentra-
tion; K1, K2 = first and second carbonic acid dissociation constants; ICw = dissoci-
ation constant of sea water; Alk, A1kB = common alkalinity and borate alkalinity;
F(h/he) _(1 - h/he) for hhe (he = u~/C3~f~ = thickness of the
Ekman boundary layer); f= avPrage (in the area under discussion) value of the
Coriolis parameter; otT = thermal coefficient of expansion of sea water; g= free-
fall acceleration; C1, C2, Cg = numerical constants; t= time.
The solution of system (1)-(12) makes ~t possible to reproduce temporal evolution
Ti (i = 0, 1, 2), /Ci/, /C0~/, /H+/, qs, qh~~, qh,~~ and h if the following values
are given: heat flow qs on the ocean's surface, the partial pressure p~p2 in the
atmosphere, the dynamic wind speed u*, the sources and flows Bi of the carbon of
organic origin, the ocean's depth H, the ratio S/S~ of the areas of the "hot" and
"cold" reservoirs, and the capacity of the source of the cold, deep waters or the
upwelling~rate w.
In this report we present the results of a numerical experiment on the seasonal
variability of the natural carbon cycle in the ocean in the Northern Hemisphere.
The required values of qs and p~~2 were taken from /5-7/. At first they were
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Table 1. Average Annual Values of the Model's Basic Variables.
-h m -h 0 h+0 ~ ~ I
TD T1 T2 qt_ 106 qt �106 /Cn/�103r /Cl/�103 /C2/�1Q3
�C ' m�~C s mole CO /E
_ _ .
-
0.87 12.27 6.18 20.1 3.73 0.50 2.20 2.13 2.29
. . . . . --.._~f.--- I
qs0 qsl qh-0 Qh+O
g C/m2�year
23.8 T 3.64 -34.6 ~ -22.9
presented in the form of a te~oral Fourier series, and subsequently only the first
four terms of the series for qs and the first two of the series for p~p2 were used.
Parameters Bi (except for B~, which was considered to be equal to zero) were as-
sumed to be equal to their average annual values; that is, B1 =-34 g C/m2�year,
B2 =-28 g C/m2�year. (see / 8/). An analogous assumption was made with respect
to u* and w. The former was assigned the value of 0.27 m/s in the area of forma-
tion of the cold deep waters and 0.17 m/s in the rest of the oceac: (values of~D
equal to 5.5�10-~ and 5.14�10'S (see / 9/) correspond to these u~), while the lat-
ter was taken to be 10-5 cm/s. The values of H and S/SO were taken to be equal to
4,000 m and 10, respectively. The dependence of constants K1, K2 and ~
on Cemper-
ature for a fixed salinity of 35 �/oo was taken according to Merbach /10/. The
value taken for Alk was 2.4�10'3 equiv/,(; AlkB, which is a tabular function of T,
/H+/ and salinity (see /10/), was computed during the solution process; in accord-
ance with / 4/, the values of C1, C2 and C3 were assumed to be 0.1, 0.24�10-3 and
100.
For the given initial values of Ti, /Ci/ and h, the system of equations was inte-
grated by the Runge-(Kutt) method. The calculations were continued, with a tempo-
ral spacing of 1 day, until the solution reached a periodic mode. The latter was
considered to be a steady-state mode when the relative difference in Ti for the
next two ~nnual periods was 0.01 percent. This condition was achieved when 560
years had passed. The results of the calculation of the annual pattern of the mod-
el's basic variables is shown in Figure 1. Table 1 gives their average annual val-
ues. As is obvious, they agree qualitatively with the experimental data.
The authors are grateful to A.S. Monin for his constant attention to their work and
to E.K. Byutner for his assistance in selecting the initial information and his
helpful coAaaents.
FOOTNOTES
1. In comparison with temperature, the salinity of sea water is a more conservative
, characteristic, and its value in the first approximation can be regarded as giv-
en.
2. The characteristics of the areas of the source of cold, deep waters, the upper
quasihamogeneous layer and the deep layer are indicated by the subscripts 0, 1
and 2, respectively.
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3. What is meant here is the formation of a new upper quasihomogeneous layer
against the background of the old one and the formation of a stepped temperat~sre
- profile in the thermocline displacement layer. The new thermocline insulates
part of the old upper quasihomogeneous layer from the direct effect of procesee5
taking place in the atmosphere, as a result of which the amount of carbon con-
tained in the layer between the new and old thermoclines is gradually re-
distributed in the entire deep layer, primarily as the result of comparatively
rare outbursts of turbulence that accompany the overturning of subsurface waves.
BIBLIOGRAPHY
1. Bolin, B., in "Fizicheskiye osnovy teorii klimata i yego modelirovaniya"
/Physical Principles of the Theory of Climate and Its Modeling, collection of
works/, Leningrad, 1977.
- 2. Bolin, B., et al., in "SCOPE Papers," Vol 13, Chapter 1, 1978.
3. Niiler, P.P., and Kraus, E.B., in "Modelirovaniye i prognoz verkhnikh sloyev
okeana" /Modeling and Predicting the Upper Layers of the Ocean, collection of
works/, Leningrad, 1979.
4. Kagan, B.A., et al., METEOROLOGIYA I GIDROLOGIYA, No 12, 1979, p 67.
5. Strokina, L.A., METEOROLOGIYA I GIDROLOGIYA, No 1, 1963, p 25.
6. Lowe, D.C., et al., TELLUS, Vol 31, 1979, p 58.
7. Bolin, B., and Bischof, W., TELLUS, Vol 22, 1970, p 431.
8. Skopintsev, B.A., OKEANOLOGIYA, Vol 15, 1975, p 830.
9. Ariyel', N.Z., et al., METEOROLOGIYA I GIDROLOGIYA, No 2, 1979, p 57.
10. Popov, N.I., et al., "Morskaya voda" /Sea Water/, Moscow, 1979.
COPYRIGHT: Izdatel'stvo "Nauka", "Doklady Akademii nauk SSSR", 1981
11746
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UDC 535.2:551.463.5
RETURN SIGI3AL MAGNITUDE DURING REMOTE LASER SOUNDING OF NATURAL WATER MEDIUMS
Moscow VESTNIK MOSKOVSKOGO UNIVERSITETA: SERIYA FIZIKA, ASTRONOMIYA in Russian
Vol 19, No 4, Jul-Aug 78 pp 64-70
/Article by A.A. Demidov, D.N. Klyshko and V.V. Fadeyev, Department of Wave
Processes, Moscow State UniversitY/
/Text/ The development of inethods of remote diagnostics for natural water mediums
is becoming an ever more urgent problem, the solution of which is a matter of in-
terest to many branches of the national economy. The composition of such mediums
is extraordinarily complex and, in accordance with this, so is the spectrum of the
return signal formed as the result of the different mechanisms of light interaction
with the medium. In this spectrum, special attention is attracted by the lines of
combination scattering (KR) of light by water (H20) molecules, which in a number of
~ cases can serve as convenient reference points when determining the concentration
of foreign bodies (such as phytoplankton) in the water /1-3/.
In this article we calculate the return signal formed during laser sounding of a
natural water medium. Quantitative estimates are made for the return signal's
spectral component, which corresponds to the Stokes component of the KR of water
with a shift v= 3,440 c~n 1 relative to the sounding radiation's wave number. The
theoretical results are then compared with the experimental resul.ts obtained by the
authors on the 18th voyage of the scientific research ship "Dmitriy Mendeleyev."
Calculation of the Return Signal. Let us discuss the propagation of a laser beam
in a water medium and the formation of the return signal arising as the result of
the light's interaction with water molecules and foreign bodies in the water. The
sounding setup is shown in Figure 1.
The radiation source is ct~aracterized by a flow of emitted photons F1 (photons per
second), linear aperture flP} and a radiation pattern of width ~91 with a maximum in
direction nl. The receiver s analogous parameters are indicated by the subscript
"2." It is assumed that a large part of the beams are propagated at small angles
~ to the z axis so that nlZZ n2z N 1(a small-angle approach %4 The test object
occupies an infinite layer between planes z= zp and z= zm$x� The object of the
investigation is a layer with thicknese Az = zmaX - zp. Refraction and reflection
on the boundaries zp and zmaX will be ignored.
The medium is assumed to be turbid; that is, in addition to luminescing and non-
elastically scatteri:ng centers such as molecules of a certain foreign body
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2pQHUf(Q~1~ 3oHdupyeHe~u CJf0ll~2~
I ~
~ I
I�p' �e, ~ eo3ayX e a
r~ ~ (3)
~ n,~ ~
~ I
~ ~ r
i ~ �pi � ez
I r~ ~ nz
I ~
~ ~ .
I I i :~/I\ \ /
z~ Z2 Z~ o Z 2rd2 ZmQx Zmax
Figure 1. Diagram of remote laser sounding of natural water me-
diums.
Key:
1. Boundary 3. Air
2. Sounded layer 4. Water
(phytoplankton, for example), it also contains absorbing and elastical~y scattering
particles. The scattering takes place on large (in comparison with the light's
wavelength) particles, so it is directed forward at small angles to the z axis (Mie
scattering).
It is necessary for us to determine the magnitude of the answering signal that is
registered by the receiver and caused by any mechanism (type) of light interaction
with the medium (fluorescence, KR, Mie and Rayleigh scattering so so forth) that is
of interest to us.
The special features of light scattering in natural water mediums makes it possible
to proceed from the general radiant energy transfer equation to the equation for
transfer with a small-angle approach / 4/:
_ ~
(~Z r ~pl -f- el 13 (r, 0) = 4n ,1 f d2U~B (r' X~0'), (1)
\ / .1
where B(r,n) = brightness at point r in direction n; a' + a= total attenuation
(extinction) factor; Q= elastic scattering coefficient; a( = absorption coeffi-
cient; ~((nn') = scattering indicatrix; 0= nl.
This equation can be solved by the Fourier method (see / 3/), assumin~ that the
scattering indicatrix is described by the exponential function (see / 4 7)
0
x~~) _ e � (2)
and the transmitter's (laser's) and receiver's radiation patterns have a Gaussian
shape.
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In connection with this, we take into consideration the fact that when laser radia-
tion strikes a unit of surfac2 in the sounded layer (of thickness dz) of the medium
- and interacts with the particles in the medium, it causes answering radiat~on
d82 (r, 0) = v(0, z) n(z) Fl (r) ~iw2dz,
where n(z) = the concentration of particles (cm 3); F(r) = density of the flow of
exciting radiation (photons�cm 2�s-1); ~~A,z) (cm2/sr~ = cross-section of the pro-
cess of laser radiation interaction with the particles in the medium, which process
was chosen in order to identify them. In the case where the particles are identi-
fied by their fluorescence, the indicatrix of which is (as a rule) a sphere,
=~fl/4~C (cm2/sr), while ~'fl (cm2) in the simplest case, where the same molecules
both absorb and fluoresce, equals ~a~l, where Qa (cm~) is the absorption cross-
section and r~ is the quantum efficiency of the fluorescence. For the case of com-
- bination scattering (in particular, the scattering particles can be water: nZ =
= nH2 0= 3.3�1022 cm 3 under normal conditions), ~_~~g(6) = the KR cross-section
in tFie given observation direction (as a rule, KR has an elongated indicatrix that
has a maximum in the forward and backward directions).
Then, by using the theory of reciprocity / 5/, we find the flow of photons regis-
tered by the receiver:
' Zmax �O ~ '
= p: = F,0~~002 ` dz ` f dxd~cr (z) ~i (t) cos [ ~W~ (z)) X
J JJ
z, o
X COS ~y~2 ~Z~~ ~~`p }-~E] 'I' EZ~ Z- 4 1~ Qx J~aY~ I
l
a,z + az= 1
1~ ~ .
V 1-~- a i(z1 _U=) Za V 1-}- S2 (z' y~~ Zs
where
~P~ (z) = a, - xz -I- (z - z,) ~~x - (z - zz) OZx,
~Pz ~z) = J~ - ?Jz i- (z - zi) ~i y - ~Z - Z"-~ ~=u~
aX = ~Pi ' (z - zl)z ~0~ Das -I- (a - z.:)= DO~x, ( 3 )
Qy - o;,; ~z - Z,~Z oo; + eyz +(Z - Zz~Z o02~,
oPz - nx2eu2r eo2 = n~ZXeOz~.
In formula (3), G and ~ are the primary hydro-optic characteristics of water on
the wavelengths of the exciting laser radiation (subscript "1") and the return sig-
nal (subscript "2"); coordinate origin z= 0 is set at the point z= z0.
In the case of a coaxial system, where rl = r2 and nl = nz, and assuming that
~A2X = ~62y =~A2, ~x2 =~y2 =~2, cSl = r~2 and cr(z)n(z) is a constant in the
sounded layer pz, we obtain
n , Zn,ax oo - 2 ( ~ j .
p~ - 4 F,on0020pZ ` dz ~ dx exp ~-(e, Ex) z- 4 a x-~- ~r azz=x ~ 4)
J
ze 0
where a2 = lf~oi + ~p2 + (z - zl)2(QAi + LIAZ).
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The effect of the air interval is not taken into consideration in formula (3); that
is, ~air=Eair='~�
It is interesting to note the characteristic dependence of the received signal on
the distance ~zl~ from the laser to the water's surface during the sounding of a
layer of a water medium (~z). It is not difficult to show that the magnitude of
the received signal is ^~L1z/(~zl~(Jz Oz)). In connection with this, at great
distances (Izl~ 77~z) the signal magnitude is -~-1/~z112, while at short distances
((z1~�/~z), it is ^-1/~zl~. Analogous results are obtained when the asymptotes of
formula (4) are examined:
ti
F~ = 2- arctg ( Q~ ~ z, I)-( e~ ~ ~ z, I z,~ I, ~ z~ ~z, ~ 5)
~
F~ n~ I z~ I~` oz. ~ (6)
Fi ~ ~nZ -I- ~02 I Zi ~ I zi
In principle, expression (."s) makes it possible to determine particle concentration
n by registering.the return signal from them. However, even in the coaxial system
that is simplest to analyze, it is necessary to check a large number of parameters,
which in practice is (as a rule) impossible.
A comparison method in which a measurement of the relationship of the return sig-
nal's spectral components that are caused by KR of the water and fluorescence or KR
of the foreign body makes it possible to avoid the necessity of checking these pa-
rameters and determine the concentraction n of the foreign body that is of interest
was proposed in / 1/, tested experimentally in /1-2/ and substantiated mathematic-
allyin/3/.
Optimization of the Laser Radar's Optical Arrangement. Expression (3) gives the
magnitude of the received signal during laser sounding of water mediums. It con-
tains parameters charactetizing the investigated object (the water medium) and the
geometric factors in the experiment (angular and linear aperCures of the laser and
the receiver and their relative positions).
?
Let us optimize the geometry of the experiment for the purpose of obtaining a re-
gistered return signal of maximum magnitude. It is obvious that the first step in
the optimization process is the creation of a coaxial system where the laser and
the receiver are located at the same point (formula (4)).
When using a lens system, the receiver's (and transmitter's) linear and angular ap-
ertures l~ 2 and QA2 are related to the original aperture values bP20 and Q920 by
~ relations~ips t~2 = f0920 and ~62 =~P2~/f, where f is the lens system's focal
length.
By substituting aP2 and ~92 into equation (4) and differentiating it with respect
to f, it is not difficult to find an equation for determining the optimum focus:
e 2 Z i aa dz ~ dz X z- z ~V'(f~X,z)
~
f4 = pso 2. ' ( 7 )
ee~ =~axdz ~ dxxc'~(f.x.=~
o
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~here
_ ~ (f. X, Z~ - - ~El ~ E.) ~ - 4 [o~~ oo2of2 ~z -zl~� x
, eP~ (8)
x ~eo; fZ'� ~ ~ (Q~ + QZ) ziV 1 ~ a~=Z1.~.
By using the mean-value theorem, it is not hard to obtain an estimate for foPt from
� formula (7):
-P �~e-o ( 9 )
fo t- .o (ZO I Z~ I)�
~
_ When sounding the layer near the surface or at great distances (~z1~~7z0):
f�Pt o0zn ~ Z' ~ ~ 10 )
zo
- Formula (10) is also correct in the case of sounding the entire water stratum (z0 =
= 0, zmaX = o~) from great distances, since the integrand in (4) diminishes rapidly
as the depth (z) increas~s and only the layers near the surface operate effectively
(the thi~kness of the effectively working layer is ^~10 m, while the deeper layers
make a contribution of 5 percent).
- Tab1e 1.
No ~ zl~ , m ~82~, rad (~P20, cm F2/F1 faPt, cm fopt~~~P20~~e20)~zl~, cm
- - for f = fopt
- 1 10 0.25 0.05 1.0�10'8 16 14
2 30 0.25 0.05 1.9�1Q-9 27 24
3 30 1 1 0.75�10-6 66 55
Table 1 shows the results of th~ calculation of fppt, on a BESM-4 high-speed com-
puter, as a function of t~e receiver's aperture a~d distance ~z1(, as well as Che
value of F2/;1 a~ computed according to formula (4) (the case of sounding the en-
= tire water stratum) and the estimated value of fopt (formula (10)).
The calculations were made for ~1 = 2.5�10-4 cm 1, ~2 = 2.6�10-3 cm 1, ~"1 =
= 1.5�10-5 cm 1, ~2 = 0.7�10-5 cm 1 and far ~1 = 0.1. The data were taken from
/b/.
~ In Table 1, line 3 corresponds to the case of signal registration by a broad-
aperture spectrometer (of the interference filter type).
Tt~e transmitter's lens system is optimized analogously. In the general case the
optimum focal lengths for the transmitter (subscript "1") and the receiver (sub-
acript "2") can be found from the solution of th~ system
~ OP~~ .~.f x ~z - zi)z e+t(f~.f::z,ij dxdz
j~ = ee2 1lX~VKI~.f,,x,z)dxdz ~
io
- (11)
~ ~t~20 x(z - zl)s e~t(f~.l~,x,z) dxdz
. f
2= Q8~ f 1 xe+~cl~,l,.x.:) dxdz ~
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wher-r.
I ~ 2 2 2 z c1p in ~~'so , (a~ -f- a:) z
4 /I '2 ~,1 + a~=~z .
ci~, f:, .Y, = - ~t, fz~ Z - -a no~~of~ -F eezof~ +~Z - z,~ ~t-
From system (11) it is not difficult to derive the relationship between flopt and
f2opt:
~ , ` ao:o en~o (12 )
f~.~c = f7 0~i ee~o oPza ~
which--in contrast to (10)--is precise and can replace any of the equatione in sys-
~ tem (11).
Gt~parison of Theory and Experiment. Experiments in the remote laser souuding of
~ sea water for the purpose of making a quantitative determination of the amount of
~ phytoplankton pre~ent were conducted on the 4th voyage of the scientific research
_ ship "Aka~emik Petrovskiy" / 1 7 and the 28th voyage of the scientific research ship
"Dmitriy Mendeleyev." Gn the latter c~s:cdsion we had an opportunity to vary the
distance from the laser radar (lidar) ~o the ocean's surface and to evaluate the
~ absolute m~gnitude of the signal that wss received.
