JPRS ID: 9721 USSR REPORT EARTH SCIENCES

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• Content Type: REPORTS

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- JPRS L/9721
8 May 1981
=3,
F'OR OFriC1A1. USF.ONLY
- USSR Report
9
- EARTH SCIENC:ES
(FOUO 4/81)
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JPRS L/9721
8 May 1981
USSR REPORT
EARTH SCIENCES
(FOUO 4/81)
CONTENTS
UCEANOGRAPHY
~ Model of the Frequency Spectrum of Internal Idaves in the Ocean............
1
Analog Registry and Processing of Echo Signals in Mapping of the 5helf..,.
12
~ Emission of Internal Waves From Rapidly Moving Sources in an
Exponentially Stratified Fluid
20
International Expedition in the Baltic Sea on the Ship 'Gidromet......
23
Tliirty-First Voyage of the Scientific Research Ship 'Akademik Kurchatov'
(Principal Scientific Results)
28
Linear Mechanism of Formation of the Spectrum of Internal Waves in the
Ocean
35
~ Generation of Internal Waves During the Uniform Linear Motion of Local
and Nonlocal Sources
42
General Circulation of the World Ocean
52
, TERRESTRIAL GEOPHYSICS
Col.lection of Articles on Geophysical Problems
57
Interpretation of Local Geomagnetic Anomalies by the 'Contracting
Surfaces' Method......................
62
PHYSICS OF ATTi05PHERE
Low-Frequency Waves and Signals in the Earth's Magnetosphere..............
75
- a- [III - USSR - 21K S&T FOUOJ
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- OCEANOGRAPHY
UDC 551.466.8(261)
MODEL OF THE FREQUENCY SPECTRUM 0F INTERNAL WAVES IN THE OCEAN
' Moscow IZVESTIYA AKADE:II NAUK SSSR: FIZIKA ATMOSFERY I OKEANA in Russian Vol 17,
No l, Jan 81 pp 67-75
[Article by K. D. Sabinin and V. A. Shulepov, Acoustics Institute USSR Academy of
Sciences, ma.nuscript submitted 2 Oct 791
~ [Text] Abstract: A comparison of the experimental fre- ~
quency spectra measured on expeditions of the
i Acoustics Institute using the Garrett-Munk mod-
el indicates the existence of two special parts
of the spectrum in which peaks of tidal and
( short-period internal waves rise over the mono- _
tonically decreasing background part. There is =
a difference in the spectral levels of the modei
and the background of the experimental spectra
~ in the equatorial latitudes. A somewhat modified
model of the background part of the frequency
= spectrum is proposed iZ which the nondependence of _
the spectral level on geographical latitude is
assumed. Some characteristics of short-period in-
ternal waves are discussed.
According to the Garrett-Munk model, the frequency spect.rutn of the vertical dis- -
placements ~ in internal waves has the form:
- stct, Z>=cN-'(Z)f,t-~vt~-~iZ MZ~~I~ (l)
' where C= 204 m2�hr 1; N(z) is the local Vaisala frequency; fl is the iaertial
frequency [1, 2].
- A comparison of the frequency spectra of temperature fluctuations in the upper
~ thermocline which we measured in a number of regions of the world ocean with model
(1) indicated that the rate of dropoff of the spectrum with frequency in the re-
gion of the spectral continuum (background) predicted by the model agrees well
with the results of the mezsurements in [3]. Major discrepancies are observed in
two frequency regions at tidal and high (near the local Vaisala frequency) fre-
i quencies, where the experimental spectra have peaks. With respect to the absolute
spectral levels of the bdckgroundq the data from point tempetature detectors
' (photothsrmographs, etc.), which constitute the greater part of the data which we
1
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analyzed, do not make possible evaluation of the vertical 3isplacements of the
thermocline with an accuracy necessary for studying the Feographical variabilir_y
oF the spe ctral leuels [3].
Distributed temperature sensors give more reliable information for the correspond-
ing evaluations [4]o The measurements made using these sensors in the Sargasso
Sea and two r!quatorial regions of the Indian Ocean the Seychzlles and the Mal-
dives [3, 51 revealed a beautiful coincidence with the Garrett-Munk model in
the Sargassa Sea and large discrepancies in the low latitudes, where the experi-
mental spectral levels were much higher than thase predicted by the model. This
result is illustrated in Fig. 1, which shows the spectra of vertical displacements
of the thermocline in the Seychelles and Maldives polygons. The measurements were
" made using four 100-m temperature sensors, which were situated at the center of
the upper therm4cline (40-100 m in the Seychelles region and 50-150 m in the Mal--
- dives region) [5]. The solid curves represent the spectra corresponding to the
first 17-hour segments of the measurements; the dashed curves reprPSent the second
- segments of the same duration. T'ne spectra computed using formula (1) are shown in
- the form of solid sloping straight lines. It can be seen that the law of decrease
of all the spectra is identical, but the Garrett-Munk spectrun is 12 db lower than
the level of the experimental spectra. The spectrum of the first segment of the
Seychelles measurements has a peak at a frequency of 3 cycles�hr-1, rising above
= the background, for which the one can use the spectrum of the second segment, by
9 db.