Below we present the numerical estimates of the theoretically derived values as ap-
plied to the lidar parameters and experimental conditiona or., the 18th voyage of the
"Dmitriy Mendeleyev." The lidar had the following characteristics: wavelength of
the sounding radiatian 532 cim, laser pulse duration 10 ne, maximum energy in
~ a puls~ 10-2 J; the linear (L1Pp) ~snd angular (DA~) apertures of the laser
transmitter (subscri~t S'1."~ ~and the reca~~r~.?� (subscript "2") were: oPio = 0.5 cm,
eeo = s.s�io-~, c~p20 = a.~s ~m, oe20 = o.2s.
The rQCeiver was gated by a pulse with duration '~gtr = 1 �s, so it registered the
_ integral nuu~'a~r c:f return signal photons formed in the layer from the surface (z =
z~~ = 0) to zmax '~strc ~100 m(c =2�1010 cm�s-l,~which is the speed of light in
a water medium.
~ One of the return signal spectrograms ob-
tN~~^m;v~a ~
~~o ~1~ tained during the sounding of the ocean s
suxfa.Ge is presented in Figure 2. The
peak on wavelength 650 nm was caused
' by the water's KR signal, while the lesser
one at 680 nm was caused by the fluor-
i0 escence of the marine phytoplankton's
chlorophyll "A."
_ We also conducted an experiment in remote
sso l s'.c ~so l.aser sounding in which we determined the
' signal's dependence on distance and the
- Fi~ure Spectrum of return signal maximum working distance of our lidar (re-
during remote sounding (,~sir = 532 turn signal registrat~.on was carried out
nm) of the ocaan's surface at a dis- with an OMA-1 system). The distance was
tar.ce of 10 m, changed by turning the lidar on a ring
Key: 1. N, photons mount (which also changed the laser beam's
angle of incider~ce on the ~oater's sur-
face). The results of these measurements are presented in Table 2.
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Table 2.
Angle of laser beam incidence on the
water's surface (degrees) 0 5 10 25 45 55 62 73
Distance zl , m 10 10.05 10.15 11 14 17.5 21 35
KR signal of H2O, photons, rel. units 175 202 188 202 106 34 24 3
The signal's dependence on the distance, which was even stronger than ~zl~-2, is ex-
plained by the noncoaxiality of the system and the fact that when the ring mount's
platform was turned, there was no optical aligrunent of the receiving system.
For sounding at a distance of 10 m, the water's KR signal was N2 = 15,000 photons.
(N2 = f FZ(t)dt) or N2/N1 = F2/F1 - 1.4�10-i1, whereas a theoretical calculation
~str ~
with formula (4) gives N2/N1 = 8.6�10-9; that is, a discrepancy factor of 600. Such
a large discrepancy is explained by the ignoring of the terms characterizing the
noncoaxiality of the system, the effect of the air interval, and (obviously) the
= larger values of � and U for the real case than those we used in our calculations
(see above).
An accurate allowance for noncoaxiality requires the ccmputation of the triple in-
tegral in (3). A gross estimate of the noncoaxiality factors shows that, in actu-
ality, for Izll ='10 m the result can differ by 2-3 orders of magnitude.
From what has been said, it follows that a change to a coaxial system wi11 bring
into play a large reserve for increasing the maximum range of answering signal de-
tection. There is also another reserve: increasing the receiving system's sensi-
~ tivity by using high-transmission (broad-aperture) spectrometers that are analogous
to an interference filter (see Table 1) and more sensitive photoelectronic convert-
ers ~FEP).
Computer calculations showed that when the water's KR signal is registered by a
broad-aperture receiver ~~Z = 1 cm,l~62 - 1 rad) with a photoelectronic converter
~ equal in sensitivity to the OMA-1 system (photoconductive camera tube 1205D) and a
- lens (telescope) 60 cm in diameter with a focal length of 60 cm is used, the work-
ing distance zl can be increased to 3 km. A further improvement is possible by
- increasing the FEP's sensitivity and the laser's energy (F1).
_ BIBLIOGRAPIiY
1. Fadeyev, V.V., "Sb. tezisov konferentsii po 1 uminestsentsii" /Collection of
Summaries From the Conference on Lumines.cence~, Szeged, Hungarian People's
_ Republic, 1976, p 7.
2. Klyshko, D.N., Rubin, L.B., Fadeyev, V.V., Kharitonov, L.A., Chekalyuk, A.M.,
and Chubarov, V.V., Sb. tezisov VII konferentsii po spektroskopii" /Collection
of Su~naries From the Seventh Conference on SpectroscopY/, People's Republic of
Bulgaria, 1976, p 204.
- 3, Klyshko, D.N., and Fadeyev, V.V., DAN SSSR, Vol 238, No 2, 1978, p 320.
38
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4. Dolin, L.S., IZV. WZOV. RADIOFIZIKA, Vol 7, 1964, p 380.
5. Yermakov, B.V., and I1'inskiy, Yu.A., IZV. WZOV. RADIOFIZIKA, Vol 11, 1968, p
624.
6. Ivanov~ A.P., "Fizicheskiye osnovy gidrooptiki" /Physi~al Principles of Hydro-
Optics/, Minsk, 1975.
COPYRIGHT: Izdatel'stvo Moskovskogo universiteta, "Vestnik Moskovskogo universite-
ta", 1978.
11746
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UDC 551.465.53
SPECTRA OF POLIMODE CURRENTS
Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 258, No 2, 1981 (manuscript re-
ceived 2 Feb 81) pp 331-334
[Article by V. N. Drozdov, A. S. Monin, corresponding member,USSR Academy of Sci-
ences, and I. G. Yushina, Institute of Oceanology imeni P. P. Shirshov, USSR
Academy of Sciences]
[Text] In accordance with the program of the Soviet-American oceanological experi-
ment POLIMODE (named after the Soviet "POLiGUN" experime~t of 1970, wtiich resulted
in the discovery of synoptic eddies in the ocean, and the American MODE or "Mid-
Ocean Dynamics Experiment of 1973, duplicating it at a somewhat lesser scale), a
_ number of institutes of the USSR Academy of Sciences and the Ukrainian Academy of
Sciences carried out long-term measurements of oceanographic parameters in the
Bermuda Triangle of the Sargasso Sea in a polygon measuring 300 x 300 km with its
center at the point 29�N, 70�W during the 13 months from July 1977 through August
1978. The principal current measurements were made at 19 anchored buoy.stations
with measuring instruments at the four depths 100, 400, 700 and 1400 m(200 digital
current meters were fabricated especially for this purpose).
With a frequency of registry of currents of 3-4 read~ngs per hour there was an ac-
~ cumulation of about 3�10-6 values of the current velocity vector. Thus, 21 synop-
tic eddies with diameters of 150-300 km with velocities of rotation in the upper
layers averaging 30-35 cm/sec and velocities of movement of 3-10 km/day, primarily
to the west, as well as a number of smaller eddies,.were registered as passing
through the polygon. Some results of the processing were published in [1, 2].
The experimentally collected data were introduced into an ivR-3000 SKh computer in
the form of a data recovery system allowing interrogations with respect to 23 par-
ameters and their combinations. The series of inean hourly values of the zonal and
meridional components of current velocity u and v present in this bank (152 ser-
ies with 10 000 u and v values at four depths at each of 19 buoys) were used in
this study in computing the frequency spectra of currents in the range of periods
from 4 to 4 000 hours. We computed the spectra of u, v and kinetic energy 1/2(u2 +
v2) for a total of 228 spectra.
In the mentioned series there were gaps created both by failure of the instruments
to trigger and also due to the rejection of nonconforming values. As an average
their percentage was 16.9% (including 13.7% at a depth of 100 m; 21.0% at 400 m;
40
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11.4% at 700 m; 19.4% at 1400 m).
Zndividu;:l gaps were filled by interpolation on the basis of ad~acent values; group
gaps were filled with the mean (N mean annual) values of the corresponding serie~.
The spectral densities of u and v were computed as the mean squares of the Fourier
transforms of the corresponding series and then smoothed by contraction using a
four-term Blackman-Harris "window" with a minimum level of the side lobes.
Period, hours
s;~9 i e
~+Err~1,
~m2I 98 C Z 9000 ZODO 1000 /00 /0 2
100
!0
~ IOO,r
~'ti K~ 400,M
7OOM
J '
ivoo,~
qoa~s ooi qoi qi qs ~
qio
Frequeneies, cycle/hour
Fig. l.
We computed the energy spectra W E(c..)) (in cm2/sec2), where ~ is the frequency (in
cycles/hour), and E(~) is the spectral density. They are convenient because on a
graph with the abscissa 1ncJ the areas under the y= cJ E(~J) curve give the con-
tributions of the corresponding frequency intervals to the total dispersion of
[luctuations of the parameter to be analyzed. However, since the cJ E(w ) values
varied by two orders of magnitude, these values must be represented on the graphs
at a logarithmic scale as well.
It was found that all 152 u and v spectra for four depths for the 19 buoy stations
with an accuracy to small and irregular insignificant extrema have an extremely
similar form with three distinct maxima in the region of the periods of synoptic
41
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eddies (on the average Z= 1365.3 hours ~ 56.9 days), diurnal and semidiurnal
tidal periods (on the average 2= 24.7 and 12.6 hours), separated by deep min-
ima at periods of about 57.7 and 14.2 hours and with a minimum immediately beyond
the semidiurnal period ^'11.9 hours). As a ruTe the v spectra were a little
above the u spectra; for example, as an average for 19 buoys at a depth of 100 m the
_ y= c.J E(cJ ) values for the periods for u(yu) and for v(y~) were as follows
2, hours 1365.3 57.7 24.7 14.2 12.~ 11.9 4.1
yu, cm2/sec2 23.60 3.49 30.78 3.55 9.18 4.11 6.32
yv, cm2/sec2 36.28 3.70 32.26 4.32 9.55 4.90 6.58
Table 1
cm2 yn-~ -3'' cm2 sec Yme n yn-~ - y~� cm2/sec2
hour vmean~
sec Depth ~oo sec Depth aoo M
1365,3 3052 5359 - 16,81 = 36,78 23,58 58,68 - 5,86 = 52,82
57,7 3,59 5,05 - 2,41 = 2,65 1,20 2,18 - 0,64 = 1,53
24,7 31,63 56,44 - 13,68 = 42,76 ]9,00 39,72 - 5,30 = 34,42
14,2 4,04 6~7 - 2,05 = 4,52 2,21 3,01 - 1,44 = 1,57
12,6 9,46 12~ 1- 7,26 = 5,25 6,81 11,07 - 4,12 = 6,95
11,9 4,54 5,79 - 3,Q2= 2,76 2,39 4,15 - 1,18 = 2,97
4,1 6,45 9,77 - 3,11 = 6,65 2,46 4,75 - 1,28 = 3,47
Depth 700 M Depth 1400 M
1365,3 19,30 35,04 - 10,43 = 24,61 5,60 8,93 - 1,76 = 7,18
57,7 0,74 1,06 - 0,47 = 0,59 0,36 0,58 - 0,17 = 0,41
24,7 33,61 49,46 - 16,61 = 32,84 11,88 17,80 - 6,59 = 11,21
14,2 2,61 3,60 - 1,86= 1,74 1,00 1,46 -0,68 = 0,78
12,6 8,79 11,50 - 6,35 = 5,15 3,63 5,65 - 2,08 = 3,57
1],g 1,9g 2,89 - 1,55 = 1,35 1,31 1,93 - 0,97 = 0,96
4,1 1,62 1,96 - 1,21 = 0,76 0,80 1,19 - 0,62 = 0,57
Henceforth we will limit ourselves only to an examination of the spectra of kin-
etic energy 1/2(u2 + v2). The mean ymean values and the variability characteris-
tics yn _ 1- y2 of the significant extrema of these spectra for 19 buoys at four
depths are given in Table 1 and curves for the mean spectra for 19 buoys at four
depths are given in Fig. 1. These data show that the mean energy spectra for all
buoys decrease monotonically with depth at all periods, exceot for the diurnal
and semidiurnal periods (and iri the interval between them), where the fluctuations
were maximum at a depth of 700 m. The synoptic maximum in the layer 100-700 m de-
creases with depth very slowly (30.52 - 23.58 - 19.30), and at a depth of 1400 m
it already has a considerably lesser value (5.60). The minimum between the synop-
tic and diurnal maxima at periods of about 57.7 hours, already detected on the
basis of data from "POLIGON-70" [3], is exceedingly deep (3.59 - 1.20 - 0.74 -
0.36); this is the lowest level of the spectra in the entire considered range of
periods. A little to the left of it on some individual spectra there were special
niaxima evidently created by atmospheric synoptic processes.
The highest maximum for almost all the spectra is observed near the diurnal period
where the tidal lines ~1~ Ql~ pl~ ~1~ N~1~ pl~ K1~ J1~ 001 are situa.ted; these
are enumerated here in the order of their increasing frequency (on the basis of
- 42
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the decrease in amplitudes of tide-forming forces they are arranged in the order
K1~ ~l~ P1~ Q1~���) and the line with the inertial period Zi = 12/sin~f hours,
where y0 is latitude (the POLIMODE buoys were at latitudes from 27�42' to 30�18',
so that the inertial period 'Li varied from 25.8 to 23.8 hours). On individual
spectra this maximum broke down into individual peaks, but their identification
requires the use of spectroscopy with a higher resolution.
A maximum which is three times lower is observed near the semidiurnal period, where
we find the tidal lines 2N2, N2, v2, M2, L2, T2, S2, K2 in the order of an in-
crease in their frequencies or M2, S2, N2, K2,... in the order of a decrease in
the amplitudes of the tide-forming forces. To the right of ~i in the spectrum a
contribution is already made by internal waves; nevertheless, the minimum with
'C = 14.2 hours between the diurnal and semidiurnal maxima and the first minimum
to the right of the.semidiurnal maximum with 2= 11.9 hours are extremely.deep,
which indicates a relatively poor development of internal waves of a nontidal ori-
gin. To the right of the minimum Z= 11.9 hours the spectra at depths of 700-1400
m drop off, whereas at depths of 100-400 m they rise. This is the sole appreciable
effect of the "noise" created by the high-frequency fluctuations of surface buoys;
at tidal and especially synoptic periods this noise is not reflected, so that the
deeply submerged buoys used by American oceanologists for contending with this
noise lead only to a loss of information on the dynamically most important upper
layer of the ocean. Here on the spectra it is possible to see small special maxima
at periods of 6 and 8 hours, possibly subharmonics of tidal periods.
~ The spatial variab~ility of the values of the spectral extrema (for different buoys)
~ is given in Table 1 as the difference yn_1 - y2 of the second greatest and the sec-
ond least values. It is greatest at the maxima, especially in the diurnal and then
in the synoptic periods (whereas the minima are relatively stable), and decreases
with depth together with the values of the mean spectra. A comparison of the spec-
tra atindividual buoys with the mean spectra indicated that usually a buoy is char-
acterized by increased or decreased spectral values simultaneously at all periods
and at all depths, The highest spectral levels were observed in the northwestern
corner of the polygon, in the immediate neighborhood of the Gulf Stream, whereas
the lowest levels were observed in the southwestern and especially in the north-
eastern corners of the polygon.
BIBLIOGRAPHY
1. Grachev, Yu. M., Yenikeyev, V. Kh, et al., DAN (Reports of the USSR Acad-
; emy of Sciences), Vol 243, No 4, 1978.
I
~ 2. Koshlyakov, M. N., Grachev, Yu. M. and Yenikeyev, V. Kh., DAN, Vol 252, No 3,
1980.
3. Vasilenko, V. M., Mirabel', A. P. and Ozmidov, R. V., OKEANOLOGIYA (Ocean-
ology), Vol 16, 55, 1976.
COPYRIGHT: Izdatel'stvo "Nauka","Doklady Akademii nauk SSSR", 1981
5303
CSO: 8144/1581
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UDC 534.24; 534.87
SPATIAL VARIABILITY OF THE ACOUSTIC FIELD REFLECTED FROM THE OCEAN FLOOR
Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 259, No 1, Jul-Aug 81
(mam~script received 24 Nov 80) pp 205-208
[Article by L. M. Brekhovskikh, academician, V. I. Volovov and Yu. P. Lysanov,
Acoustics Institute imeni N. N. Andreyev and Institute of Oceanology imeni P. P.
Shirshov, USSR Academy of Sciences]
[Text] As indicated by numerous experimental investigations, the coefficient of
, reflection of an acoustic wave from the ocean floor experiences substantial changes
with a change in the position of the researc.h ship. [In this article reference is
to wave reflection with normal incidence on the bottom.] It has now been estab-
lished that there are at least three spatial scales of such variability, each of
which has its own nature, its own characteristic properties and its own sphere of
practical applications.
The greatest scale is some tens and hundreds of kilometers and corresponds to a
change in general ocean floor relief. For example, with movement from regions with
a level bottom to regions of oceanic ridges the effective reflection coefficient
decreases by 6-16 db [1, 2].
The minimum spatial scale of change in the reflection coefficient falls in:the
range from fractions to tens of the wavelengths of sound. For example, at a fre-
quency of 10 KHz it varies in dependence on the region from 0.1 to 2-3 m. A num-
ber of studies have been devoted to an investigation of the characteristics of
this scale of variability, in particular the generalizing studies [1, 3]. The phys-
- ical cause of the variability is that the reflected signa.l at the point of recep-
tion is formed as a superposing of the waves scattered by individual irregularit-
ies on the bottom and nonuniformities in the thickness of sediment. During move-
ment of the receiving-radiating system there will be a redistribution of the phase
difference of individual components, which will lead to a change in the amplitude
of the reflected signal.
The discovery of small-scale variability of the reflection coefficient and the de-
termination of the statistical nature of the reflection process have served as a
basis for a new direction in acoustic investigations of the ocean floor and made
it possible to propose new methods for solution of the problem of great practical
importance of remote determination of the parameters of bottom microrelief ([1, 3,
4] and others), and also measurements of the absolute speed of the ship relative
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to the bottom, its speed on course and at drift [5, 6J.
d
~
!00
60
ZO �
6
P
!00
60
ZO
0 '/00 B00 IZ00 1600 2000 R,n~
Fig. 1. Fluctuations of amplitude of signals reflected from bottom, received by
different detectors (a and b) with great duration of process. Linear scale.
P
~p 3SOM
~
, /1 n
, ,
20 ~ ~
~ ~ i i ?
~
~ ~ ~ ~ ; ~ ~ I~ n ~ ~ t l ~ ; I~~
\ / \ I ~ i ~ i ; 11 \ ~ , / 1
~ ~ V J
i
!0 ` r i ~ .
_ ~i
~ f000 Z000 J000 y000 R,M
Fig. 2. Spatial variability of amplitude of reflected signals after filtering of
process. Linear scale.'
N {0 �
'~~3
i Z
i 6'
i ~
; qs ~
i ~
~ ~
1.
,t=~~~ 0
- ' - /,ZS - (0 - Q7S - QS -Q2S 4ZS 4s L{7S /0 {2S ~S dR,x~?
Fig. 3. Changes of cross-correlation coefficient of two processes in relation to
spatial shift between them: 1) without averaging; 2) averaging using 7 values; 3)
averaging using 21 values.
45
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There is also a third, intermediate scale of variability of the reflected acoustic
field which was already mentioned in [7]. This article is devoted to the results
of an experimental investigation of precisely this scale.
Figure 1 shows a record of the normalized amplitude of the reflected wave (reflec-
tion coefficient) as a function of the movement of a ship lying at drift relative
to the bottom. The two records correspond to the records for two hydrophones sit-
uated on one and the same ship and spaced by 60 m along its axis. It can be seen
that in addition to the high-frequency fluctuations, which were mentioned above,
there are considerable low-frequency components in the spectrum of the process.
The thick lines in Fig. 1 represent variability of the latter kind after filtering
of the high-frequency components. The measurements indicated that the spatial per-
iod of such variability in regions of the deep ocean with a level bottom is hun-
dreds of ineters to a kilometer and their intensity is approximately equal to the
intensity of the high-frequency components [8]. It can also be seen from Fig. 1
that the correlation of the low-frequency components in processes registered by
different detectors is very high. At the same time, the measurements indicate that
there is virtually no correlation with respect to the high-frequency component,
that is, the spacing of the detectors is much greater than the spatial correla-
tion radius of these spectral components.
Available data indicate that the low-frequency spectral components are not governed
by interference effects (like the high-frequency components), but by a considerable
or complete change of the bottom region participating in the formation of the re-
flected signal and the associated change of the mean characteristics of the irreg-
ularities and nonuniformities of the bottom and also the physical properties of
the sediments and the internal structure of the ground, which is especially impor-
tant in the case of a stratified bottom. This conclusion is confirmed by the fact
that the spatial correlation radius of the low-frequency components in order of
magnitude coincides with the extent of the reflecting region of the bottom [1, 8].
Table 1
Degree of filtering Maximum correl- Correlation Variation
ation coeffic- radius coefficient
ient
Without filtering 0.35 462 44
Averaged for 7 values 0.70 450 31
Averaged for 21 values 0.82 455 28
Until recently such a spatial variability of the reflection coefficient was the
least studied. We formulated special experiments for checking the fact of its uni-
versal existence in the abyssal regions of the ocean with a level bottom and its
temporal stability. They were carried out using ships moving in the wake at speeds
11-11.5 knots at different, but each time fixed distances from one another,�vary-
ing from 0.4 to 3.6 km. On each of the ships there was autonomous radiation and
- registry of the amplitude of the reflected signals using an echo sounder in a
pulsed-tonal regime at a frequency of 9.6 KHz with a duration of the signals of
250 msec and a repetition rate of 1.5-4.0 sec. The objective of the experiment
was identification of the pattern of variability at an intermediate scale, obtain-
ed on each of the ships, with a corresponding spatial shift, an evaluation of the
depth of these fluctuations, and also the maximum correlation coefficient between
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the two determined spatial processes in dependence an the degree of filtering of
the high-frequency components of the initial processes. In Figure 2 the solid and
dashed curves represent the records of the amplitudes of a reflected signal on
different ships, averaged for 21 signals and displaced relative to one another
with allowance for a time delay equal to the distance between the ships (in this
case 3.6 km), divided by their speed. Figure 2 clearly shows fluctuations with a
spatial scale of 200-400 m; the records for the different ships were highly cor-
related.
Figure 3 shows the correlation coefficient N of signals as a function of the un-
compensated difference in the distance ~ R between the ships. The Q R= 0 value
corresponds to the total comFensation of the time delay when in computation of the
correlation coefficient one record was displaced relative to the other for a time
equal to the distance between the ships, divided by their speed. If it is assumed
that the ships ideally follow in the wake of the other, the curves in Fig. 3 wilZ
coincide with the autocorrelation coefficients. The different curves correspond to
different averaging intervals. Figure 3 shows that with impoverishment of the pro-
cesses with high-frequency components the maximum of the correlation coefficient
increases monotonically, in this case attaining a value 0.82. Some quantitative
characteristics of the processes obtained with different degrees af filtering are
given in Table 1.
It can be seen from the cited data that the filtering of processes leads to a
sharp increase in their correlation, which is accompanied by a decrease in the
variation coefficient. The spatial correlation radius of the processes is vir-
tually not dependent on the degree of filtering. This indicates that the trans-
formation of the processes by means of the averaging of the individual amplitude
values, accomplished during processing, virtually does not affect their low-fre-
quency part.
V. V. Krasnoborod'ko and V. A. Sechkin�pa~ticipated in the formulation and imple-
mentation of the experiment (Figures 2 and 3) and the authors express appreciation
to them.
BIBLIOCRAPHY
1. AKUSTIKA OKEANA (Ocean Acoustics), Moscow, "Nauka," 1974.
2. Volovov, V. I. and Zhitkovskiy, Yu. Yu., OKEANOLOGIYA (Oceanology), Vol 6, No
6, 1086, 1966.
3. Volovov, V. I. and Lysanov, Yu. P., MORSKOYE PRIBOROSTROYENIYE, SER. AKUSTIKA
(Marine Instrument Making. Acoustics Series), No 2, 25, 1972..
4, I3rekhovskikh, L:M., et al., VOPROSY SUDOSTROYENIYA, SER. AKUSTIKA (Problems in
Shipbuilding. Acoustics Series), No 10, 3, 1978.
5. Volovov, V. I., Lysanov, Yu. P., et al., OKEANOLOGIYA, Vol 17, No l, 158, 1977.
6. Volovov, V, I., Lysanov, Yu. P., et al., AKUSTICH. ZHUF.N. (~.coustics Journal),
Vol 25, No 2, 293, 1979.
47
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! 7. Volovov, V. I., Lysanov, Yu. P. and Sechkin, V. A., AKUSTICH. ZHURN., Vol 19,
No 1, 16, 1973.
8. Volovov, V. I., AKUSTICH. ZHURN., Vol 24, No 6, 934, 1978.
COPYRIGHT: Izdatel'stvo "Nauka", "Doklady Akademii nauk SSSR", 1981
5303
CSO: 1865/224 '
.
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SELECTED ABSTRACTS OF UNPUBLISHED ARTICLES ON GEOLOGY AND GEOPHYSICS
Moscow IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENIY: GEOLOGIYA I RAZVEDKA in Russian
No 2, Feb 81 pp 54, 65, 74
UDC 543.05;551.G8.018.6
I tiSE OF DURABLE PLASTIC SHELLS FOR AUTONOMOUS INSTRUMENTS. AND APPARATUS FOR '
GEOLOGICAL AND GEOPHYSICAL INVESTIGATIONS OF THE WORLD OCEAN ~
[Abstract of article by Kontar', Ye. A.]
[Text] The article gives the results of an analysis of the principal characteristics
of durable tightly sealed plastic shells applicable to the problems involved in fab-
~ ricating on their basis components and assembliea for au~tonomous instruments and ap-
paratus for abyssal geological-geophysical inve5tigations of the ocean. The author
gives examples of the use of such shells in the construction of aut~nomous instru-
ments and apparatus in the form of float elements, including a~yssal autonomous sam-
- plers of the "Bentos" and "Bumerang-N" type, durable tightYy sealed containers for
sensors and recorders of bottom geophysical stations, durable tightly sealed hous-
ings for light and radio beacons of abyssal autonomous samplers of:the "AP-6000"
and "AP-passat" models, in syatema for underwater hydroacoustic sflunding used with
autonomous inetrumente and apparatus, and also as power units for abyasal samplers
of the "AP-bazal't" model and sources of elastic oscillationa for deep sei~mic sound-
in~ .in the ocer~n. 10 pages. Manuecript depoeited at the All-Unior~ Institute of Sci-
entif.ic ~ind Technical Information, No 4525-80DEP, dated 27 October 1980.
� UDC 550.837.05
MF.THOD FOR COMPUTING DIGITAL FILTERS FOR INTEGRAL TRANSFORMS IN EL~CTRIC PROSPECTINC
~ ~
[Abstract of article by Belash, V. A.J
[Text] A method is proposed for computing digital filters making use of integral
Bessel and Fourier transforms used in geoelectric prospecting. The transfcrmed nuc-
lear function is approximated by integration using a trinomial, after wh:i.~_h nurner-
ical integration is carried out in intervals increasing in a geometric progression.
The integration esaentially involves a multiplication of the v?~ues.of the nuclear
function by precomputed filter coefficients and summation of the products. As a re-
Ault, the process of integration on an electronic computer is accele~ated by
. 49
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hun~ir~eds ~~f times. The realization of the filter �or computing the impeda�.ice func-
tion mad~ it possible to compute it with an accuracy to 0.1%. 14 pa~ges. Manuscript
depo3ited at the All-Uaion Institute of Scientific and Technical Information, No
4690-80DEP, dated S November 1980.
UDC 543.05;551.48.018.6
PROBLEMS IN OPTIMIZING 'BALLAST-BUOYANCY' SYSTEMS OF AUTONOMQUS INSTRUMENTS AND
- APPARATUS FOR ABYSSAL GEOLOGTCAL-GEOPHYSICAL INVESTIGATIONS IN THE OCEAN
(Abstract of article by Kontar', Ye. A.]
[Text] A study was made of th~ principal characteristics of "ball.ast-buoyancy" sys-
tems of aut~nomous instrumentg and agparatus with and without floats.for abyssal
geolc~gical-g~ophysical investigations of ~he ocean. In the example of autonomous
_ samplers of the "~entos" type (United States), "Bumerang-N" (West Germany), "AP-
6000," "AP-passat," "AP-kal.'m~tr," and also an autononous multishell bottom station
o� the "MADS-6" type (USSR) it is de~nstrated that the improvement and use of
"ballast-buoyancy" systema of autoncmous instruments and apparatus is promising.
a 11 pag~s. Mxnuscripr dep~sited at the All-Union Institute of Scientific and Tech-
nical Information, No 4524-80D~P, dated 27 October 1980.
COPYRIGHT: "Geologiya i razvedka"
53Q3 .
' CSO: 1865/113
~
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UDC 551.463.5:535.31
FEATURES OF DETECTION OF SEA SURFACE INHOMOGENEITIES BY THE RADAR METHOD
Moscow IZVESTIYA AI~ADEMII NAU'~C SSSR: FIZIKA ATMOSFERY I OKEANA in Russian Vol 17,
No 7, Jul 81 (manuscript received 25 Feb 80, after revision 29 Jul 80) pp 754-761
[Article by A. I. Kalmykov and A. P. Pichugin, Institute of Radiophysics and Elec-
tronics, Ukrainian Academy of Sciences]
[TextJ Abstract: The article gives the amplitude
(mean and fluctuation) and spectral charac-
� teristics of radar reflec*_ions of the uniform
sea surface and inhomogeneities in the form
of slicks. It is shown tha*_ reflections from '
' slicks in a bro~d sector of ~ngles of inci-
dence are described within the framew~ork of a
model of selective scattering (two-scale mod-
- el). Typical examples of the results are used
in discussing the possibilities of processing
of radar signals for the purpose of detecting
slicks and determining their principal para-
meters.
One cf the promising methods for the remote detectiori of spills of petroleum pro-
ducts on the water surface is the radar method. As is well known, the level of
radar reflections by the sea surface is determined by the height of the ripples
and the basis of contrast observation of spills of petroleum products is the ex-
tinction of ripples in these sectors. By use of the radar method it is possible
to detect spills of petroleum products with a film thickness less than O.i � m[1].
, However, in addition to petroleum spills a wide range of phenomena transpiring
both at the surface of the ocean and also in its depths is also observed in the
form of a decrease (extinction) of the spec:tral density of the high-frequency com-
ponents of surface wav~s. These inhomogeneities of the sea surface are usually
called slicks.
As indicaCed by experiments, changes in the high-frequency components of waves can
be caused by wind nonuniformities [2], the effects of emergence of~internal waves
[3], currents, etc. A peculiarity of slicks of such an origin is that most of them
51
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appear when there are low waves (less than class 3); the slicks of spills of pet-
roleum products aYso exist stably when there are waves of considerable height.
Many of the effects creating slicks can be used in determining both the charac-
teristics of these disturbing phenomena and the parameters of the ocean surface
[4) .
Most investigations of slicks until recently have had a descriptive character (for
example, [5]). The detection and measurement of the parameters of slicks over great
- areas of the ocean is possible only by reu~ote methods, the most sensitive of which,
as noted above, is the radar method. In order to make broad use of this method it
is necessary to know the laws of change of the radar reflections of inhomogeneit-
ies of this type slicks.
Comparative characteristics of radar reflections of the homogeneous sea surface and
sectors of slicks. The radar reflections of a homogeneous sea surface were invest-
igated in considerable detail. A model of these reflections [6] the selective
scattering of the small-scale structure (ripples) and modulation by energy-carry-
ing waves for the most part reliably desc-ribes the diversity of experimental
data. ,
The appearance of slicks should lead to a change in the characteristics of radar
reflections from the sea surface. Radar observations of slicks have had a sporadic
character [l, 2]. These and other studies give only the changes of the mean values
of the reflected signal in slicks; the fluctuation charact~eristics of reflections
from slicks ha.ve virtually not been investigated. The principal measurements, whose
results are cited below, were carried out in the radiohydrophysical polygon of the
Marine Hydrophysical Institute Ukrainian Academy of Sciences. A feature ~f the men-
tioned polygon is the broad scanning sector and the diversity of the observed
slicks, created by currents, the effects of emergence of internal waves, wind velo-
city fluctuations, etc. The instrumentation and the measurement method were dis-
cussed in [lJ. The characteristics of the reflections from slicks cited below were
obtained at a wavelength of 3.2 cm with a sounder resolution LP n
10 m. Most of
the experiments were carried out with sea waves with a class less than 3.
A typical record of the level of radar reflections E with antenna scanning in the
- space R is shown in Fig. 1. The operator places a mark over Lhe record to indicate
the place of intersection of the slick with tl:e axis of the antenna diagram. There
are reflections from a uniform sea to the left and right of the slick. The record
in Fig. 1 was obtained k�tth a vertical polarization with a glancing angle
4.5�; sea waves are of class 2. The slick zone, reflections from which are shown
in Fig. l, was formed by a current; the current velocity attained 0.5 m�sec-1..On
this t.ypical record there is a characteristic decrease in the mean level of reflec-
tions in the slick Esl in comparison with reflections of the uniform sea E~ea. The
decrease in the level of reflections in the slick is characterized by the contrast
KE = Esea~Esl or KE (db) = 20 lg (Esea~Esl~� ~1)
In these experiments the KE contrasts were varied in the range from 3-5 to 20 db
or more. The lower values of the observed contrasts are limited by the character-
istic fluctuations of reflections by a homogeneous sea. Under our conditions with
scanning by the antenna the region of frequencies characterizing fluctuations of
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reflections from slicks FSl LP) is situated below 2-3 Hz and for it the fluctuations of the
mean level of reflections from the sea in the case of waves up to class 3 is 2-3
db.
�D,ae ab ~
0
12 95% o
� o
0
9 0 0
~ o
6 �
o�
d
6 9 ~z K~,a6 db
Fig. 2. Diagram used in comparing contrasts of reflections from slicks, determined
from mean values (KE) and dispersions (KD). [Note: Figure 1 is not reproduced here.
It shows a typical example of a record of the level of radar reflections from the
sea with an ~nhomogeneity in the form of a slick. The slick is denoted by a mark.]
s,ae db
ao .
16
1
!2
B
2
4
95�%
~ 30 60 90 f rq Hz
Fig. 3. High-frequency parts of spectra of fluctuations of reflections by a homo-
geneous sea (curve 1) and part of slick (curve 2).
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- Most slicks of natural origin are characterized by the presence of sharp boun-
daries of sea-slick and slick-sea reflections, whose extent in Fig. 1 corresponds
- to an element of resolution of the sounder L~o N10 m. With a deterioration of reso-
lution LP the duration of the transition boundary increases, as corresponds Co
[1] .
In the observation of slicks in the form of spills of petroleum products at radio-
waves longer than ~1=3.2 cm, for example, at i1 N 10 cm [1], there can be a smoother
= dropoff of the mean level of reflections with transition from the homogeneous
sea to a slick due to the relatively slow attenuation of long~aave ripples (wave-
length J~.~ S cm) in comparison with short-wave ripples (i1^ 1.5 cm); this smooth
dropoff is observed only from the windward side of the slick. Thus, changes in the
mean level of reflections from the slick against the background of reflections from
the homogeneous sea have a pulselike character.
A distinguishing characteristic of reflections from slicks is also a decrease in
the dispersion of fluctuations in comparison with a homogeneous sea. As indicated
by radar observations of slicks, the contrasts
KD Dsea~Dsl or KD (db) = 10 18 ~Dsea/Dsl)~ ~2)
determined from the ratios of the dispersions of the levels of reflections from
the homogeneous sea Dsea and slicks Dsl, were close to the values of the contrasts
Kg, determined from (1). The discrepancies KD and KE fall within the limits of ex-
perimental accuracy. Figure Z shows data from different experiments for the above-
mentioned slicks of natural origin. It can be seen that the resul~s of the experi-
ments confirm the coincidence of the contrasts determined from (1) and (2). This
coincidence is natural because within the framework of the model of selective
scattering [6] both the mean level and the fluctuation characteristics of the re-
flections are dependent on the height of the ripples. Only with very glancing
angles 1�, when in addition to reflections from ripples, there are reflection
bursts from the wave crests [7], can there re a difference between KE and KD.
As indicated by numerous investigations, a feature of radar reflections by the
homogeneous sea is a single-mode character of the distributions of the levels of
the reflections. In our experiments the distributions of levels of reflections
by both the homogeneous sea and by slicks have a single-mode character. These dis-
tributions differ with respect to mean values and dispersions.
In choosing a modPl of radar reflections from the homogeneous surface of a sea with
slicks it is of interest to examine the spectra of radar reflections. The nature
- of the spectra of reflections by a nonuniform sea is described completely by a
model of selective scattering [6]: the low-frequency components of the spectrum
are dependent for the most part on the energy-carrying waves, whereas the high-
frequency components F> 10 Hz (for 3 cm) are determined only by ripples.
As indicated by recent experiments [8], the spectrum of rises of ripples has the
character �
Sh (F ) F'~* - F'S . ( 3 )
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The spectrum of fluctuations of the reflected signal SE(F) to the levels -20 -
-30 db is determined for the most part by the orbital movements of the ripples and
therefore
- gE(F~~.F2gh~F~...F-2 _ F-3. ~4)
This character of the high-frequency part of the spectrum is manifested in the
spectra of reflections SE(F) shown in Fig. 3. Here we have shown only the high-
frequency parts of the spectra of reflections from a homogeneous sea (curve 1)
and a sector of the slick (curve 2). These spectra were obtained during scanning
by the antenna and the spectral density of reflections from the slick in the fre-
quency region F~ IO Hz is not statisticallq ensured.
The typical slopes of the high-frequency parts of the Sg(F) spectra, which we ob-
served with reflections from the sea and slicks, are close and fall in the range
gE~F~.., F-1.5 _ F-3,
This agrees well with the computational relationships (4). With respect to the lev-
els of spectral density of reflections from the slicks, in accordance with the
model [6], due to a decrease in the height of the ripples in the slicks there
should be a contrast
KS - Ssea~ssl or KS (db) = 10 lg (Ssea~ssl~~ ~5~
where Ssea is the spectral density of reflections by the homogeneous sea, Ssl
is the spectral density of reflections by a sector of the slick. In accordance
with the model [6] we should have
KE + KD = KS.