S(r),M`�4 S({),M2�y m2�hour
20 f0
10 ~
~

~ 2
\
'
o,s
~
~ 0,2
qs ~
~ o,t
0, 2
Olf 0,0j
1
01OS 0,02
0, 01
o,nz n,s f s fo
cycles/hour
Fig. 1. Spectra of vertical displacements of thermocline in the Seychelles (a) and
Maldives (b) regions.
It can be postulated that the extrapolGtion of the conclusions drawn by Garrett and
- Munk on the basis of ineasurements in the extratropical latitudes is not entirely
correct for the low latitudes since it gives consi.derably understated spectral
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levels. The approximation of the experimental spectra of vertical dispiacements
is improved if model (1) is somewhat modified, assuming that the spectral 1_evels
at frequencies considerably greater than the local inertial frequency are *_iot de-
_ pendent on geographical latitude:
st (t, Z) =CtN-'(Z)f-'yf~-f~=� (2)
Here C is some constant whose value can be found, taking into account the good
corres~ondenc~ of the experimentai data and model (1) in the subtropical lati-
- tudes: Cl = Cfi = 204 m2�hour-1�0.042 cycle�hour'I = 8.5 m2�hour2 (0.042 cycZe�
hour'1 is the inertial frequency at 30� latitude). The corresponding spectra,
illustrated in Fig. 1 by sloping dashed lines, far better agree with the experi-
mental data for the Seychelles and Maldives regions.
; Since the range of free internal waves (from fi to N) broadens with a decrease in
geograptiical latitude and a nondependence of the high-frequency part of the
spectrum on the inertial frequency means that the total energy of the internal
wavu-s does not remain constant and is equal to 0.4 J�cm 2, as was postulated by
Garrett and Munk, butAchanges with latitude, In actuality, according to [2], the
- di.mensionless energy E of internal waves in a column of water of a unit section is
m ff E(a, co)dadca EA(%)B(w)dk dw, (3)
f!
0 0
where B(W 271-1 e-i1 ~-1(u12- 41i2)-1/ 2; u) znd eA), are the dimensionless current
: and 1oca1 inertial frequencies;ocand a are dimensionless wave numbers; A is nor-
malized in such a way that co
, J A(A )dA = 1.
Similarly 0
co
S B( W) dcJ = 1.
0
The replacement of the product Cfi into expression (1) by the constant value Cfi
- (30�) = 8.5 m2�hour-2 is equivalent to the introduction of the new frequency
function B' (cJ) = C2B(w)wi-1, as a r2sult of wh~ich in place of
~
~ `B(w)dw = 1 we have J B'(,w)dc,j = C2/wi,
~ J
0 0
~ that is~ theexpression for energy (3) becomes dependent on the inertial frequency:
E ('ZE J1 l.
Since at latitude 30� the Garrett-Munk modeY describes the spectrum o� internal
- waves well, it can be assumed that CZ = cai(30�), from which, converting to dimen-
sional values, we obtain the following expression for the dependence of the energy
of internal waves on geographical latitude Sp (for 5P> 0) : -
E=0,2/sin (p J� cm 2. (4)
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[Note: Using the estimate of the kinetic energy of the quasistationary circulation
of the world ocean from [h] (1018 J) and relating it to a column of water with a
- section 1 cm2 1018 J/3.61�1018 cm2N 0.3 J�cm we find that in the low .lati-
tudes this is much less than the total energy of the internal waves (with V= 5�,
for example, E= 2.2 J�ciri 2), although it must be remembered that the intensity
of quasistationary circu?ation in the equatorial latitudes is also intensified.]
�N- 34( i00
LDO
f00
30
40
.30
10 ~
f0
.3
4
.3
z
1
c
n
0,5
El
q;~ 300
+
t

1+
~
r~ foOG
~J
f Z j 4 6 B
q/v
ZIM
cycles/hour
Fig. 2. a) High-frequency ranges of spectra of rises of the thennocline in differ-
ent regions; b) prof iles of Vaisala frequency: 1) North African basin, 2) Hydro-
physical polygon, 3) Bay of Bengai, 4) Iberian basin, S) Seychelles region, 6)
Sargasso Sea
A change in the total energy of internal waves with a change in the width of the
frequency range of their existence appears extremely probable, as is the reten-
tion of the level of the high-frequency part of the spectrum of internal waves
with a decrease in fi, which resembles the nondependence of the equilibrium part
of the spectrum of wind waves on wind force and the position of the spectral max-
imum. The nature of the "equilibrium character" of the high-frequency part of the
spectrum of intercial waves remains unclear. This can indicate, for example, some
limiting, saturated state of the corresponding spectral components, as occurs in
wind waves.
Another characteristic property of the experimental spectra is that in the high-
frequency region their attenuation does not conform to the general law. Here the
energy of these spectra is increased, which ts manifested in the form of individ-
ual peaks or plateaus. Figure 2,a shows the high-frequency parts of the spectra
measured in different regions of the Atlantic and Indian Oceans and relating to
the upper tiorizons, Whare, as a rule, thesP pealcs were most clearly expressed. The
measurements were made with both distributed and point anchored temperature
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NSS 2 vv
. f
v�
+ 2
v o
wo�o v n 3
� % � 0 4
00 0
~ �p ~ � o S
o p Q oov
. v o 0 0 0 ~ 6
o+o v
v v o .0 o � K
v o 'b +o. o
0
v ~4gdc0ad v
e o � o
v ~ o eo~ .

pe Qh e. o+ +
o+
N+:b � o 
~o +
. 
f  � Q O. O " *
1$ Q ~ OA O ~ e .P . +
sensors. Figure 2,b shows the profiles of the Vaisala frequenzy N(zj for all the
considered regions. The following pattern can be seei: in the analysis of these
two figures: the fr.equencies of tlie peaks falling in the range 1.5-3 cycles�hour-1
fall closer to tte Frequencies Nli at which there is a 5tiarp broadening of the
waveguide in the th,,:!rmocline than to the local Vgisala frequencies. In actuality,
the local Vaisala frequencies for the considered measuremants were from 4 to 13
cycles�hour-1 and exceeded the frequency of the peaks by a factor of 2-6. At the
same time, all the observed N(z) curves have the following common characteristic:
a more or less narrow peak of the VAisala frequency corresponding to the waveguide
in the upper thermocline (depths from 10 to 100-200 m); with an increase in depth
there is a rather sharp replacement by layers with a slow change of N(z) and the
frequency of this sharp transition from the peak to quasiconstant values of the
Vaisala frequency Nb in all the considered cases is in the range from 1 to 2
cycles�hour-1, that is, only a little below the frequency of the spectral peaks.
15
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a
 �0 00 p 0 G
~
OLA OG ~ A
4~ ~ � n� � � ' ~ � ov
4+eo � ~v
 + o 1O

N
i+
a
+4
:
~ ;'4.
.
0 i . ~ 1 ~
rn- 1 fn fn +f f~+Z cycles/hour
Fig. 3. High-frequency peaks of spectra of internal waves. For notations see Fig.
2; K designares the Calif.ornia region.
'Che reasons for the appearance of the high-frequency peaks are not entirely~~clear.
' The cc~nsiderable differences in the frequency of the peaks from the local Vaisala
- frequency, and also the virtually single-mode structure of the short-period inter-
nal waves [7, 8],do not correspond to concepts on the formation of the high-fre-
quency peaks due to the addition of many modes near the boundary of the waveguide
- [9) and therefore such a purely kinematic explanation is scarcely justified, at
least under the conditions of the upper thermocline.
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A clirect identification af ttle observed waves with Kelvin-Helmholtz shear instab-
il:ity waves, as was done, for example, in [10], is impeded by the f3ct that short-
period internal waves are propagated relative to the medium with a considerable
phase velocity (close to the theoretical value for the first mode) [7], whereas
Kelvin-Helmholtz waves are virtually motionless [11].
It can.be postulated that the appearance of a peak near the frequency of a sharp
, broadening of the waveguide Nb is attxibutable to some quasiresonance properties
of the thermocXine examined in [12, 13] or the processes of absorption and scat-
tering of waves in ttie deep layers of the ocean (the 0. M. Phillips hypothesis,
- e-oressed at the Soviet-American Symposium on Internal Waves which was held in
Novosibirsk in 1976 [141). Finally, it can be assumed that the sporadically ap-
pearing short-period internal waves are radiated by wave-eddy turbulence of the
- upper quasihomogeneous layer of the ocean with the appearance of critical veloc-
' ity shears there [15] or arise as a result of nonlinear decay of ].onger waves.