Figure 3 shows that the spectral density of the reflections from the slick Ssl on
the average is 8 db lower than Ssea~ that is, KS = 8 db. The values of the con-
trasts KE = 7.43 db and KD = 8.85 db, computed in accordance with (1) and (2), with
the confidence interval taken into account, coincide satisfactorily with KS. The
results of the processing of reflections from the slicks and other parameters con-
firm the data cited above. The similarity of these characteristics and the rela-
tionships of the levels of spectral density of the reflections by the homogeneous
sea and slicks serve as an additional confirmation of the correctness of the mech-
anism of selective scattering [6) for reflection from slicks as well.
Thus, proceeding on the basis of the data cited above on the mean, fluctuation and
spectral characteristics, the field reflected by a sea surface with slicks, can be
represented as
Esea~R, t) with R~Rs1, 6
E(R,t) = Es1~R9 t) = Esea(R, t)/K with R E RS1,
where Esea~R, t) is the field reflected by the homogeneous surface of the sea,
which is described by the model [6], Esl(R, t) is the field reflected by a sector
of the slick in the region of space Rs1 and characterized by the contrast K
K=KE=KD=KS.
Characteristics of reflections from an inhomogeneous surface. Taking into account
the characteristics of separate reflections of the homogeneous sea surface and
slicks cited above, it is possible to interpret the results of observation of
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reflections from the nonuniform sea surface. Experimental investigations have in-
dicated that the distributions of levels of signals reflected by the nonuniform
sea have a two-mode character (Fig. 4). These distributions were obtained for one
and the same slick with a different extent of the homogeneous sea. The first mode
characterizes reflections from the slick; the second characterizes reflections by
the homogeneous sea. Numerous observations have indicated that a two-uo~de dis-
tribution of the amplitudes of the radar reflections indicates a nonuniformity
_ of this sector, that is, the presence of a slick.
w
,
J ~
II Z f
. 2 1 1i ,
i
i
~ ~ /
% I~ / .
, 0,2 0,4 0,6 O,B rE
LMQRO
~ max
Fig. 4. Distributions of the levels of reflections by a n,onuniform sea with dif-
ferent relative extents of the slick (Lsl~Lobs~~ 1) 0.22; 2) 0.47.,
R ~ ,
O,B
0, 6 ~
0, 4 ~ �
2
02 3 r
0 '
0,02 0,04 0,06 O,OB T
T" Tobs
Fig. 5. Correlation functions of radar signals reflected by a nonuniform sea with
a relative extent of the slick 0.045 and the contrasts: 1) 20; 2) 10; 3) 5.5 db.
On the basis of the model discussed above the ratio of the amplitudes correspond-
ing to the maxima of the distributions determines the contrast of the reflections
from the slick relative to the homogeneous sea K. Using distributions similar to
those cited in Fig. 4 it is fundamentally possible to determine also the relative
dimensions of the slicks as A
q~
Ls1~Lobs ~ J W~A) dA~
0
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where LS1 is the extent of the sector of the slick, Lobs is the extent of the ob-
served sector of the sea surface, A= E/E~X is the relative level of the reflec-
tions, E~X is the maximum value of the level of reflections, A~ is the level sep-
a~ating the reflections from the slick and the homogeneous sea (for Fig. 4 Ap ti 0.3),
w(A) is the probability dens ity of the relative level of reflections A. For the
distributions citen in Fig. 4 the evaluations with (7) taken into account give KE
= 9.54 db, KD = 9.82 db; Lsl~Lobs = 0.22 (continuous curve) and Kg = 9.54 db; KD
= 8.3 db; Ls1~Lobs � 0.47 (dashed curve); the corresponding parameters of the
reflections from the slicks, computed on an electronic computer on the basis of a
record of a signal similar to Fig. 1, are: KE = 8.84 db, KD = 9.63 db, LSl/Lobs �
0.24 and Ls1~Lobs - 0.48.
As indicated by experiments for different slicks, the data from computations of the
parameters of slicks on the basis of the proposed model correspond we11 to the re-
- sults of computations of these characteristics on an electronic computer. The use
of this method for determining the parameters of slicks is desirable with con-
trasts K~ 5 db and Ls1~Lobs ~ 0.1, when the distributions of reflections from the
slick and the homogeneous sea are separated reliably. The considered method can
be realized using a level analyzer.
r,a6 db
, Z~ o
;
o '
15 �
8
~
!0
~
0
x ~
S ? ~
0
x
0 .
o ~
x .
~o� ao� ao� s ~
Fig. 6. Change in the contra sts of reflections from slicks with angle of incidence
B. The different symbols denote observational data for different slicks; waves up
to class 3.
The appearance of slicks sho uld also change the correlation function of radar re-
flections of the nonuniform sea surface. In accordance with the model of reflec-
tions from the nonuniform surface the correlation function of signals from the non-
uniform sea R(r) should represent the characteristics of the correlation function of
signals from the uniform sea and the pulsed character of reflections from the
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slick (6). As is well known, the correlation function of a rectangular palse has
the shape of a triangle. This characteristic is also manifested in the correlation
functions of reflections by a nonuniform sea.
- Figure 5 shows typical correlation functions of signals reflected by a nonuniform
sea, with different contrasts K and a relative extent of the slick LSl~Lobs -
0.045. The correlation functions of the reflections from a nonuniform sector with
a slick contrast K= 5.5 db were obtained as a restil.t of processing of a real sig-
nal (curve 3). Processes with other contrasts (20 and 10 db) were modeled on an
_ electronic computer using records with a contrast of 5.5 db in accordance with
(6); the corresponding correlation functions are given in Fig. S(curves 1, 2).
Figure 5 is characterized by the above-mentioned coincidence of fine-structured
details in all the correlation functions. This is attributable to the use of one
and the same record of r.eflections from the sea surface for the modeling of slicks
with different contrasts on the surface. Figure 5 also shows the triangular char-
acter of the correlation function of reflections from a slick.
A change in the length of the slick leads to a change in the point of intersection
of the triangular part of the correlation function with the axis of the normalized
argument'L/Tobs. With Ls1/Lobs S 0.1 the values of the argument at the point of
intersection 'G/Tobs ~ Ls1~Lobs ~Tobs is the observation time). Figure 5 shows that
this parameter is not dependent on the contrast K. The value of the contrast K
determines the place of intersection of the continua.tion of the triangular part
of the correlation function with the axis R= 0. As indicated by experiments, us-
ing correlation processing it is possible to detect slicks and determine their
principal parameters with the contrasts K~ 3 db.
Region of applicab ility of radar method for detecting slicks. The region of angles
of incidence in which the radar method for detecting slicks is applicable is deter-
mined by the region of applicability of the model of selective scattering by
ripples [6]. As indicated above, for the detection of slicks with small glancing
angles ty S 3� it is necessary to take into account the appearance of reflection
bursts from the crests of waves prior to their collapse [7]. Reflection bursts are
cbserv~d for the most part in horizontal polarization; in vertical polarization
they are 15-20 db lower. Thus, for improvement of the conditions of radar observ-
ation of slicks in the case of small ~ angles (from a ship, from shore) it is de-
sirable to use vertical polarization of radiation. This also increases the range
of observation of reflections from the sea, that is, the range of detection of
slicks.
The contrast observation of slicks from aerospace carriers is possible at angles
of incidence e y 15-20� (~ 25� most of the detected slicks have a considerable contrast
K~10 db. In this region of angles it is common to observe slicks with contrasts
K> 20 db .
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With a decrease in the angle of incidence e the contrast K usually decreases in
such a way that with B:%20� the K value is < 5 db. For virtually all slicks whose
contrast is different with e> 25� the contrast value in the region Bz 15� is equal
to zero, that is, reflections from the slick are not manifested against the back~
ground of reflections by the uniform sea.
Finally, with 15� the contrast becomes negative, that is, the reflections from
the slicks already exceed the reflections from the homogeneous sea; in this region
of angles there is a predominance of quasimirror reflections. The angle e%r15�, for
which K= 0, determines the transition region where scatterings from ripples and
reflections by quasiplane elements are comparable. This agrees with data from spec-
ial experiments [9], where it is noted that with average wave heights and angles
of incidence B~ 6� there is a predominance of Kirchhoff reflection by quasiplane
elements, with B>18� selective scattering by ripples, and the region of trans-
ition from one reflection mechanism to another is at angles 6< e< lgo.
Conclusions. Investigations of thF: statistical characteristics of radar reflections
by a sea surface with slicks shour:
1) the appearance of slicks can be reliably detected by the radar method,
2) the mean levels, dispersions and spectral densities of reflections in slicks
- decrease to an identical degree in comparison with the corresponding characteris-
tics of reflections from a homogeneous sea,
3} in a wide range of angles of incidence from glancing to almost vertical (8~ 15�)
the characteristics of the reflections from slicks are described in accordance
- with a model of selective scattering [6],
4) the statistical characteristics of reflections by an inhomogeneous sea can be
used for the detection of slicks and determination of their principal parameters
contrasts (the degree of extinction of ripples in them) and sizes.
In conclusion the authors express deep appreciation to B. A. Nelepo for stimulat-
ing discussions of the work.
BIBLIOGRAPHY
1. Galayev, Yu. M., Kalmykov, A. I., Kurekin, A. S., Lementa, Yu. A., Nelepo,
B. A., Ostrovskiy, I. Ye., Pichugin, A. P., Pustovoytenko, V. V. and Tere-
khin, Yu. V., "Radar Detections of Petroleum Contaminations of the Sea Sur-
face," IZV. AN SSSR: FAO (News of the USSR Academy of Sciences: Physics of the
Atmosphere and Ocean), Vol 13, No 4,~pp 406-414, 1977.
Z. Ecklund, F., Nilsson, J. and Blom~uist, A., "False Alarm Risks at Radar Detec-
tion of Oil Spills," PROC. URSI Com. II: MICROWAVE SCATTERING AND EMISSION
FROM EARTH (BERNE 23-26 Sept 1974), edited by E. Schanda, Berne, 1974.
3. Ewing, G., "Slicks, Surface Films and Interna.l Waves," MARINE RES., Vol 9,
No 3, pp 161-187, 1950.
4. Fedorov, K. N., "Observations of Oceanic Internal Waves From Space," OKEANO-
LOGIYA (Oceanology), No 5, pp 787-790,'1976.
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S. Babkov, A. I., "Aerovisual Observations of the Sea Surface," METODY IZUCHEN-
IYA MORSKIKH TECHENIY S SAMOLETA (Methods for Study of Sea Currents From an
Aircraft), M:oscow, Nauka, 1964.
6. Bass, F. G., Fuks, I. M., Ka.lmykov, A. I., Ostrovsky, I. E. and Rosenberg,
A. D., Very High Frequency Radio Wave Scattering by a Disturbed Sea Surface,"
IEEE TRANS. ANTENNAS PROPAG., Vol 16, No 5, pp 554-568, 1968.
7. Kalmykov, A. I. and Pustovoytenko, V. V., "On Polarization Features of Radio
� Signals Scattered From the Sea Surface at Sma.ll Grazing Angles," ~EOPIiYS. RES.
(OCEAN AND ATMOSPHERE), Vol 81, No 12, pp 1960-1964, 1976.
8. Mitsujasu, H. and Honda, T., The High-Frequency Spectrum of Wind-Generated
Waves," OCEANOGR. SOC. JAPAN, Vol 30, No 4, pp 185-198, 1974.
9. Galaev, Yu. M., Bol'shakov, A. N., Yefimov, V. B., Ka.lmykov,. A. I., Kurekin,
A. S., Lementa, Yu. A., Nelepo, B. A., Ostrovskiy, I. Ye., Pichugin, A. P.,
Pustovoytenko, V. V. and Terekhin, Yu. V., NEKOTORYYE KHARAKTERISTIKI RADIO-
LOKATSIONNYKH OTRAZHENIY POVE~OST;'.YU MORYA PRI UGLAKH PADENIYA BLIZKIKH
K VERTIKAL'NYM (Some Characteristics of Radar Reflections of the Sea Surface
With Angles of Incidence Close to Vertical), Preprint No l, MGI AN UkrSSSR,
Sevastopol', 1978, 22 pages.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika atmosfery i okeana",
1981
5303
CSO: 1865/222
,
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UDC 551.466.81
RADIATIVE INSTABILITY OF SHEAR CURRENTS IN A STRATIFIED FLUID
Moscow IZVESTIYA AKADEMII NAUK SSSR: FIZIKA ATMOSFERY I OKEANA in Russian Vol 17,
No 7, Jul 81 (manuscript received 7 Feb 80) pp 766~768
[Article by L. A. Ostrovskiy and L. Sh. Tsimring, Institute of Applied Physics,
USSR Academy of Sciences]
_ [TextJ The problem of the generation of internal waves by a shear current, as is
well known,.is extremely important for_oceanvgraphy. This problem has already
_ been examined in the literature (for example, see [1-3J). However, in all the con-
sidered models the radiated waves were generated due to instability of the Kelvin- .
Helmholtz type, possible in a stratified fluid onlq for qu3te short-wave disturb-
ances. The energy losses from radiation from the shear laqer lead to a partial
stabilization of the instability. ~
_ . Re ~ N#0
I a
z
j N=0
U ~
I .i~.�
N ~ �t-.
o pZ o` ' ~~I
pi p k~ kl k* k# k
Im tu ~ N=0
a N#0
~ - k~ . kZ k* k* k
Fig. 1(at left). Vertical density profile /~(z). Fig. 2. (at right). Dispersion
curves. Dependence of real (a) and fictitious (b) parts of frequency on horizon-
tal wave number with N= 0(thin line) and N~ 0(thick ~inej.
Below we examine another mechanism for the radiation of internal waves associated
with an increase or growth of negative energy waves. As is well known, the excita-
tion of such waves does not increase, but decreases the total energy of the system.
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In hydrodynamics waves of such a type were evidently examined for the first time
by Benjamin [4] (also see [5-7]). The negative charaeter of the energy means that
introduction of any mechanism for the removal of energy will lead to its increase,
that is, to current instability. As one of the possible mechanisms in [6] Cairns
examined viscous friction. In our case the removal of energy was caused by the ra-
diation of internal waves into a layer of stratified fluid. A fundamental differ-
ence from the cases examined in [1-3] is that here radiation does not suppress in-
stability, but on the contrary, serves as a necessary condition for this.
We will formulate the problem in the following way. The plane z= 0 is a discontin-
uity above which (z~ 0) the fluid is homogeneous.and moves with the velocity U rel-
ative to the lower region, where the fluid is fixed and also stratified there
with respect to density~o , and specifically
p= Pl (Z>o), P=i�2 -o~cZ cZ/~ 1, o~ > 0(Fig. 1). We will assume that in the region of 3nterest to
us the Boussinesq approximation is corre t; then it is ossible to consider the
Brent-V2lisal~ frequency N=(-g PZ' /P )1~2 ~~g~ ~P 2~ 1~2. Here g is the accelera-
tion of gravity.
- A solution of the problem of the stability of such a eurrent is found by the usual
method. In the linearized Eu1er and continuity equations it is necessary to con-
sider perturbations of aIl the parameters to be proportional to exp[i(kx + mz -
~J t)]; then in the upper homageneous half-space muP = ik, whereas in the lower,
stratified layer
mlow = k[(N2/cJ 2) - 1]1f2. ~2)
Using the boundary conditions at the discontinuity (continuity of pressure and
normal velocity component) it is easy to demonstrate that ~ and k satisfy the dis-
persion equation
/~1~w - kU>2 + 2(~4 - x2u12~1~2 (3)
-gk~P2 -Pi> = o.
Here we will add the conditions of disappearance of disturbances when z-? + ao ,
which with k> 0 is ensured by the relationship mup = ik, and with z-*- Im mlow
< 0. In addition, the vertical component of the energy flux SZ of the wave ge~er-
ateci in the region zC 0 should be directed downward (or is equa.l to zero when c~J ~
N). In this case
SZ = pw Re~~mlow~ P~ W~ 2
k 2 ' (4)
where p and w are pressure perturbations and vertical velocity; the line denotes
averaging for x. Accordingly, the generation (radiation) condition has the form
Re(cJmlow~ = Re(N2 - cv2)1/2? 0. (5)
These conditions determine the signs on the roots in (2) and (3). The stability of
the current is determined as usual by the sign on the fictitious part ~ with real
k. Figure 2,a shows the dependence of the real, and Fig. 2b shows the dependence
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of the fictitious parts of aJon k with N= 0 and some N~ 0. ThP continuous curves
correspond to solutions satisfying all the mentioned boundary conditions. With N=
0 we arrive at the classical Kelvin-Helmholtz instability problem in a two-layer
fluid [8]. The current is unstable with respect to quite short waves for wYAich k~
k~~ = 2g 2-/~1) /P 2U2. However, we are interested in the region k< k,~~, wt~ere
u~ is real with N= 0. It is important that in this region for one of the branches
of the dispersion equation w changes sign with k= kl ~ k*~/2, It is easy to show
(5] that in the interval kl < k< k2 the energy of the wave corresponding to the low-
er branch will be negative. The mechanism of removal of energy necessary for in-
stability appears if N~ a; then with c~1< N the tangential discontinuity radiates
interna.l waves downward. This immediately leads to an increase in the per~urba-
tions in some range of wave numbers kl < k< k2, where the mentioneci interval is
separated from the region of Kelvin-Helmholtz instability by the stable interval
k2 < k< k*. It follows from (2) that with complex cJ the vertical wave number mlow
is also complex. In the presence of instability (that is, in the spectral interval
kl< k< k2) Im mloW < Q and the amplitude decreases with increasing distance from
the discontinuity, that is, there is a mode localized with respect to z. This en-
sures correctness of the formulation of the problem adopted here. The characteris-
- tic depth of the dropoff is the lesser the greater the instability increment. In
the segments of the dispersion curve denoted by the dashed curve in Fig. 2 Im mlow <
0 and the amplitude of the wave 3.ncreases exponentially with depth for fixed x.
Such :.~ructures of the wave field are kn.own in optics [9] under the name "leaky
_ waves." They are not characteristic solutions of the equations for a field without
sources and therefore for a correct examination of such waves it is necessary to
make the boundary and initial conditions more specific.
The radiative instability examined here has a direct analagy with the anomalous
Doppler effect [10]. In this case an oscillator, moving with a velacity greater
than the speed of light, radiates energy and in the process itself passes into a
more excited state. In our problem the role of such oscillators moving at a speed
greater than the speed of light is played by liquid particles osciZlating in the
vertical plane. The velocity of their translational motion, equal to the mean cur-
rent velocity U~ 1/(P 1+~0 2), is greater than the phase velocity of the wave in
_ the region of negative energy.
The increment of radiative instability is usually small in c~mparison with the maxi-
mum increment in the region of Kelvin-Helmholtz instability, but in our opinion
this mechanism can play a definite role in the formation of the field of internal
waves in the ocean. In actuality, for the ocean the tangential discontinuity con-
, sidered here usually approxima.tes some transition layer of the finite thir_kness h,
which is possible un~ier the condition kh k* the rpal part of the frequency
is usually greater than N, so that even ~~ith kh->0 the waves generated in this re-
gion are propagated along the discontinuity without radiating into the depth of the
ocean.
We will cite one evaluation of the characteristic scales of radiative instability.