S(f),zpaa: y degree2/hour
f0
10- I
-2
f, u/4.
cycles/liour
~ Fig. 4. Spectrum of temperature fluctuatians in hydrophysical polygon of 1970: fi
is the inertial frequency, 01 is the solar diurnal period, M2 is the lunar semidi-
iurnal period, 2M2, 3M2 are harmonics af the lunar period.
Due to Doppler distortions associated with the mean transfer of water relative to
fixed instruments, the meas ured frequency can differ substantially from the true
frequency, by whi ch we will understand the frequency of waves in a reckoning sys-
tem moving together with the medium in which they are propagating. Therefure, with-
out attempting to establish any more defiuite relationships between the measured
frequencies of the peaks and the Jaisala frequency, we note that the mean frequency
uf a11 the peaks fP = 2 cycles�hour'1 is very c?ose to the frequency o'L the sharp
broadening of the waveguide Nb = 1-2 cycles�hour'1 in all the described observation
regions, as should be observed in the case of resonance properties of the
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thermocline [12, 131 or ttie influence of wsve absorption in the spirit of the Phil.-
lips hypo thes ir, .
Now we will attempt to discriminate the high-frequency peaks, excluding the back-
ground part of the spectrum. [de will assume that the differences in the absolute
spectral levels of the high-frequency parts of the spectra which are shown ir. Fig.
2,a were caused by errors in determining the vertical temperature gradients TZ'
used for conversion of the temperature spectra ST(f; into vertical displacement
spectra S4 (f) = (TZ')-2ST(f). If the values determined by expression (2) are used
as the true values of the spectral background above which the high-frequency peaks
rise, we obtain the following formula for computing the corrected spectral ordin-
ates of the peaks themselves:
[tr= peak ] NSc� (f) -4Sc (f ) -C+f-Z� (5)
T.he cori ection factor q is dE _�:L:-ninPd at the point fp, directly precading the high-
freq uen::y peak, where the decrease of the spectrum with frequency ceases: q=.
C1f0-2SS -1(f0 In the case of ineasurements with distributed sensors, making pos-
sible a more precise evaluation nf the vertical displacements, the correction fac-
tor was not introduced and the ordinates of the peaks were determined directly as
rises above the measured background.
Figure 3 shows all the peaks discriminated in this way, which also were ma.tched in
frequency. Here also as a comparison we have plotted a peak measured by Pinkel
near California 18, Fig. 71 and denoted by the letter k. The spectrum was evalu-
ated direr_tly from the vertical displacements of the isotherms; its frequency was
3.5 cycles�hour 1. In this same figure we h.ave plotted a curve more or less satis-
factorily approximating the high-frequency peaks:
1PSc� (1) =C. (f -fo) ` exp[-3 (1-1o) 1,
(6)
where " denotes normalization to a frequency 1 cycle�hour 1, CP = 180 m2 and
Io = 0.7. In this case the frequency of the peak is equal to its mean value 2
cycles �hour 1.
i However, it is eas} to obtain the dispersion of the vertical displacements of the
thennocline caused by short-period internal waves:
SG (f) df = 0,1Cr. l N.
i.
(7)
ldith a typical value CP = 180 m2 this gives the mean square amplitude CN 4.2fN-, m.
The greatest differences from the curve are observed in the Seychelles and Sargasso
poly gons, and also near California. These three spectra, in contrast to the others,
correspond to relatively brief ineasurements (8 hours for California, 6 hours for
the Sargasso Sea and 17 hours for the Seychelles polygon). However, only the Sey-
chelles peak, evidently, would approach to the approximating curve, measuring
over a long time i.nterval, since already in the next 17-hour segment of the meas-
urements this peak is not manifested. The small height of the peaks measure6 near
the shores of California and in the Sargasso Sea probably corresponds to a lesser
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= amplitude of the short-period waves rhan in other regions because the spectrum of
the adjacent segmenr of ineasurements ir. the Sargasso Sea does uot contain a peak
and the heights of the peaks obtained by Pinkel from the longer records (see [81)
are even less significant.
Thus, the approximation of internal waves (fi) wtiich we obtained can make no pre-
- tense to broad representativeness and is not so much a univer.sal as a typical
form of this spectrum. By varying the values of the coefficient Cp and the fre-
quency position of the peak, possibly associated with the frequency of the sharp
broadening of the waveguide, it is possible to achieve a better description of
the peak in each specific case. Nevertheless, the small number of reliable meas-
urements for the time being still does not make it possible to draw any conclusions
conqirn:^.b the geographical variability of the peak. However, some ideas can be ex-
press:!d concerning the temporal variability of the peak on the basis of data on the
intermittence of short-period internal waves [16]. Assuming that the ratio of the
1oca1 time of existence of the short-period internal waves to the entire sufficient-
ly great observation time is 1:3 with mean Cn = 180 m2, we find that CP varies from
zero in the absence of trains of high-f requency internaJ, waves to 540 m2 within
such chains. This corresponds to a change in the mean square amplitude of inter-
nal waves from 0 to 3 m, with a typical value N= 6 cycles�hour 1.
One of the invariable characteristics of the f requency spectra of internal waves
in the ocean is a peak corresponding to tidal fluctuations. The amplitude of this
~ peak is subject to sharp changes in time and space, which can be attributed to
the great role of local topography of the bottom and hydrological conditions [17].
E., reliable and representative illustration of ocean internal tides is the ob:.zrva-
nons of the well-expressed narrow-band semidiurnal temperature f luctuations in
the Hydrophysical Polygon of 1970 in the Atlantic. Figure 4 shows the spectrum of
temperature fluctuations at the 200-m horizon of this polygon, computed on the
basis of all available observations for a six-month period using a photothermo-
graph with a high resolution ~'jfo = 0.0025 cycle�hour 1 and a number of degrees
of freedom of about 200. The narrow and high peak of semidiurnal f?uctuations, hav-
ing a max:imum in the period of the lunar semidiurnal tide 'C M2 = 12.4 hours, con-
tains about 13% of the total dispersion of the temperature fluctuations. The ratio
_ of ttie central frequency (fM2 = 0.08 cycle�hour'1) to the width of the peak near
its base (Ll f= 0.02 cycle�hour'1) is 4, which indicates the narrow-band charac-
ter of the tidal fluctuations. Figure 4 shnws the second and third harmonics of
the semidiurnal fluctuation and the peak near the inertial frequency, which may
be a consequence not so much of vertical, but instead, horizontal displacements
in the inertial waves in the presence of horizontal temperature gradients in the
thermocline, where they play a significant role.
In summarizing, the following conclusions can be dra*N� concerning the struc*_ure
of the frequency spectra of internal waves in the upper layer of the ocean. The
frequency spectra of the vertical disp lacements of the thermocline consist of
- a background part, decreasing monotonically with frequency, over which rise narrow
and high peaks of tidal (primarily semidiurnal) fluctuations and b roader peaks of
short-period internal waves (with f requencies f rom 1 to several cycles per ho ur).
'rhe background part is satisfactori.ly described by the Garr.ett-Munk model with
8
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some correction ('L) relating tu dependence on geographical latitude.
ML
1
5,0
4kI4
cycles/hour
Fig. 5. Generalized frequency spectrum of vertical displacements of the thermo- -
cline in internal waves for different geographical latitudes cP. The broken line
corresponds to the Garrett-Munk model for ~P= 10�; the solid curves correspond to
a modified model for ~P = 10 and 15�.
Short-period internal waves are essentially nonstationary in time and nonuniform
in space. They are manifested in the form of chains of relatively narrow-band
fluctuations intermittent with sectors of more random and less intense "background"
fluctuations. The duration of the trains is some hours; the intermittence of the
trains, that is, the ratio of the total time of their existence to the entire time
of the observations, is usually characterized by a few tens of percent. The height
of the waves within the trains can attain 10 m or more, which is close ta the typ-
ical height of the semidiurnal waves in the thermocline.
Figure 5 shows the generalized frequency spectrum of rises of thF thermocline in
internal waves, canveying all the above-mentioned characteristics of such a spec-
trum nondependence of the high-frequency part on geographical latitude, the
esistence of semidiurnal and high-frequency peaks. Here also the dashed line rep-
resents the Garrett-Munk spectrum (1) for a latitude of 10�; the solid curves rep-
resent the spectra (2) for latitudes 10 and 15�. The difference in latitudes is
reflected only in the lowest-frequency part of the spectra. The width and height
of the peaks, as well as the position of the high-f requency maximum, can vary in
dependence on the place and time of the measurements. The figure corresponds to
some typical values in the upper thermocline in the ocean. The typical values of
the mean square vertical displacements of the upper thernacline in the short-
periad, tidal and background internal waves are related as 1:2:3; the absolute
values of the corresponding amplitudes can be evaluated approximazely using the
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producL ~./NZ4; 8 and 13 m�hour-0�5. (The values for the background part cor-
_ respond Lo the suh*ropical latitudes.) `
In conclusion we emphasize that the small numbpr of observations at our disposal~ _
generally speaking, does not make it possible to draw reliable conclusions cort-
_ cerning the change in the spectrum of intermal waves with latitude. We attempted
to tie in the great difference in the energy of waves in the Sargasso Sea and
_ two equatorial regions of the Indian Ocean with the great flifference in geograph-
- jcal latitudes, although it is also impossible to preclude the inf3.uence of any
other local factors, such as bo*tom topography, currents, etc. In this connection '
the proposed modification of the Garrett-Munk model with respect to the dependence
- on inertial freqsency has a preliruinary character and requixes checking, which can
be accomplished within the framework of a further study of the geography of inter-
nal waves 'Ln the worl.d ocean. '
BIBLIOGRAPHY
1. Garrett, C., Munk, W., "Space-Time Scales of Internal Waves," GEOPHYS. FLUID
nYN., vo1 3, No 3, 1972.