We will assume that U= 0.1 m/sec, (p 2-p 1>/P 2= l0-3, N= 10�2 rad/sec. Then
this instability is manifested in the interval of horizontal wavelengths 5.2-6.3 m.
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The frequency of the radiated waves ~n this ca~e varies from 0 to N and the ver-
tical wave number, according to (3),. varies from ~ to 0, The greatest f.ncrement
corresponds to a frequency c.~ = N/ ?2 (the period in this example is 7 minutes);
n in thLs case m= k, that is, the wave is propagated at an angle 45� to the ver-
tical. The time for increase of such a wave is about 1-2 hours.
�BIBLIOGRAPHY
1. Lindzen, R. S. and Rosenthal, A. J., "On the Stability of Helmholtz Velocity
~ Profiles in Stably Stratified Fluids When a Lower Boundary is Present," J. GEO-
PHYS. RES., Vol 81, No 9, pp 1561--1571~, 1976.
2. Grimshaw, R. H. J., "On Resonant Overreflection of Internal Gravity Waves From
a Helmholtz Profile," J. FLUID MECH., Vol 90, Pt 1, pp 161-178, 1979.
_ 3. McIntyre, M. E. and Weissman, M. A., "On Radiating Instabilities and Resonant
Overreflection," J. ATMOS. SCI., Vol 35, No 7, pp 1190-1196, 1978.
4. Benjamin, T. B., "The Threefold Classifi~ation of Unstable Disturbances,"
J. FLUID MECH., Vol 16, Pt 3, pp 436-450, 1963.
5. Voror.ovich, A. G. and Rybak, S. A., "Explosive Instability of Stratified Cur-
rents," DOIa.. AN SSSR (Reports of the USSR Academy of Sciences), Vol 239, No
6, pp 1457-1460, 1978.
6. Cairns, R. A., "The Rol~ of Negative Energy Waves in Some Instabilities of
Parallel Flow," J. FLUID. MECH., Vol 92, Pt 1, pp 1-14, 1979.
7. Craik, A. D. D. and Adam, J. A., "ExpJ.osive Resonant Wave Interaction in a
Three-Layer Fluid Flow," FLUID. MECH., Vol 92, Pt 1, pp 15-33, 1979.
8. Landau, L. D. and Lifshits, Ye. M., MEKHANIKA SPLOSHNYKH SRED (Mechanics of
Continuous Media), Moscow, Gostekhizdat, 1954, 725 pages.
9. Fel'sen, L., "Quasioptical Methods in Diffraction," KVAZIOPTIKA (Quasioptics),
Moscow, Mir, pp 11-62, 1964.
10. Nezlin, M. V., "Negative Energy Waves and the Anomalous Doppler Effect,"
UFN (Advances in the Physical Sciences), Vol 120, No 3, pp 481-496, 1976.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika atmosfery i okeana",
1981
5 303
CSO: 1865/222
64
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TERAF.STRIAL GEOPHYSICS
UDC 550.34.016
S AND F wF.VE ATTk`NT;RTI~N OF THE CRUST AND UPPER MANTLE BENEATH THE WEST SIBERIAN
FLATE AND SIBERIA;:` PLA'I'FQRM
Moscow IZVES'~IYA RKAC~EMII NF~UK SS~R: FIZIKA ZEMLI in Russian No 2, Feb 81 pp 37-50
[Article by t~. V. Ye~;orkin, V, v. Kun and N. M. Chernyshev, Special Regional Geo-
~,hysical ExpPdition, 5~~~ntific Production Association, Soyuzgeofizika, USSR
Ministry af Geci~~yy~
(T�ext; '1'he :~a~an value of the figure of inerit Qp in Siberia in-
creases fr~:m 7.~? in the range of depths of 0-150 km in the consol-
idar.e~ _r~.~st *0 445 at H ti 150 km. The value of Qp decreases to
190 w* c'.e~ths on the ordez of 150-210 km and then increases again,
reachix~g ~y~ ati H ti 400-450 km. The attenuation of P and S waves
is ess2:~*i.ally i~entical.
Considerable atr..~ntican is devuted in the literature on the structure of the earth's
, lithosphere tA para-~eters that characterize attenuation of P and S waves. However,
*_he ntanber of experimental data on these values is low, which one can judge, for
~
example, from ~:i~e su~naries presented in [1-5). The possibility of usi~ng data on
attenuation of ~ei5mic energy during study of the earth's deep interior is limited
in this regarci.
One of the ler.~st investigated is the problem of ratio of P and S wave attenuation
in t~:e lithosphere. ~ata are presented in this article on the attenuation coeffi-
~ cients of S anu P waves in the earth's crust and upper mantle (to a depth of 600
- km), obfiained from materials of explosion seismol.og} during investigations in west-
_ ern and eaGtern Siberia. The results of studya.ng the attenuation coefficients of
- P waves in tl~e upper mantle to a depth of 100 km, obtained by the authors during
similar investigations in regions of the Russian platform, the Caspian depression,
the ~rals ard K.ezakhstaii, were published in [6]. Seismograms obtained in Siberia
~ on two longitudinal profiles (Figure 1) were processed to calculate the attenuation
~ parametErs. PowPrful industrial explosions that provide adequately intensive re-
~ c~rdir~g of P and S waves at epic~ntral distances up to 3,200 km (Figure 2) were
used as the sources. A systesn of counter an~ overtaking hodographs was found on
~rof:�'~s I and TI. 'L'he l~ngth of the hodograph from one explosion station was
s~~t l.ess ~han SOd ~n. The distance between the points of recording the oscilla-
- tions comprised 7-12 km. 'I'hree displacement companents: one vertical and two hor-
izontal (alez?g the iine of the profile and perpendicular to it), were recorded.
. '."ti~.~ rennrc~.inqs weze obtained by means of NSP-3 seistnographs and Tayga stations with
- fiYa~-a*_ion ha~Fing maximum frequency characteristic ~n the range of 4-5 Hz. The
~�~;.:;ye ~f ana~ yz.e3 ~requencies co~rprised 1-8 Hz.
J E5

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~e ~2 r :^e n> >a ~u
r---- - - ~ - ~1--~ _
~ ,t~,s
~e ~ ~1~ ~
a o3. ~ ) ' ~c ~ 0)
~3) a
~
~ B%lr�~c
k~5~ ~i;,f~~ ^ ~
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(16) ; . ~ ~ ~
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� 22) s
e~orrlqr,~ K~iri~r.y.~ ~�ti`
~ ~
~23 ~ ~ ~l~~
,9 ic;~ir:~ 1 (24) i
f'~.... T~_oco j ~e
n +a a+ ve ioe i~o ~e
Figure 1. Layout of Profiles
Key :
- l. Dikson 13. Vilyuy River
2. Vorkuta 14. Yakutsk
3. Noril'sk 15. Ust'-Uda
4. Salek.~ar 16. Irtysh River
5. Berezovo 17. Ob' River
6. Yenisey River 18. Angara River
7. Nizhnaya Tunguska River 19. Profile II
g . ~a 20. Lena Ri.ver
9. Profile I 21. Novosibirsk
10. Tiksi 22. i~asnoyarsk
11. Lena River 23. Irkutsk
12. Aldan River 24. IQzilok
.
The attenuation coefficients of P and S waves were deternuned by variations of
their amplitude spectra as the distance R of the observation point from the source
of the oscillations increased (by the decrease of the normalized spectral amplitude
with distance). The method proposed by Vasil'yev [7] and used earlier in
[1, 4, 6, 8] was used. The advantage of this method compared to others is that the
� effect of the divergence of the wave front and the different increase of the record-
~ ing channels on the decrease of amplitude is eliminated in the calculations. The
latter is especially important during observations on large legs of the profile by
means of several seismic stations simultaneously. Each determination of ap~g was
made from seismoqrams of one explosion only at epicentral distances within which,
= judging by kinematic and dynamic parameters of seismic recordings, there is not
wave shift [6J. Based on analysis of these parameters, the range of epicentral
distances of 10-3,200 ]an is divided into seven legs: 10-200, 190-500, 350-850,
900-1,500, 1,500-2,200, 2,000-2,700 and more than 2,500 kmo
66
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A'
' S f0 ' f5 20 tpea-~tNUba 6~,c
D
. _
16
~ -
93
y .
84 _
f2t
F~ Kn~t
Figure 2. Example of S Wave Recordings Registered on Profile I
Refraction-refracted waves, called Pk(Sk~~ Pnl~Snl)~ Pn2~ Pn3~ Pn4~ Pn5 and Pn6,
respectively, are recorded within each leg. The first of them is propagated pri-
marily in the upper part of the consolidated crust, penetrating to 15-30 km. The
main part of the path of Pn waves is located in the upper mantle: Pnl from the
Moho discontinuity to depths of 65-75 km, Pn2 to 75-95 km, Pn3 to 100-140 km, Pn4
to 150-210 ]an, Pn5 to 400-500 km and Pn6 greater than 600 km.
The boundaries of the recording legs were determined for each explosion station on
the basis of analyzing the amplitude graphs A(R), the graphs of the maxiunum spec-
tral frequency fmax(R) and the averaged graphs of the first onsets.
Special attention was devoted to correlation of waves recorded in the initial part
of the seismograms and to determination of the legs where each of the Pn waves is
determined in the simplest form (outside the interference zones with other waves)
when selecting the profile interval on which the attenuation coefficients were
calculated. The attenuation coefficients found in this case correspond to the
depths at wh~ct: the wave propagates in a direction close to horizontal (depths of
maximum ray penetration) [9j.
The results of calcul.ating *_ne parameters that describe the attenuation of P and S
waves are presented in TaD'les 1-3. The following notations are used: ~R is the
interval of epicentral distances at which the wave was recorded, ~f is the fre-
quency range for which the attenuation coefficient was calculated, K is the angular
coefficient for the straight line that averages the dependence of the attenuation
coefficient on frequency (a = Kf), s/km, and it is equal in absolute value of the
attenuation coefficient a at 1 Hz, Ug is the mean square error of determining the
values of K, OK is the range of values of K at fiducial probability of 0.9, Q is
67
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the figure of inerit (Q =~t/K~1), ~Q is the range of values of Q with regard to the
fiducial interval for K and V is the mean interval velocity of longitudinal (trans-
verse) waves used when calculating Q. The geological structures within which at-
tenuation was determined are indicated in the last column of the tables. Z'he
relative error of calculating the value of K fluctuates from 2.5 to 37.5 percent
with a prevalent error of 6-8 percent. The actual error of determining the values
of K and a is obviously greater since part of the pulse in some time interval ~t is
used to calculate the spectra at each observation point; it is practically impossi-
ble to isolate the entire oscillation corresponding to each wave.
Attenuation of longitudinal waves in the consolidated crust (Table 1) in the in-
vestigated area varies within a considerable range: range K comprises 0.9�10-3
to 7.05�10'3 s�]an'1 and Q comprises 69-562. The mean values for these parameters
(K, Q) are equal to 3.28�10-3 s�km'1 and 202, respectively. Kp = 2.78�10-3 s�km-1
and 227 without abnormally high values (Kp > 5.0�10-3 s�km'1).
Relatively stable values of K(3.0�10-3 to 4.72�10'3 s�km'1) and of Q(114-161)
were found within the West Siberian plate (Nos. 1-4 of Table 1) and the Vilyuy
syneclise (Nos. 14 and 15 of Table 1); the values of K for these regions comprise
3.84�10-3 s�]an-1 and 3.87�10-3 s~lan-1 and those of Q comprise 133 and 136. k is
less (2.60�10-3 s�k.n 1) while Q is greater (212) in the region of profile II (the
Tunquska syneclise, Angara-Lena stage), where the standard deviation of the con-
sidered values is also low.
The greatest variation of K and Q is noted within the central part of profile I
(the Mirnyy-Aykhal saddle, Nos. 5-13 of Table 1). The maximum attenuation (K =
_(6.01-7.05)�10-3 s�km-1 was found here from Pk waves that passed through the
zones of a deep fault separating the Mirnyy-Aykhal saddle and the Vilyuy yneclise.
For this region IC is equal to 3.27�10-3 s�km 1 and Q= 242. K= 2.34'10 ~ s�km-1
and Q= 290 without regard to the two maximum values.
Attenuation of longitudinal waves in the upper mantle. Based on analysis of Table
2, one can make the following conclusions.
1. The investigated ranges of the depths of the upper mantle (from 0 to 600 km
from the M discontinuity) differ significantly by the values of the attenuation
coefficients of longitudinal waves and by the nature of their variation in area.
2. High variability of the values of coefficient K in area and the figure of inerit
calculated by it is typical for the uppermost part of the upper mantle (H ~ 0-20
km). The value of K, calculated from the data of two profiles, is equal to
1.80�10-3 s�km'1f the range of its variation are relatively broad--K =(1.02-3.60)'
'10-3 s�3an'1. Deviations of K from the mean value are significant, on the order
of 20-60 percent. The range of variation of the figure of inerit is from 106 to
370 and Q= 241. The wide range of the derived values of K and Q correlates to
the ~~;nificant variations of the boundary velocity through the surface of the up-
per mantle found in profiles I and II (Vg = 8.2-8.7 km/s). The existence of an
inverse correlation of the dependence between the values of coefficient K and
- velocity Vp was shown earlier [6].
68
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69
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t~ O~~Y' ~7'00 O c7NW cD o0N u~ N~ 00
~ ~ .-~00 00 ~ GOO O 00 O 000 0 ~
i 0 rl
U 0
W
ti o-~n ~n c~ ~n c~ cV c~ v~ o ca t~ - c~ c~ n ~n
N n o c~ ao r~ cv - r: o c~ c. - o c, o c~ ao n
f c~7 N~ ~ ~ V' - N C.~ C7 00 C) C] L.-� M CD Q~ O
.^]:V.~+ N NNN NN N,
N z I I I I I I I I I I I 1 I I 1 I I I I I
v-c~ i- - i- � -o c~ c--c n
A a i r_- o ccr~ c~ ooa~ ~u~~ oo 'a~G
.7 cl ? oC O C. ~ N~ N N N~ N N N
(O r. .r
H
~ > i~.-. ~ ; >
r. ~
y ~ - _ ..r
o - ;
v
71
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[Key continued from preceding page]:
1. Profile 10. Taymyr.massif, Yenisey-
2. Hertz Khatanga downwarp
3. s�]aa 1 11. Angara-Lena stage
4. km/s 12. Siberian platform, Angara-Lena
5. Geological structures stage
6. West Siberian plate 13. Siberian platform, Mirnyy-Aykhal
7. Siberian platform, Tunguska syneclise saddle, West Siberian plate
8. Siberian platform, Vilyuy syneclise 14. Siberian platform, Angara-Lena
9. Siberian platform, Mirnyy-Aykhal stage, Baykal downwarp
saddle 15. Siberian platform
The range of values of K and Q calculated by Pn2 waves and corresponding to depths
of 30-50 km (from the M discontinuity) is narrower than for P 1 waves; the absolute
values of K are lower and those of Q are higher; IC = 1.19�10-~ s�km 1 and Q= 345.
The deviations of the values of K from K are less than in the first interval.
The very large value of K equal to 6.54�10'3 s�km-1, found on profile I on the leg
of the Verkhnetembenchinskiy uplift of the Tunguska syneclise,* should be especial-
ly noted. The high attenuation and the reduced figure of inerit of the upper mantle
on this leg were apparently determined bv the Pxistence of a zone of deep tectonic
disturbance penetrating into the upper mantle. This is confirmed indirectly by the
abnormally high v31ue of K(3.6�10'3 s�km'1) found on this same leg from the Pnl
wave at the other explosion station.
4. The values of ap and Q calculated by the Pn3 wave correspond to depths on the
order of 60-95 lan below the M discontinuity. Attenuation is less here than for the
other intervals, while the figure of inerit is higher. The value of K varies from
0.607�10-3 to 1.67�10'3 s�km 1, K= 0.910�10'3 s�km-1 and Q= 445; deviation of
single determinations from the mean value are less than 30 percent. An exception
is the region of the Katanga saddle of the Tunguska syneclise, for which an abnor-
mally high value of K(1.67�10-3 s�km 1) was found.
5. The value of K increases to 1.98�10'3 s�km'1 while that of ~ decreases to 193
at depths of 150-210 km, where attenuation was studied from the amplitude spectra
of the Pn4 wave. Individual values of K are included in a rather narrow range
(1.59�10'3 to 2.40�10-3 s�km 1) and are close to those fnund for the mass lying
near the Moho discontinuity.
6. The values of K determined from the Pn5 wave and which characterize attenua- ~
tion at depths of 400-500 km differ significantly from data of different detona-
tion stations (from 0.40�10'3 to 2.58�10-3 s�km-1) and K= 1.45�10-3 s'km 1. The
maximum deviations from the mean value are 80 percent and Q= 347.
7. A single value of K= 1.97�10-3 s�km'1 and Q= 145 was found from the Pn6 wave.
*
This value was eliminated when calculating K for Pn2 waves.
72
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~ K c ~ ^
O n c+~ o r. ~ C op c~ o to
N ~ ~ NN OC ` CCC-+O
~ C O O -G G G~
~ ~ ~
3 O ~ ~ d_' ~ C l~ c._. ~ G~
v
I 4 C N O t+') O N O O
Y
v
~ a .C7 ~ ~C"' ~ N ~MCNC7
~ d .
~
~ ~ ~n v~ c~~~ ^ ~S $ c~coo GJ
N O ~ ~ ~ i~ N t` ~!'~N
q ~ ~'j ~ r~ c~: c.i cc j., R7 N~
~
~ � ~ N U ~
] ' .c., c'�. CO ~ ~ ~ N
~ ~G~ ~ a vT ?C N L:
R7 a�. ~ t~�~. m E+ < E+
~ r v ~ es ey a ea ~ d
z o ~ _ ~
~ F 0 V C t7 O .