2. Garr.ett, C., P':iink, W., "Space-Time Scales of Internal Waves. A Progress Re-
- port," J. GEOPHYS. RES., Vol 80, No 3, 1975,.
3. Sabinin, K. D., Serikov, A. N., Shulepov, V. A., "Frequency Spectra of Internal '
Waves," VOPROSY SUDOSTROYENIYA. AKUSTIKA (Problems in Shipbuilding. Acoustics),
No 2, 1978.
' 4. Sabinin, K. D., "Use of Distributed Temperature Sensors for Measuring Inter-
= nal Wavea," POVERKHNOSTNYYE I VNUTRENNIYE VOLNY (Surface and Internal Waves),
_ Izd. MGI AN UkrSSR, Sevzlstopol', 1978.
_ 5. Sabinin, K. D., Serikov, A. N., "Spatia:l-Temporal Parameters of Short-Period
Internal jdaves in the Indian Ocean," GIDROFIZICHESKIYE I OPTICHESKIYE ISSLED-
- OVANIYA V INDIYSKOri OKEANE (Hydrophysical and Optical Investigations in the
- Indian Ocean), Moscow, "Nauka," 1975. _
6. i~ionin, A. S., Kamenkovich, V. M., Kort, V. G., IZMENCHIVOST' MIROVOGO OKEANA
- (Variabi.lity of the World Ocean). Leningrad, Gidrometeoizdat, 1974.
7. Brekhovskikh, L. M., Konjaev, K. V., Sabinin, K. D., Serikov, A. N., "Short- _
Pariod Internal Waves in the Sea," J. GEOPHYS. RES., Vol 80, No 6, 1975. -
8. Pinkel, R., "Upper Ocean Internal Wave Observations from FLIP," J. GEOPHYS.
RES., Vol 80, No 27, 1975.
- 9. Desaubies, Y. J. F., "A Linear Theory of Internal Wave Spectra and Coherence
Near the Vaisala Frequency," J. GEOPHYS. RES., Vol 80, No 6, 1975.
10. Korotayev, G. K., P anteleyev, N. A., "Experimental Investigations of Hydro-
dynamic Instability in the Ocean," OKEANOLOGIYA (Oceanology), Vol 17, No 6,
1977.
10
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11. Terner, Dzh., 1;FFEKTY PLAWCHESTI V ZHIDKOSTYAKH (Buoyancy Effects in Fluids),
- Moscow, "Mir," 1977.
12. Sabinin, K. D., "Correlation of Short--Period Internal Waves With the Vertical
Density Gradient in the Sea," IZV. AAI SSSR, FAO (News of the USSR Academy of
Sciences: Physics of the Atmosphere and Ocean), Vol 2, No 8, 1966..
13. Kase, R. l.i., Clarke, R. A., "High-Frequency Internal Waves in the Upper Ther-
mocline Tiuring GATE," DE1:P SEA RES., Vol 25, No 9, 1978.
14. Mirapol'skiy, Yu. Z., Sabinin, K. D., "Soviet-American Symposium on Internal
Waves in the Ocean," OKEANOLOGIYA (Oceanology), Vol 17, No 2, 1977.
15. Sabinin, K. D., Serikov, A. N., "Characteristics of the Spatial Spectrum of
; Short-Period Internal Waves in the Ocean," OKEANOLOGIYA, Vol 16, No 5, 1976.

16. Sabinin, K. D., "Some Characteristics of Short-Period Internal Waves in the
- Ocean," IZV. AN SSSR, FA0, Vol 9, No 1, 1973.
17. Lyashenko, A. F., Sabinin, K. D., "Spatial Structure of Internal Tides in the
Hydrophysical Polygon of 1970 in the AClantic," IZV. AN SSSR, FAO, Vol 15,
' No 8, 1979. - COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika atmosfery i okeana",
1981
5303
CSO: 1865/85
I
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UDC 550.834.087.4:528.47.629.472
ANALOG REGISTRY AND PROCESSING OF ECHO SIGNALS IN MAPPING OF THE SHELF
Moscow GEODEZIYA I KARTOGRAFIYA in Russian No 12, Dec 80 pp 39-43
[Article by A. I. Svechnikov and Ye. V. Brener]
- [Text] The use of ar_oustic research methods for solving pr.oblems in the mapping of
- bottom depusits on the shelf is determined by the following principal factors:
high productivity of the s urvey due to the continuity of the process of acous-
tic measurements during movement of the ship;
possibi.lity of carrying out a continuous areal survey with the use of side-view
sonars;
possibility for obtaining information not only on the depth of the water body,
but also on the nature of the bottom deposits.