N r ~ d, ~ F F~ U~ 1d
~ p" ~ b c~ ~ p ~ b
K
V u C~ C C C CYi ~ ~~~j
~ X GQ ~=00 c~~ ~ rG0 r�~ a;
o b I~ i~~ " ~ ^ v . . .
u G ~ G m G' m m ~S
C ~ ~ 4 y.~
~ F" ^ O a c c a a~.F-.. i~ F. ~ L i
j~ w se R~ w a ~ W Q
W Cj E~ U H U E~ U E-~ i ~
ro b ~
w
o ti ~~ti~~~~ ~ ~ ~oooo~o a a a
~ C'7 M C*? c: C^ M M C'7 C'7 M Cn O \ U: l!'~ ~ ~f? ~/j lIJ
~ o~~~~oN~ d ro ~ ~ >
~ ~ ~ti~~ ti
o-. x�R c~ m .r ~ r c~ c*~ o o v: tD ~�'i �rl �.~1 R!
d ~ c+'] c*; ct o'J co cq c+~ V~ t/~ N V' M V' ~n N'n R1 ~1 ~I ~1
~ p`~. ~j `j ~j I I I I I I I I I ~,j I I t I I I I o 3 N N N
n c= cc ~r c. n c~ cv ~ o c~ oc o~ oo t~ o ~ r- A A A r-I
~ l4{ a q C'~J C. C/_ J N~CY~ [n l~ ~ O ~ C: ['7 N V' ~~~r+
O p N N N N N C'7 K CrJ ` C'7 V~ ~ ~r: N lT! CrJ M~: N � V) V~ VI V~ UJ
^ O
p O
~ ~ ~ c~D CNC.~'7GM~'UU~y ~M O p M ~ON~C~O~~ � � � � �
~ N C.' C+~ N M M C: M C*~ ~ y~ N~: C'7 C'7 V' N ~17 l~ I~ ~ Ql O
al
W c+: ~ OC c? c~ t~ c"~ N ~ QO N O 1~ tC ~D
~ 00 W C' :.._t: O 00 N ~I: C 00 ~:~t~ C?
p j (rj NNC^NNNCV NN ~ N. n1^
~ S 1 I I I I I i I I I I ~ i I I 1 1 I I
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aC O L~ n l~ L~ M\ C1~ CD N f^ ~ V) ~ N~;
V N N-~ ^ N r+
(f~ d ~vj N N Ch N N N N
~
L'' ~ N^i c'7 O~..V'G'~...CV
'ya~ ~ ON~^C~a~+ NN N ~ NN.rN-"~G?N
Y O C O O O O O O O C O p' O O O O O O O
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w o~ ~ ~ � ~
C[~ u') C: Q~ O N l~ V' N GO N 00 c0 00 ~
OC.t: NO_~'~MV' G?~ tr N V)G?cDC'n~N
~ ~X M NNt.NNNN '~"'N N`"'~`"r'.~+Nr'
V ~ r~ ~
U
~ ~'?`coy_'o,~n oQ `n o0 o~noo~n~no ~
0 ~ ' cD ~ oo ao ao ao cD ~ c~ ~ cri cD u~ ca ~ c: u~ cn ~-I
I I I I I i i I ,n I I I I I I I I
~ ~ pp p7.^NNOt00 O~ O V~NOt+70~~ U1
ro d N NN�~.MNNN e:~.. O erOr.p.n
~ F c 1~'~t ~ c.�~ con~n.r�M~ Gl ~
~ x `j ~ I I I I I I I I I I I I 1 I I I I ~ ~-1 b+
i~ ~p c: cr_ v~ x-~ c~ c~ m o~ N g g c~ oo u~ c7 ~H '~y N rO-I
Q ~ cv c*~ c*~ r. o o r c~ C
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c~~ -~-oi-ao c.o ~ "=,~.~,~~~~.a'.
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73
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The ratios of the mean values of IC and Q, calculated for depth ranges of II-V, to
the mean values IC1 and Q1 found for the uppermost part of the upper mantle are
equal to ic2/ICl_ 0.66, Rg/icl = 0.50, K4/K1 = 1.10 and K5/Rl = 0.80; Q2/~l = 1.43,
Q3~1 - 1�90~ Q4~Q1 - 0.80 and Q5/Q1 = 1.44. Similar values of R2/IC1 (0.60) and
Q2/~1 (1.55) were also found in [6].from materials of seismic investigations within
the Urals, the Turan plate and the Russian platform.
6~0 ~ ~
~
~~a .
500
-
~100 ~----C
. o- ~ o--o I
o .
.~00
r~~-~p-~ ' a~.
1DO ~ 1 0--9--0 ~
o.o o E
n.a e ~ �"-~.~.r `
� j~ � ~
100 ~ � P,E',Y1J,YID~II
o-o
~ 300 f000 1500 2000 2300 ~000
1iSM
Figure 3. Dependence of Figure of Merit Qp of Consolidated Crust and of
Upper Mantle on Profile I on the Distance of the Range of De-
termination of Qp to the Source (detonation point): I-IX cor-
respond to the indices of the detonation points on profile I
(Tables 1 and 2, Appendix 1)
It must be noted that the derived values of the attenuation coefficients character-
ize only layers with relatively increased velocities of body waves. And it is
those very layers to which the refracted waves emerging during the first onsets are
related. The figures presented in the article do not give an idea of the degree of
attenuation of seismic energy in layers with reduced S and P wave propagation
velocities.
Analyzing the data given in Table 2 and in [6), one may note (also see Figure 3):
1. The maximum attenuation (K1 = 2.40-2.96)�10'3 s�km-1 and Ql = 130-160) in the
uppernast layer of the upper mantle was found for the Urals, the Kazakh folded
country, the Turan plate, the Taymyr massif and the Mirnyy-Aykhal uplift. Z'hese
reqions are usually characterized either by relatively low values of P wave propa-
gation velocity (7.8-8.1 km/s) or by a developed network of tectonic disturbances
that encompass the upper mantle. The values of R1 and Q1 are similar to the mean
74
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values (K1 =(1.70-2.02)�10'3 s�km 1 and Q1 = 220-240) in the Moscow, Tungusska
and Vilyuy syneclises, where Vp > 8.2 km/s. The maximum figure of inerit (Q1 =
= 250-290) is observed in the Caspian depression and the Baykal downwarp, i.e.,
in Yegions with higher velocity of P waves (Vp > 8.4 ]an/s).
2. Attenuation in the second depth range (75-95 lan) depends to a lesser degree on
the region of invest~gations. According to available data, an inverse ratio is
noted between Q1 and Q2: reduced value~ of Q2 correspond to zones of increased
values of Q1 (higher than the mean value). Thus, the mean value of this parameter
is equal to 258 in the Caspian depression, 275 in the Tungusska syneclise, on the
order of 320 in the Urals and in central Kazakhstan and 330 in the Mirnyy-Aykhal
uplift.
3. The lowest attenuation in the entire mass of the upper mantle occurs in the
third depth range (100-140 km). It is still difficult to talk about any principles
in the distribution of Q3(K3) with regard to the small amount of available data.
One can note only that the mean value of 43 (five determinations) is equal to 450
for the Siberian platform and it is equal to 495 (two determinations) for the west
Siberian plate. A single determination for the Moscow syneclise [6] yielded a
value of Q3 = 430.
4. The figure of inerit of the layers of the upper mantle, corresponding to tt�e~
fourth (150-210 ]an) and fifth (400-500 k:m) depth ranges, is somewhat higher on the
Siberian platform (Q4 = 225 and Q5 = 260-450) than on the west Siberian plate (Q4 =
= 160 and QS = 200).
Attenuation of transverse waves and comparison of it to attenuation of longitudinal
waves. The attenuation of S-waves was determined from the amplitude spectra of Sk
an3 Snl waves. Recordings of the X- and Y-channels were used. Graphs of the de-
pendence o~ ln[A(fi)/A(fm)J(R), plotted from the S-wave spectra for X- and Y-channels
separately, hardly differ from each other. The attenuation calculated from them is
" essentially identical with regard to confidence intervals. Therefore, attenuation
by the spectra of the X- and Y-recordings processed jointly was calculated in the
final version. Data on the values of K and Q are reduced in Table 3. Unlike
Tables 1 and 2, four columns are added to Table 3 in which the values of K and Q
are presented for p waves found approximately in the same intervals of the profile
as I~ and Qg. It is obvious from Table 3 that the accuracy of determininq Kg and
Qg is the same as for P-waves.
The values of Kg for Sk waves, i.e., for the consolidated crust, are included in
the range from 1.77 to 3.28�10'3 s�lan-1. Their mean value is equal to 2.60�10'3
s�lan-1. The figure of inerit of the consolidated crust varies from 260 to 505 and
= 345. 'I'he main part of the calculations of KS was carr`.ed out within the
Mirnyy-Aykhal saddle, where ~g = 2.81�10'3 s�km-1 and Kg = 310. Somewhat lower
values of Kg were found for the Tungusska syneclise and the Angara-Lena stage, but
there are only two determinations each in these regions.
Attenuation of S waves in the upper part of the upper mantle was studied only for
the Tungusska syneclise. The ~~alue of Kg varies from 1.24�10-3 to 2.58�10'3 s�km-1~
the figure of inerit varies from 260 to 539, ICg = 1.75�10-3 s�km-1 and ~g - 390.
75
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Analysis of the data (Tables 1-3) shows that the attenuation coefficients of P and
S waves are approximately identical in the consolidated crust and in the upper part
of the upper mantle, while the figure of inerit for S-waves is higher. The ratio
I~p/ICS (QP/Q5) is equal to 1.07 (0.66) for the crust and 1.03 (0.62) for the upper
mantle. Considering these ratios only for cases when Kp and Kg was calculated on
the same interval of the profile (Table 3), one may note: a) single determinations
- of Kp/KS lie within the range of 0.49-2.79 for the consolidated crust and 0.58-3.40
for the upper mantlej b) the maximum values of Kp/K5 were found in zones of tectonic
disturbances, which is in agreement with the data of other investigators [10]; and
c) the mean value of RP/ICg (Qp/QS) is equal to 1.07 (0.65) for the consolidated
crust and 1.24 (0.67) for the upper mantle without maximum values.
Comparison of the data with the results of previous investigations is made diffi-
cult to a significant degree with regard to the different degree of detail of the
measurements, the different method of calculations, the use of recordings of dif-
ferent types of waves and so on.
The value of Kp fluctuates from 0.98�10'3 to 6.50�10'3 s�km'1 for P waves and Qp
fluctuates from 70 to 525 in the consolidated crust, according to the figures (on
the order of 30) presented in [1, 3, 7, 11-16]. The mean values of Rp = 2.70�10-3
s�km-1 and Qp = 185. Thus, the range of variation of the parameters in Siberia
that characterize attenuation in the crust (Table 1) and the mean values of Rp and
Qp are similar to the published experimental data for other regions of the earth.
Data on the attenuation parameters of P-waves are available in (1, 6, 7, 13-16] for
the first 10-20 km of the upper mantle. According to the literature (40 determin-
ations), the value of K fluctuates from 0.8�10-3 to 6.67�10'3 s�km'1 and Q fluctu-
ates from 60 to 530. The mean values are equal to 2.15�10'3 s�km'1 and 180, re-
spectively. The mean value of K, calculated from the seismograms of large
explosions [1], is equal to 1.9�10'3 s�km'1. Thus, good agreement between pub-
lished data and the data which we found is also observed for the mean values of
parameters that characterize attenuation in the uppermost part of the mantle.
Determinations of Qp were made by a number of investigators in rather thick masses
for greater depths. T'hus, Berzon et al [8] give Qp = 220, Kanamori [17] gives 100
and Dorman (18] gives 475 for the 0-100 km layer; the following fi.gures were
found for a thickness of 0-760 km: 530 + 150 [7], 150 [17] and 1n6-272 [19].
Moreover, curves of the dependence of QP on depth were published. A summary o~
these data is available in [20~. The results of calculating Qp in the upper mantle
of Siberia are in quite satisfactory aqreement with the data of [6], the results
for thickness of 0-100 km are in agreement with those present~d in [8] and the
results for the 0-760 km layer are in agreement wi.th those presented in [19].
The mean value of Qp in the investigated area of Siberia is similar to data of
Antonova et al and Veith and Clawson (220, 240 and 260, respectively, on the graph,s
Qp (H) [20, 21] in the depth range of 250-700 lan. At the same time there are ap-
preciable differences in the values of Qp and in the nature of their variation
with depth at H< 200 km. Thus, the maxi.mum values of the figure of inerit (approx-
imately 450, according to the models of Qp(H) indicated above, are confined to the
- uppermost part of the mantle (near the Moho discontinuity) and decrease gradually
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to a depth on the order of 100-120 km (a layer with reduced propagation velocity of
elastic oscillations), the figure of inerit then begins to increase and becomes
equal to 240-260 at H~ 350 km. The figures presented in Table 2 show that if the
layer with reduced velocity, present in the upper part of the mantle of the Siber-
ian platform [22l is excluded, then one can talk about an increase of Qp from 260
near the Moha discontinuity to 440 at a depth of approximately 200 km. Thus, the
distribution of the figure of inerit which we found for the upper 160 km of the
mantle in layers with relatively increased velocity of body waves is directly op-
posite to that which is presented in [20, 21].
Comparison to MM8 and SL 1, 2, 3 models [5, 23J permi~s one to note the following:
a) Qp used in these models for the earth's crust is 5-20 times highEr than the
values determined in the Soviet Union and b) the mean value of the figure of inerit
in the first 160 ]an of the mantle are similar to those found in Siberia for SL 1,
2, 3 models and is lower by approximately a factor of 1.5 for the MM8 model. The
nature of variation of Qp with depth is approximately the same in SL models as that
shown in [20, 21]; and c) the values of Qp in the considered models are appreciabay

- higher (by a factor of 1.5-3) than on the Siberian platform for the depth range of
200-700 km.
The reason for the disagreement of the data of different authors on the figure of
merit of the earth's crust and the upper mantle may be the use of different methods
of calculation and different types of waves and also the horizontal inhomogeneity
in distribution of the attenuating properties of the object under study [6, 20, 24].
Moreover, some fixed value of Qp/Qg (usually Qp = 3/4(Vp/Vg)~Qg [5, 20, 23]), not
having adequate experimental substantiation, is used in some cases when plotting
the functions of Qp(H).
The problem of the ratio of the attenuation coefficients (figure of inerit) of
longitudinal and transversal waves in the crust and upper mantle has b~en discussed
repeatedly in the geophysical literature. Very different conclusions were made in
thi.s case. For example, otp ~ o~, and Qp < Qg [15, 16, 25) 1.7 ap and Qp = Qg
[4, 17] and qg ~ 4.25 otp and Qp ~ 2.5 QS [26]. These differences can be explained
by factors used previously to explain the differences in the values of Qp. How-
ever, we feel that the main reason is the calculation of Qp/Qg by values de~er-
mined from seismograms of P- and S-waves with significantly different trajectories.
There are very few data on the values of ap/ as and Qp/Qg for the crust and mantle
obtained by using an identical method on longitudinal and transversal aaves with
similar propagation paths. Thus, 2. P. Pasechnik found the following values for
the upper mantle of Central Asia (the region of recording refracted waves at 200-
1,000 }an): Kp/Kg = 1.03 and Qp/Qg = 0.5 [1] and E. P.Sumerina determined that
Kp/Kg ~ 0.8 and Qp/Qg ~ 0.75 [16J from Pr and SPr waves in the North German de-
pression. According to IQialturin's materials [11], Kp/FCg = 1.1 and Qp/Qg = 0.53
in the consolidated crust. E. P. Sumerina cites the followinyl figures for the con-
solidated crust of the North German depression an3 the region of Tashkent [15, 16]:
Kp/Kg is included in the range of 1.18-1.33 while Qp/QS is included in the rangL of
0.45-0.50.
A considerable number of determinations of ap and ag in the frequency band of 0.4-
24.0 Hz is presented in [27] for the crust and upper mantle (depth from 26 to 160
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- FUR nFNI('lAl, lltil? ON1..1'
_ yvleJ
s o
o.
w
- ~ o
a
. 2
1 ~
0
_
~ y 4 6 B
~F~ ~s
~ Figu~ce 4. Dependence ~f Ratio af P- and S-Wave Attenuation Decrements on
Vp/v5: Points--experimental data for the crust and upper mantle

_i of Si~eria. The region of the most probable values of ~P/~S for
hard rock according to (3,29] is cross-hatched.
km) of Kamchatka. It followe ~YOm these data that ap/Ctg varies from 0.82 to 1.22
in the crust with a mean ~ral~xe of 0.99. The mean value of the considered parameter
is equal to 1.00 (range of 0.50-1.87) at depths of 26-54 km and is equal to 1.02
(ranqe of 0.29-2.0) in the range of 55-84 km, it is equal to 0.98 (range of 0.42-
1.75) at 85-120 Ian and it ~s equal to 1.13 (range af 0.75-1.80) at 120-160 lan. A
direct estimate of the value of (ap - ag) was also made along with measurement of
ap and as. It was shown that attenuation of longitudinal waves is more intensive
than of transvexse wa~es al6ng routes passing through a region of modern volcanism
and that attenuation of shear waves is no .less than that of compression waves on
routes thrc%~~h the ~aca'1 layer.
~ ~ir.ec~t analysis r~f the ratio of caefficiezts KP and KS was also made for Siberia
~ (28J. It was esta~blished thst Kp/Kg ~ 1 for the consolidated crust and the upper
20-3Q km of the upper mantle.
The re{~::~~ af possible value~ c~f the ratio of P- arzd S-wave attenuation decrements
dp/~~ ~t r~iiier~t values of ~Ip%VS is outlined in Figure 4 from data of [29] based
,~K :,urevi~~ arualyslm sr~c3 qen~ralizaticn of the summary of experimental results
All our results of
preQent.ed i~~ (3. 29, 3~)*t ~p~g a Olp~$~1F~S - KP~.~'VP~S'
a #Editaz's not~. The aources of th~ experimental data are incorrectly shown in the
~ summs~ries nf (?1 and (29J borrawed mainly from [30].
~ Foc~t~n�~~e c:ant~Yn~~E+d on f~Zlowing pagej ~
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- ~~-e~n,,:,;:,;.;;; k:~~ and k~ in the crust and mantle according to Table 3 are preaented
ir. :...~.G s�j:,e fi~+~re. �s can be seen, with few exceptions they are in good agree-
- ,;,ent _;..re~~ich's theoretic.l func~ion. Incide~tally, we note that since >
_ , : _ ~ ; , f Figure 4 ~nr "compact" rock, according to Gurevich, at ~p/~g
u~ Yr ~ V x~~~~~ which corres nds to many of the experimental
> 1 i~uned;iateiy ~ ~_ows ~S QP~ P~
resuits mertioned abc�.~e.
S~.aunarizing available data on the ~on~idered value~~, one may note that the exper-
a imen~cal values of ap/ag and Qp/Qg for the consolidated crust and upper mantle are
' characterized by a significant spread, but the mean values of these parameters
� four.d in different regions are very si.milar and ap/as ~ 1 and Qp/Qg ~ 0.6.
Conclusians
1. The figure of m~rit of the consolidated crust and supper mantle in Siberia dif-
fer significantly in area. The degree of its variation decreases somewhat as depth
increases.
2. The mean figure of inerit Qp of the upper mantle increases from 241 to 445 as
the depth increases to approximately 150 ]an (one has in mind layers with relative-
ly increased velocities to which re~racted waves emerging during the first onsets
are related). The value of ~P decreases to 190 at H~ 150-210 km and Q= 345 at
depths of 400-500 lan. '
3. 2'he attenuation coefficients of longitudinal and transversal waves in the con-
solidated crust and upper part of the upper mantle vary with depth, remaining prac-
tically equal to each other, while the mean value of Qp is approximately 1.7 times
less than the mean value of Qg.
iFootnote continued from preceding page]
Table 7, page 413 in the column "Source" in [3] should read: [65] instead of (213],
[213] instead of [219), [219] inst~ad of [139], [139] instead of [119] for the sed-
imentary mass and for granite and [102] instead of [119J for loess, [119] instead
of [99, 100] and [99] instead of [175] for granite and (175~ for rock of the earth's
mantle. Moreover, reference [16] should be replaced by [8J from [20]; all figures
are from the bibliography in [3].
The table in the column "Source" in [29] should read: [12J instead of [13], [13]
instead of [14], [14] instead of (15J, [15] instead of [16] [16] instead of [17],
[18] instead of [19], [19] instead of [20] and [20J instead of [211. Moreover,
reference [18J should be replaced by [8J from [1J; all the figures are from the
bibliography of [29].
The entire bibliography in (20] is shown correctly.
We note in passing that "the most accurate and reliable results" of determining
the attenuation coefficients of longitudinal and transverse waves in granites (for
that time) noted in Figure 2 in [30] by the large circle: ap = a5, were presented
in [8] from [301. When these materials were processed, the meth~d of interpreta-
tion was both developed and used for the first time whicY: ~s aZso used by the
authors of this article.
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BIBLIOGRAPHY
1. Pasechnik, I. P., "IQzarakteristika seysmicheskikh voln pri yadernykh vzryVakh
i zemletryaseniyakh" [Characteristics of Seismic Waves During Nuclear Explo-
sions and Earthquakes], Moscow, Nauka, 1.970.
2. Jackson, D. D. and D. L. Anderson, "Physical M~echanisms of Seismic Wave At-

~ tenuation," REVIEW OF GEOPHYSICS AND SPACE PHYSICS, Vol 3, No 1, 1970.
3. Gurevich, G. I., "Deformiruyemost' sred i rasprostraneniye seysmicheskikh
voln" [The Deformability of Media and Propagation of Seismic Waves], Moscow,
Nauka, 1974.
4. IGogan, S. Ya., "Seysmicheskaya energiya i metody yeye opredeleniya" [Seismic
Energy and Methods of Determining It], Moscow, Nauka, 1975.
5. Anderson, D. L. and R. S. Hart, "Attenuation Models cf the Earth," PHYSICS OF
THE EARTH AND PLANETARY INTERIORS~ 1978.
6. Yegorkin, A. V. and V. V. Kun, "Attenuation of Longitudinal Waves in the
Earth's Upper Mantle," IZVESTIYA AN SSSR, FIZIKA ZEMLI, No 4, 1978.
~ 7. Berzon, I. S., A. M. Yepinat'yeva, G. N. Pariyskaya and S. P. Starodubovskaya,
Dinamicheskiye kharakteristiki seysmicheskikh voln v real'nykh sredakh"
'[Dynamic Characteristics of Seismic Waves in Real Media], Moscow, Nauka, 1962.
8. Berzon, I. S., I. P. Pasechnik and A. M. Polikarnov, Determining the Param-
eters of P-Wave Atter..uation in the Earth's Mantle," IZVESTIYA AN SSSR, FIZIKA
ZEMLI, No 2, 1975.
9. Berzon, I. S., I. P. Pasechnik and A. M. Polikarnov, Supplement to the
Article 'Deternunation of the Parameters of P-Wave Attenua.tion in the Earth's
Mantle [1, 2]'," IZVESTIYA AN SSSR, FIZIKA ZEMLI, No 10, 1979.
10. Pustovitenko, B. G. and T. G. Rautian, "Investigating the Attenuation of
Seismic Waves in the Crimea and the Regional Characteristics of Focal Radia-
tion Through the Crust," Proceedings of the Symposium "Modern Methods of
Recording arzd Interpretation of Seismic Observations," Report Topics, Yalta,
1979.
11. IQzalturin, V. I. and N. B. Urusova, "Estimating the Attenuation of Longitudin-
al and Trans�~ersal Waves in the Earth's Crust From Observations of Local Eaxth-
quakes," TRUDY INSTITUTA FIZIKI ZEMLI AN SSSR, No 25 (192), 1962.
12. Tulina, Yu. V. and G. A. Yaroshevskaya, "Vnutrennyaya struktura Zemnoy kory"
[The Internal Structure of the Earth's Crust], M~oscow, Nauka, 1976.
13. "Glubinnoye seysmicheskoye zondirovaniye zemnoy kory v SSSR" [Deep Seismic
Sounding of the Earth's Crust in the USSR], Leningrad, Gostoptekhizdat, 1962. ~
80
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14. Vol'vovskiy, I. S. and V. S. Vol'vovskiy, "Razrezy zemnoy kory territorii
- SSSR po dannym glubinnogo seysmicheskogo zondirovaniya" [Profiles of the
Earth's Crust in the USSR From Deep Seismic Sounding Data], Moscow, Sovetskoye
radio, 1975.
15. Sumerina, E. P,, "Determining the Attenuation and Scattering Coefficients of
Longitudinal and Transversal Waves Recorded by 'Zemlya' Stations," in "Razve-
dochnaya geofizika" [Exploratory Geophysics], Issue 59, Moscow, Nedra, 1973.
16. Sumerina, E. P., "Attenuation of Longitudinal and Transversal Waves," in
"Sostoyaniye i perspektivy razvitiya metodov poperechnykh i obmennykh voln v
_ seysmorazvedke" [The State and Prospects for Development of Methods of Trans-
versal and Body Waves in Seismic Prospecting], Moscow, Rotaprint, VNIIGeofizika,
1977.
17. Kanamori, H., "Spectrum of P and PcP in Relation to the Mantle-Core Boundary
and Attenuation in the Mantle," JOURNAL OF GEOPHYSICAL RESEARCH, Vol 72, 1967.
18. Dorman, L. M., "Anelasticity and the Spectra of Body Waves," JOURNAL OF GEO-
PHYSICAL RESEARCH, Vol 73, No 12, 1968.
19. Mikumo, T. and T. Kurita, "On Distribution for Longperiod P-Waves in the
Mantle," JOURNAL OF PHYSICS OF THE EARTH, Vol 16, 1968.
20. Antonova, L. V., F. F. Aptikayev, R. I. Kurochkina et al, "Eksperi.mental'nyye
seysmicheskiye issledovaniya nedr Zemli" [Experimental Seismic Investigations
of the Earth's Interior), Moscow, Nauka, 1978.
21. Veith, K. F. and G. E. Clawson, "Magnitude from Short-Period P-Wave Data,"
BULLETIN OF TI~ SEISMOLOGICAL SOCIETY OF AMERICA, VO1 69, No 2,1972.
22. Vinnik, L. P. and A. V. Yerogkin, "Wave Fields and Models of the Lithosphere
and Asthenosphere from Seismic Observation Data in Siberia," DOKZADY AN SSSR,
Vol 250, No 2, 1980.
23. p.lderson, D. L., A. Ben-Menahem and C. B. Archambeau, "Attenuation of Seismic
Energy in the Upper Mantle," JOURNAL OF GEOPHYSICAL RESEAR~H, Vol 70, No 6,
1965.
24. Vinnik, L. P., "Issledovaniya mantii Zemli seysmicheskimi metodami" [Investi-
gations of t:ne Earth's Mantle by Seismic Methods], Moscow, Nauka, 1976.
25. Attewell, P. B. and J. V. Ramana, "Wave Attenuation and Znternal Friction as
a Function of Frequency in Rocks," GEOPHYSICS, 1966.
26. K,~vach, R. L., "Attenuation of Seismic Body Waves in the Mantle," GEOPHYSICS
JOURNAL OF THE ROYAL ASTONOMICAL SOCIETY, 1967.
27. Boldyrev, S. A., "Spectre of Elastic Waves from Weak Lartnquakes and Analysis
of Attenuation Under Kamchatka," in "Seysmichnost' i seysmicheskiy prognoz,
svoystva verkhney mantii i ikh svyaz' s wlcanizmom na Kamchatke" [Seismicity
and Seismic Forecasting, the Properties of the Upper Mantle and Their Rela-
tionship to Volcanism on Kamchatka], l~iovosibirsk, Nauka, 1974.
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28. Yegorkin, A. V. and G. V. Yegorkina, "Transversal Waves During Deep Investiga-
tions," GEOIAGIYA I GEOFIZIKA, No 6, 1980.
2g. Vasil'yev, Yu. I. and G. I. Gurevich, "The Ratios Between the Attenuation
Decrements and Propagation Velocities of Longitudinal and Transversal Waves,"
IZVESTIYA AN SSSR, SERIYA GEOFIZIKA, No 12, 1962.
30. Vasil'yev, Yu. I., "~ao Summaries of Attenuation Constants of Elastic Oscilla-
tions in Rock," IZVESTIYA AN SSSR, SERIYA GEOFIZIKA, No 5, 1962.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika Zemli", 1981
6521
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COLLECTION OF ARTICLES ON DYNAMIC THEORY OF SEISMIC WAVE PROPAGATION
Moscow VOPROSY DINAMICHESKOY TEORII RASPROSTRANENIYA SEYSMICHESKIKH VOLN in Russian
No 20, 1981 (signed to press 7 Jan 81) pp 3, 212
[Foreword and table of contents from collection of articles "Problems in the Dynam-
ic Theory of Seismic Wave Propagation", edited by G. I. Petrashen', Izdatel'stvo
"Nauka", Leningradskoye otdeleniye, 1300 copies, 216 pages]
[Text] Foreword. The articles contained in this number of the series are naturally
subdivided into groups relating to extremely important directions in modern seis~-
mics, to wit: 1) study of wave processes in anisotropic and isotropic elastic media;
2) algorithms and methods for computing seismic fields; 3) theoretical and experi-
mental investigations in the field of seismic prospecting, and finally, 4) statis-
tical approaches in evaluating geophysical information. As a result of the abun-
dance and diversity of articles it would be very difficult here to attempt to give
a detailed description of their contents. This, to be sure, is not required, since
a general idea concerning their content can be obtained from the abstracts.
The most important feature of this collection of articles is its international char-
acter, being a direct result of our scientific contacts with the geophysicists of
the countries of the Socialist Economic Bloc, wh~~ with each passing year are becom-
ing more and more close. For example, this collec.tion contains a Iong article by our
colleagues from Czechoslovakia V. Cerveny and J. Zahradnik and from West Germany
K. Fuchs and G. Muller, as well as two articles by our colleagues from East Germa.ny
G. Peschel, H. Poppitz, A. E. Gotz and P. Kalyschkov. It wi11 undoubtedly be of in-
terest to familiarize our Soviet readers with these articles.
- Another feature of the collection of articles to which it is evidently fitting to
draw attention is that its appearance is related to the beginning of our scientific
~ttack on all that is unclear in the field of seismic anisotropy. The fact of a need
for taking into account the anisotropy of seismic media in the choice of their suf-
ficiently adequate models is scarcely in need of argumentation. However, the aniso-
tropy of seismic media until now has been poorly taken into account in modern seis-
mics. And this occurs primarily due to the widespread opinion that allowance for the
anisotropy of inedia in wave propagation processes is unreliable due to "insuperable"
mathematical difficulties and the excessive unwieldiness of any analytical solutions
:;f wave propagation problems.
We resolutely dispute such a pc.int of view and it is our purpose to show that with
some departure from the traditional classical approaches to problems the obtaining
= of effective quantitative solutions of the main problems of wave propagation in
anisotropic elastic media becomes an entirely real task, not requiring even a great
expenditure of time and work. We have presented a~ull proof of such an assertion
83
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in a special monograph. [G. I. Petrashen', RASPROSTRANENIYE VOLN V ANISOTROPNYKH
= UPRUGIKH SREDAKH (Wave Propagation in Anisotropic~Elastic Media), Leningrad,
"Nauka," 1980.]
To be sure, here I would like to devote attention to each article in the collection
and characterize its merits with at least one or two sentences. But I will limit
myself solely to directing the attention of readers to the articles of M. M. Popov
and L. G. Tyurikov, devoted to computation of the geometrical divergence of beams
of rays in arbitrary inhomogeneous isotropic media. TEiese articles give a very
refined and simple solution of the problem and therefore great satisfaction can
be obtained from their reading.
G. Petrashen'
Contents
3
Foreword
Molotkov, L. A. "Wave Propagation in Layered Transversally-Isotropic Media
With Discontinuities" 4
Krauklis, P. V. and Tsepelev, N. V. "Love Waves in a Transversely-Isotropic 18
Inhomogeneous Half-Space"
Ozerov, D. K. "Constructive Interference Method for Love Waves in an Aniso- 20
tropic Medium"
Molotkov, L. A. and Lopat'yev, A. A. "Investigation of Wave Propagation in 22
Layered Thermoelastic Media by the Matrix Method"
Krauklis, P. V., Krauklis, L. A. and Burago, N. A. "Attenua.ting Waves in the 38
Case of a'Itao-Layered Casing of a Borehole"
Krauklis, P. V. and Ibatov, A. S. "Attenuation of Normal Waves in a Borehole" 45
Kouzov, D. P. "Very Simple Model of an Acoustic Medium With Absorption" 52
Popov, M. M..and Tyurikov, L. G. "T~ao Approaches to Computation of Geometrical 61
Divergence i~t an Inhomogeneous Isotropic Medium"
Tyurikov, L. G. "Computation of Geometrical Divergence for Vertically Inhomo-
geneous Media and for Media With Spherical or Cylindrical Symmetry" 69
Ledovskaya, Ye. M. "Program for Constructing Theoretical Seismograms for the
Total Field of Reflected Multiple Waves in the Case of a Three-Layer Medium" 75
Volin. A. I. and Zhidkov, A. V. Program in FORTRAN Language for Computing the
Kinematics of Body Waves in thet'Case of a Three-Dimensional Inhomogeneous 79
Medium"
Cervey, V., Fuchs, K., Muller, G.and Zahradnik, J. "Theoretical Seismograms for 84
Inhomogeneous Elastic Media"
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Tsymbal, T. M. and Antonova, L. N. "Analysis of Wave Field Characteristics in
the Field of a Transformed Fault, According to the Results of Numerical
Modeling" 110
Golikova, G. V. and Chizhova, M. V. "Influence of Screening Phenomena on the
Kinema.tics of Different Types of Waves" 119
Neprochnova, A. F.; Ozerov, D. K. and Smirnova, N. S. "Discrimination of a
Layer of Reduced Velocity in the Sedimentary Stratum of the Black Sea De-
~pression" 124
Miroshnikova, 0. V. and Shop in, Yu. G. "Correlation Between Wave Fields and
Some Structural Characteristics of a Complex of Magmatic Rocks" 129
= Bykov, I. A. and Tikhonova, I. M. "Algorithms for the Digital Processing of
Borehole Amplitude Observations" 135
Rudakov, A. G. "Condition for Monitoring the Form of a Direct Wave in Ma.rin~
Seismic Prosp~.cting" 156
Peschel, G, and Gol'tsman, F. M. "Reduction in the Form of Reflected Seismic
_ Signals at the Lower Boundary of a Low-Velocity Zone" 161
Peschel, G., Poppitz, H. H., Gotz, A. E. and Kolyschkov, P. "Analysis of the
Form of Reflected Seismic Signals Using Classification Methods" 164
Troyan, V. N. "Statistical Algorithm for Recurrent Evaluation of the Parameters
of Seismic Waves" 173
Troyan, V. N. "Application of Spline Functions for the Approximation of Geophys-
ical Information" 184
Inagimov, P. Sh. "Method for Hyperbolic p-M Summation of Seismic Records" 198
- Ozerov, D. K. and Latyshev, K. P. "Transformation of Seismograms Using Random
Mixing" 207
Artem Pavlovich Volin 210
COPYRIGHT: Izdatel'stvo "Nauka", 1981
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PAPERS ON MATHII~iATICAL METHODS FOR INTERPRETIPIG GEOPHYSICAL OBSERVATIONS
Novosibirsk MATEMATICHESKIYE METODY INTERPRETATSII GEOFIZICHESKIKH NABLYUDENIY
in Russian 1979 (signed to press 26 Dec 79) pp 2-3, 175-177
[Annotation, table of contents and abstracts from collection of articles "Mathe-
matical Methods for the Interpretation of Geophysical Observations," edited by
Anatoliy Semenovich Alekseyev, Vychislitel'nyy tsentr SO AN SSSR,
600 copies, 178 pages]
[Text] Annotation. This collection of articles is devoted to problems related to
the development, validation and numerical application of inethods for solving di-
rect and inverse problems in the theory of wave propagation and diffraction and
photogrammetry. The collection is of interest for specialists in the fields of
geophysics and mathematical physics, and ~lso for students and graduate students
specializing in the field of geophysics.
' Contents
4
Foreword
Belonosova, A. V. and Tsetsokho, V. A. "Computation of Geometrical Divergence 5
in Cartesian Coordinates"
Vorodin, V. V. "Numerical Solution of the Z~ao-Dimensional Problem of Diffrac- 12
tion of an Elastic Wave on an Elastic Body III"
Yelinov, V. D. "Restoration of the Coefficients on the Lower Derivatives in 30
the Acoustic Equation"
Yerokhin, G. N. "On the Problem of 5tability in Determination of Radiating 35
Point Ob~ects"
Marchuk, A. G. "Methods for Computing Tsunami Waves Within the Framework of 50
Approximate Models"
Martynov, V. N. and Mikhaylenko, B. G. "Numerical Modeling of the Propaga-
tion of Elastic Waves in Anisotropic Inhomogeneous Media (Case of a Half- 85
Space and Sphere)"
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Fat'yanov, A. G. and Mikhaylenko, B. G. "Numerical Solution of the Lamb Prob-
lem for an Inhomogeneous Boltzmann Medium With an Elastic Aftereffect" 115
Sharafutdinov, V. A. "On Geometrical Divergence" 161
Abstracts
UDC 550.344
COMPUTATION OF GEOMETRICAL DIVERGENCE IN CARTESIAN COORDINATES
[Abstract of article by Belonosova, A. V. and Tsetsokho, V. A.]
[Text] The article gives a system of six ordinary differential equations for deter-
mining the geometrical divergence of the central field of seismic waves in a medi-
~ um without discontinuities. In contrast to the studies of other authors, in deriv-
i ing the equations use was made only of a Cartesian coordinate system in which the
~ characteristics of the medium are stipulated. It is also demonstrated~in the study
that the advantage of any system of differential equations for the numerical deter-
mination of geometrical divergence is related not so much to the number of equations
in the system as to the number of arithmetical operations required for computing the
right-hand side of the system at one point.
UDC 517.948:519.6
~
i
~ NUMERICAL SOLUTION OF THE TWO-DIMENSIONAL PROBLEM OF DIFFRACTION OF AN ELASTIC
WAVE ON AN ELASTIC BObY III
[Abstract of article by Voronin, V. V.~]
~ [Text] The author in general features describes an algorithm for the numerical ap-
' plication of a method proposed and validated in the earlier articles of the auth-
~ or. The elimination of singularities is used in computing the coefficients of. the
i matrix obtained after discretization of a system of singular integral equations.
! The results of numerical experiments are given. Figures 5; references 4.
~
UDC 517.544
RESTORATION OF THE COEFFICIENTS ~N THE LOWER DERIVATIVES IN THE ACOUSTIC EQUATION
[Abstract of article by Yelinov, V. D.]
[Text] The article examines the problem of the uniqueness of determination of the
coefficients on the lower derivatives in the acoustic equation. The initial problem
is reduced to the known problem ~f integral geometry. References 3.
87
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UDC 517.9!+5
ON THE PROBLEM OF STABILITY IN DETERMINATION OF RADIATING POINT OBJECTS
[Abstract of article by Yerokhin, G. N.]
[Text] A study was made of the stability of solution of the inverse problem in de-
termination of "brightness" and coordinates of a finite number of luminescent
sources on the basis of the informa.tion stipulated in the form t;f some blurred im-
age. In two special cases a function characterizing this stability was determined
in explicit form.
UDC 550.345
METHODS FOR COMPUTING TSUNAMI WAVES WITHIN THE FRAMEWORK OF APPROXIMATE MOT~ELS
[Abstract of article by Marchuk, A. G.]