The active echosounding method is the basis for the acoustic research method. As a
result oF interaction between an acoustic sounding pulse and the object of the in-
vestigation an echo signal is formed which carries information both on the dis-
tance to the object, but also on its properties [3].
The registry of echo signals arising during the interaction of acoustic radiation
with bottom sediments on the paper tape of an automatic recorder creates only the
prerequisites, shows the possibility for the extraction of information from the
echo signal not only on the fact of reflection, but also on the nature of the bot-
tom deposit5, their 1ithological composition.
Bottom deposits of different litholegical type have definite differences in physico-
mechanical properties [6]. They lead to changes in the echo signal and can be mani-
fested ir_ the character of the echogram. For example, with a contrasting transition
from acoustically soft to acoustically hard sediments. Only under these conditions
can a visual interpretation of the echo grams obtained on paper tape give good re-
sults [2].
It is obvious that only a changeover from a visual, qualitative interpretation to
the measurement of the principal characteristics of an echo signal and on this ba-
sis, revelation of the regular correlation between the nature of changes in the
echo signal and specific lithological types of bottom deposits, can facilitate the
improvement of remote diagnosis methods.
, The measurement and computation of the characteristics of echo signals is possible
both in the registry process and in the interpretation process. For the processing
of data from acoustic investigations in the interpretation stage it is necessary to
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register the echo signals on a carrier which will ensure the possibility of re-
peated repraduction of the registered signals with minimum distortions with respect
to echo signals registered in the course of the survey.
We will examine the possibilities of using an analog magnetic record for the rcgis-
try and prolonged storage of echo signals.
Among the fundamenta]. premises which determine the possibility of using an analog
magnetic record are the following:
- the poss3bility of the registry of ;:coustic information at a re.al time scale;
relative simplicity in the registry cf large volumes of data;
the possibility of multiple reproduction of the magnetic records, which makes
possible the use of a whole set of processing procedures in the interpretation
process.
Tte use of two-channel analog registry, in addition, makes it possible to register
additional service information.
In the mapping of bottom deposits on the shelf by acoustic methods it is necessary
to solve two fundamental problems determine the depth of the bottom deposits
and the nature, lithological type of sediment. The first problem involves the reg-
istry o� the propagation of an echo signal from the bottom surface. It is obvious
that the reg.istry accuracy will be determined both by the geometrical measurement
errors characterizing the sounding pulse and the accuracy in registering the time
intervats on a magnetic tape, which for the most part is dependent on fluctuations
in the rate of the magnetic tape relative to the recording and reproducing heads
[1]. Fluctuations of the rate of the magnetic tape usually are evaluated using the
coefficient of rate fluctuation or the detonation coefficient [5]. For example,
with the registry on a magnetic tape of the time intervals related to depth meas-
urements in a range up to 200 m with an absolute error of 20-40 cm, the detonation
coefficient for the magnetic recorder must not be greater than 0.1%.
In the remote determination of the lithological type of bottom sediment the empha-
sis is on the depth of penetration of acoustic radiation into the sediments and
the changes arising in the echo signal durir.g their interactiono The reflected
echo signal carries information on the lithological type of sediment and therefore
the accuracy in registry of the echo signal on the magnetic tape should ensure a
reliable separation of the bottom deposits on the basis of the mersured character-
istics of the echo signal. For example, the maximum value of the echo signal enve-
lope determines such an important characteristic of bottom sediments as the reflec-
tion coefficient. According to the data in [6], the reflection coefficients for
sandy deposits fall in the range 0.41-0.37, for sandy-clayey deposits 0.32-0.21,
for clayey deposits 0.25-0.17 and for silty deposits 0.16 or less. According-
ly, for reliable separation of bottom sediments into four major lithological groups
the accuracy in the registry of the amplitude value of the echo signal must not be
less than �10%.
Thus, assurance of t11e necessary accuracy in the registry of time intervals and re-
liable reproduction of the registered amplitude values of the echosignals is pos-
sible when as the magnetic recorder for the registry of acoustic infortnation use is
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made of specialized apparatus for preci.se magnetic recording or special measuring
- magnetic recorders.
Among the different types of Sovie-L. apparatus for precise magnetic racording it ie
possible to employ the MEZ-74 two-channel magnetic recorder [4].