[Text] The author proposes a number of inethods for computing the problems involved
in the ge*~eration, propagation and breaking of tsunami waves on the shore. The
generation problem is solved within the framework of a nonlinear system of equa.-
tions for shallow water. A model ~f an ideal incompressible fluid is also proposed
for use in solving generation problems. Numerical experiments were used in invest-
igating the dependence of the characteristics of tsunami waves on the parameters
of bottom movements. A method for separate calculations in deep aad shallow parts
of the basin was developed for computing the problems involved in the propagation
of tsunami waves in a basin of variable depth. Also discussed in the article is
the problem of the energy of tsunami waves and its relationship to focal energy. A
refined formula is proposed for estimating this energy. An original method related
to transformation to an oblique coordinate system is proposed for computing the
problems involved in the rolling of tsunami waves onto a sloping shore. The re-
_ sults of numeri~al computations by the mentioned methods are given. Figures 22,
references 9.
UDC 518.61.550.344
NUMERICAL MODELING OF THE PROPAGATION OF ELASTIC WAVES IN ANISOTROPIC INHOMOGENEOUS
MEDIA (CASE OF A HALF-SPACE AND SPHERE)
[Abstract of article by Martynov, V. N. and Mikhaylenko, B. G.]
[Text] The article gives algorithms using finite integral transforms in combina-
tion with numerical methods for solving problems in the propagation of elastic
waves in a transversally isotropic half-space. A method is also developed for a
radially inhomogeneous tangentially isotropic model of the earth. Also examined is
the problem of the use of finite integral time transforms for solving the problem
of the propagation of elastic waves in inhomogeneous anisotropic media with absorp-
tion. References 10.
88
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UDC 518.61.550.344
NUMERICAL SOLUTION OF THE LAMB PROBLEM FOR AN INHOMOGENEOUS BOLTZMANN MEDIUM WITH
AN ELASTIC AFTEREFFECT
[Abstract of article by Fat'yanov, A. G. and Milchaylenko, B. G.]
_ [Text] The article consists of two parts. The first gives a solution of the Lamb
problem for an inhomogeneous (with respect to depth) half-space f311ed with a
Boltzmann medium with an exponential function of the aftereffect. The second pro-
poses an approximate meth~d for solving this problem for an arbitrary function of
the aftereffect. The convergence of the methods for a homogeneous medium is demon-
strated. Theoretical seismograms are given for a layer on a half-space with differ-
ent absorption. Figures 8, references 22.
UDC 513.73
ON GEOMETRIGAL DIVERGENCE
[Abstract of article by Sharafutdinov, V. A.]
[Text] It is demonstrated in this study that the computation of geometrical diver-
gence can be reduced to solution of zhe Cauchy problem for the Jacobi equation and
the symmetry of geometrical divergence is also demonstrated for the case of an
anisotropic medium. References 4.
COPYRIGHT: VYCHISLITEL'NYY TSENTR SO AN SSSR
5303
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PHYSICS OF ATMOSPHERE
UDC 551.507.551.513:551.507.551.508.551.513.590.2
PAPERS ON ROCKET SOUNDING OF THE ATMOSPHERE
Moscow TRUDY TSENTRAL'NOY AEROLOGICHESKOY OBSERVATORII: FIZIKA VERKHNEY ATMOSFERY,
SERIYA A: RAKETNOYE ZONDIROVANIYE in Russian No 144, 1981 (signed to press 23 Jan
81) pp 2, 133
[Annotation and table of contents from collection of articles "Transactions of the
Central Aerological Observatory: Physics of the Upper Atmosphere, Series A: Rocket
Sounding", edited by G. A. Kokin, doctor of physical and mathematical sciences,
Izdatel`stvo Moskovskoye otdeleniye Gidrometeoizdata, 370 copies, 134 pages]
[Text] Annotation. This collection of articles contains papers devoted to meth-
ods for carrying out a rocket experiment in the upper atmosphere. For the most
part the authors examine problems involved in the method for determining small
component~ in the atmosphere and also the problem of aerodynamic modeling of pro-
' cesses of interaction of ineasuring instruments with a flow of supersonic rarefied
gas. Some results of rocket sounding are discussed. The collection is of interest
for scientific specialists interested in problems relating to physics of the upper
atmosphere, the aerodynamics of rarefied gas, and also specialists concerned with
the development of scientific rocket and laser instrumentation.
Contents
Borisov, A. I., Kikhtenko, V. N. and Pakhomov, S. V. "Preliminary Results of Meas-
urements of the Parameters of the Charged Component of the Upper Atmosphere on
Meteorological Rockets" 3
Brengauz, G. Ye., Glotov, A. P., Pakhomov, S. V. and Sinel'nikov, V. M. "Use of
the Doppler Method for Measurements of Electron Concentration on Meteorological
Rockets" $
Yastrebov, A. A. "Evaluation of the Influence of Photoemission From the Surface
of a Probe on Measurements of the Electron Concentration in the Lower Iono-
sphere" 15
Galadin, N. F., Neyelov, I. 0. and Pakhomov, S. V. "Evaluation of the Coeffic-
ie~it of Turbulent Diffusion in the Mesosphere by the Radar Method" 22
Lysenko, Ye. V. "Error in the Method for Measuring Atmospheric Temperature Us-
ing a Resistance Thermometer" 28
,
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Bu[ko, S. "Error in Measuring Atmospher�lc Pressure Using a'Po[al Pre~sure M,~nu-
meter Carried Aboard an M-100B Meteorological Rocket" ~+5
Avdeyev, V. N., Lysenko, Ye. V. and Chernova, G. G. "Aerodynamic Error in Meeeur-
ing Atmospheric Temperature" ~5
Ivanovskiy, A. I. and Chernova, G. G. "Measurements and Compute3 Estimate o~ ~Tem-
perature of the Supporting System for a Rocket Thermometer" ~1
~ ~amsonov, N. A. and Sankovich, V. M. "Investigation uf Heat Excfiange B~t~ee~:
a Cylinder and the Air Flows in a Transient Streaml3ne Regime"
Kononkov, V. A. and Perov, S. P. "Methods and Preliminary Results of I.abc~r.a~o~r.y
Investigations of Chemiluminescent Ozone Sensors at Low Piessures" ~I
Perov, S. P. and Tishin, S. V. "Some Results of In~re~tigatioi. of Cit~.mu:x~in-
escent Gas-Phase Reactions"
I' Yermakov, V. I., Komotsk,ov, A. V. and Moshnikov, I. S. "Standardized Rocket
i Probe for Network Sounding of the Atmosphere" R~
i
j Yermakov, V. I., Ignatov, V. I. and KomotskAV, A. V. "Superregenerative Radar
i Responder for Meteorological Rockets" g4
I~ Grinchenko, V. D. and Kadygrov, Ye. N. "Multichannel Analog-Digital Converter
j of the Measurement Data From Meteorological Rockets" 98
; Grinchenko, V. D. and Kadygrov, Ye. N. "Channel and Cycle Synchronization in
~ the Reception of Telemetric Information From Meteorological Rockets" 103
~ g P g
' Kozlov V. I. Desi n of an 0 timum Filter for a PWM-FM Si nal Detector" ~ 110
~ ~
~ Vyazankin, S. A., Glazkov, V. N., Marchevskiy, V. A. and Rozenfel'd, S. Kh.
"Model of the Flight of a Rocket Probe and Error in Computing the Wind" 113
~ Rybin, Yu. N. "Processing of Data on the Tracking of Meteorological Rockets
! Using an Equation of Motion" 120
COPYRTGHT: Tsentral'naya aerologicheskaya observatoriya, 1981
' S303
CSO: 1865/201
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~
UDC 551.593+551.510.536
_ 7~~w ~'A~ FR~~ aN ATMOSPHERIC OPTICS
. ~�~?!.T~~ INSTITtITA EKSPERIMENTAL'NOY METEOROLOGII: OPTIKA ATMOSFERY in Russian
;;~,:,:u, 1981 ~signed to press 28 Jan 81) pp 2, 102
_ ;4nr.,otation and table of contents from collection of articles "Transactions of the
In~~titu~e of Experimental Meteorology: Atmospheric Optics", edited by V. N. Lebed-
inets, Izdatel'stvo Moskovskoye otdeleniye Gidrometeoizdata, 430 copie~, 102 pages]
' [T~xt] Annotation. '~'his collection of articles includes 12 original and review ar-
ticles devoted primarily to instrumental-meihodological problems in the following
principal research directions: development of instrumentation tor optical investi-
gations of the atmosphere and accompanying measurements of ionospheric parameters;
calibration of radiometric apparatus and computation of ineasurement errors; meth-
ods for remote optical sounding of the atmosphere; results of ineasurements of com-
position of the upper atmosphere and the optical characteristics of atmospheric
f.ormations. The authors describe a number of instrwnents for surface and rocket
investigations of the atmosphere developed at the ~nstitute of Experimental Meteor-
ology at the level of the best Soviet and foreign m4dels. The papers give the re-
sults of the first systematic investigations of the layer of Ca+ ions in the USSR
near the mesopause by the method of surface spectral twilight observations. The
collection is intended for a wide range of specialists in the field of atmospheric
~ optics, physics of the upper atmosphere and optical methods for remote sounding of
the atmosphere.
Contents
. Vasil'yev, A. S. and Davletshina, R. A. "Instrumentation for Fabricating Wedge 3
Interference Filters"
Allenov, M. I., Mamonova, I. G. and Tret'yakov, N. D. "Possible Errors"in 7
Radiometric Apparatus"
Kal'sin, A. V., Klimentov, A. M. and Mikheyev, Yu. P. "Spectrometer for Low- 17
Energy Electrons"
Kal'sin, A. V. and Mikheyev, Yu. P. "Determination of the Angles of Orienta-
tion of Rapidly Rotating Geo~hysiGal Rockets Using Solar and MagL:tic Sensors" 29
Gusev, S. V. and Tereb, N. V. "Energy Calibration of a Spectrometer for the 40
Observation of ~ailight Sky Emissions"
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Allenov, M. I., Bulgakov, V. G., Ivanova, N. P. and Tret'yakov, N. D. "Investi- 43
gation of Brightness Fluctuations of Stratocumulus Clouds"
Allenov, M. I. and Bulgakov, V. G. "Statistical Structure of Effective Thick-
nesses of the Field of Cumulus Clouds" 49
Tereb, N. V. "Formation of Stable Layers of Metal Ions in the Upper Atmo-
sphere" S~
Tereb, N. V. "Measurements of the Intensity of Ca II Emission in Kirgizia" 61
Barysheva, V. I. and Troyanova, N. M. "Influence of a Number of Fa~ctors on the
Level of Solar W Radiation Scattered by the Ozonosphere" 66
Kamenogradskiy, N. Ye. and Shashkov, A. A. "Experimental Investigations of
Atmospheric Carbon Dioxide (Review)" 73
Aref'yev, V. Iv. 3nd Visheratin, K. N. "Molecular Absorption of Radiation in 91
the Window of Relative Atmospheric Transparency 3.5-4.1~J1.m (Rev~ew)"
COPYRIGHT: Institut eksperimental'noy meteorologii (IEM), 1981
5303
CSO: 1865/200
~
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r
, r
COLLECTION OF PAPERS ON INVESTIGATION OF THE IONOSPHERE AND MAGNETOSPHERE BY
ARTIFICIAL MODIFICATION METHODS
Apatity IS~LEDOVANIYE IONOSFERY I MAGNITOSFERY METODAMI AKTIVNOGO VOZDEYSTVIYA
in Russian 1977 (signed to press 8 Jul 77) PP 2~ 81
[Annotation and table of contents from collection of papers "Investigation of the
- Ionosphere and Magnetosphere by Artificial Modification Methods", edited by Ye. M.
Filatov, Uchastok operativnoy poligrafii Ordena. Lenina K~ol'skogo Filiala imeni S. M.
Kirova AN SSSR, 300 copies, 82 pages]
[Text] Annotation. The authors of the papers in this collection of articles de~cribe
the principles of operation and give the principal technical specifications of an
apparatus for modification of the polar ionosphere by powerful short~aave radia-
tion and also the results of experiments carried out during the period 1975-1977
using this axid similar. apparatus, in particular, the results of observations of
radiation at combined frequencies in the auroral zone, measurements of the polar-
ization of signals at combined frequencies, investigations of the effects of scat-
tering of a radio signal from the region of the ionosphere subjected to the influ-
ence of powerful short-wave radiation, and the effects nbserved during vertical
sounding of this region. Also examined are possible mechanisms of the influence of a
powerful radio wave on the ionosphere and magnetosphere, as well as the probable
mechanisms of the influence of this wave on the generation of VLF emissions.
Contents
Kapustin, I. N., Pertsovskiy, R. A. and U1'yanchenko, A. A. "Apparatus for Modify-3
ing the Ionosphere by Powerful SW Radiation"
Vasil`yev, A. N., Kapustin, I. N., Loginov, G. A., Raspopov, 0. M., Smirnov, V. S.,
Solov'yeva, L. Ye. and U1'yanchenko, A. A. "Observation of Radiation at Com- 7
bined Frequencies in the Auroral Zone"
Vasil'ye~~, A. N., Kapustin, I. N., Raspopov, 0. M., Smirnov, V. S., Titova,
Ye. Ye. and Ul'yanchenko, A. A. "Modulation of Low-Frequency Radiation at 21
Combin~d Frequencies"
I~olchanov, 0. A., Mogilevskiy, M. M., Ma.rkeyeva, Yu. M., Raspopov, 0. M. and
~ Titova, Ye. Ye. "Possibility of Modification of VLF Emission by a Low-Frequency25
Transmirter"
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Getmantsev, G. G., Budilin, A. V., Kotik, D. S., Mityakov, N. A., Mironenko, L. F.,
Rapoport, V. 0., Sazonov, Yu. A. and Vasil'yev, A. N. "Measurement at Two
Points of Combined-Frequency Signals Excited by a SW Transmitter in the Aur-
oral Ionosphere" 30
~ Getmantsev, G. G., Budilin, A. V., Ivanov, V. A., Kotik, D. S., Mityakov, N. A.,
Rapoport, V. 0., Sazonov, Yu. A. and Arykov, A. A. "Measurement of Polariza-
tion of Combined-Frequency Signals" 32
Kotik, D. S., Mityakov, N. A., Rapoport, V. 0., Tamoykin, V. V., Trakhtengerts,
_ V. Yu. "Some Geophysical Effects Arising Under the Influence of Powerful
SW Radio Radiation on the Ionosphere" 35
Shvartsburg, A. B. and Molchanov, 0. A. "Resonance Generation of Low-Frequency
i Disturbances in the Polar Ionosphere" 42
Pertsovskiy, R. A. and Molchanov, 0. A. "Experimenta~. Investigation of Scatter-
ing of a Radio Signal From a'Region of the Ionosphere Subjected to the Influ-
ence of Powerful Radio Radiation" 49
Kalitenkov, N. V., Lukosyak, Yu. P., Miroshnikov, Yu. G., Pertsovskiy, R. A.,
Siyekkinen, K. Kh., Timofeyev, Ye. Ye., Uryadov, V. P, and Uspenskiy, M. V.
~
Anisotropic Scattering of Short and Ultrashort Waves From the F Region of an
Artificially Modulated Ionosphere" 55
Royzen, A. M. "Effects Observed Auring the Vertical Sounding of an Auroral Ion-
osphere Disturbed by Power�ul SW~Radiation" 62
Shvartsburg, A. B. "Selective Heating of the Lower Ionosphere" 70
Arykov, A. A. and Mal'tsev, Yu. P. "Arti~icial Alfven Resonance in the Magneto-
sphere" ~ ~g
COPYRIGHT: Kol'skiy filial AN SSSR, 1977
i 5303 ~
' CSO: 1865/220
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ARCTIC AND ANTARCTIC RESEARCH
UDC 551.510.536
LASER SOUNDING OF THE UPPER ATMOSPHERE AT THE ANTARCTIC STATION MOLODEZHNAYA
Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 258, No 2, 1981 (manuscript re-
ceived 2 Feb 81) pp 334-335
[Article by M. F. Lagutin, Yu. ~e. M~gel', N. N. Petrov, A. A. Zarudnyy, V. N.
Kuznetsov, V. Ye. Mel'nikov, N. P. Mustetsov and N. G. Baranov, Khar~kov Institute
of Radioelectronics]
[Text] In accordance with the national program for investigating the middle atmo-
sphere, systematic experiments for laser sounding of the upper atmosphere of the
south polar region were initiated for the first.time in world practice in May 1979
at the Antarctic station Molodezhnaya (69�~) during the 24th Soviet Antarctic Exped-
ition. The purpose of this study was an investigation of dynamic processes for meas-
uring the concentrat~on and vertical distribution of the naturaY sodium layer in the
Antarctic mesosphere under polar night conditions.
The atmosphere was sounded using a lidar of original design based on a tunable laser
with a radiation line width 0.1 A. The surface antenna used was a telescope with a
dish having a diameter of 80 cm and an angle of the field of view 5�10-3 rad. The
photodetector with an interfilter bandwidth 25 A operated in a photon-counting re-
gime. The registry system is a 100-channel memory system with digital elements; the
width of the sounded range interval was 1 km; the routine display of information for
a single sounding and in an accumulation regime was on a screen of an original de-
sign; the documentation of information was on a digital m~~-netic recorder. The nor-
nialization of the sounding results was accomplished using molecular scattering sig-
nals from an altitude of 30-40 km, where aerosol scattering is not observed.
A preliminary analysis of information during the observat.'.vn period (May-October
1979) indicated that the sodium concentration in the soutt; polar region 69�S is sub-
ject to the influence of a number of dynamic processes. The observed vertical dis-
tribution decreases sharply in the sector 3-5 km due to the influence of turbulent
diffusion. The turbulence coefficient, computed on the basis of the character of the
change in concentration with altitude, corresponds to the values characteristic for
the middle latitudes. The mean altitude of the layer is 91t1 km.
The dynamics of the upper part of the layer at an altitude of about 100 km ana the
sodium concentration in a column is probably due to the influence of ineteor streams.
At individual moments there is a considerable stratification in the distribution
with a width of the layers N 1 km in which the concentration substantially exceeds
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the mean value, indicating a presenc~ of atmosplieric disturbance~ specific for
the auroral zone, for example, due to the leakage of energetic particles. A per-
iodic modulation of density is also observed in the pattern of molecular scatter-
ing signals. The method of digi.tal filtration of signals revealed waves of the
vertical gravitational waves type with a period of 12, 8, 6, 4, 3.6 and 2.8 km.
There is a change in the phase of waves with a velocity of 0.6-3 km/hour propagat~
ing both downward and upward, which indicates a different nature of the sources of
their excitation.
Thus, the results determine the fundamental possibility of carrying out e~:tensive
laser investigations of the atmosphere in Antarctica with the use of resonance
luminescence, molecular and aerosol scattering of laser radiation.
It is of special interest to carry out complex investigations by radiometeor, rocket
and other methods with simultaneous laser sounding for the purpose of studying dyn-
amic processes caused by stratomesospheric interactions with the discrimination of
phenomena of auroral origin.
COPYRIGHT: Izdatel'stvo "Nauka","Doklady Akademii nauk SSSR", 1981
5303 _ g~ _
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