Among forPign analog magnetic recorders for this purpose it is possible to use a
"B & K" (Denmark) magnetic recorder type 7001, which is a two-channel recording
instrument with a frequency range 0-20 KHz, with a linearity of more than 1%, with
- distortions not greater than 1.5% and integral vibrations of about 0a1-0.15%/
It should be noted that determination of depth in the water with a sufficiently
high accura:.y is possible when using acoustic emitters with a radiation frequeucy
of about 50-150 KHz, whereas for solution of problems in the classification of
bottom sediments it is necessary to use radiation frequencies of about 1-7 KHz.
'I'ao-channel magnetic analog registry makes possible rather simple solution of the
problem of registry and storage of information received in the survey process from
high- and low-f requency emitting systemso
- Figure 1 is a block diagram of apparatus for carrying out work for the mapping of
bottom deposits with the use of a two-channel analog magnetic recorder.
Fig. 1.
KEY :
1)
2)
3)
- 4)
5)
- 6)
- 7)
8)
9)
Low-f requency emitter
Generator for excitation of acoustic systems
Express-recorder
High-frequency receiver-emitter
Control unit
Tao-channel magnetic recorder
Receiver
Measuring amplifier
Curve plot ter
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The outfit iiicludes a high-frequency receiving-emitting system with a working fre-
yuency of 140 KHz, a 1ow-frequency emitting system with a maximum of the emission
apectrum at a frequency of 4 Khz, a generator for the excitation of the acoustic
syatems, a receiver, measuring amplifier, two-channel analog magnetic recordery ex-
press information recorder, curve glotter and control unit.
b
P flu � f0Pao 104 0 1 2 3/l0�10
f, 5
_ h=-lZM
j -10 -
0 -
-pti -ZO
~
.I -i.5 M
24 D,B .1,2 h,
BpcMa, M/c Time m/sec
Fig. 2.
I
Figure 2 shows the shape of the pulse generated by the low-f requency emitting sys--
tem and a curve of the change in peak pressure developed by the emitter with depth.
with an excitation voltage of 2 KV. Measurements of peak pressure were made using a
spherical hydrophone with a response of 10 �.V/bar.
The generator for the excitation of acoustic systems produces voltage puZses with a
frequency of 1 Hz with a capacitance of the reservoir capacitors of 100 � F and a
voltage 100-10 000 V. The echo signal amplifier used was a U2-7 measuring amplifier
- with a frequency range 0-20 KHz and a nonuniformity of the frequency characteristic
less than 0.3 db with an amplification factor 10-80 db. The receiver response is
10 V/bar. The registry of the echogram is on electrothermal paper on an express-in-
formation recorder of the "Paltus-M" type. Simultaneously with registry of the echo-
gram there is registry of echo signals on magnetic tape of a two-channel magnetic re-
corder with the frequency range 31.5 Hz-16 KHz, a detonation coefficient of 0o07%
and harmonic distortions of less than 1.5%. The registry of the echo signal charac-
teristics after processing is accomplished using a two-coordinate plane table curve
plotter of the PDP-4 type. Figure 3 is a block diagram of the control circuit. The system ensures the registry
of information directly during the course of acoustic investigations, the reproduc-
tion and analog processing of survey materials.
In a regime with registry of the synchronization pulse a timer prodi+ces a synchron-
ization signal which is fed for registry in the first track; this determines the
- moment of onset of registry. In addition, the timer feeds a signal to the circuit
for blocking the receiving channel of the outfit, thereby ensuring protection of
, the reception channels from an overload when generating a sounding pulse. Then 1
msec after the synchronization pulse, a pulse is fed for triggering the generator
for the excitation of acoustic systems. A high-frequency echo signal passes through
' the blocking circuit to the shaping circuit. There it is converted into a rectangu-
lar pulse with an amplitude of about 0.5 V and a duration of 100 � sec and this is
fed to an amplifier for registry of the reading "bottom" in the first track of the
magnetic recorder.
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The low-frequency echo signals reflected from the sedimentary layers are fed to a
- measuring amplifier through a blocking circuit which forbids the passage of echo
eigr_als in definite registry limits controlled by a timer. By means of the timer
it is possible to carry out both manual setting of the regis try limits and automat-
ic tracking of the stipulated time interval of regi.stry in the limits (0.1-100
msec). Low-frequency noise is suppressed by an active high-freqiiency filter with a
cutoff steepness 40 db per octave at a cutoff frequency 1000 Hz.
- After time selection and frequency limitation the echo signals are fed to an ampli-
~ fier for registry in the second channel of the magnetic recorder.
In the reproduction of the magnetic record the control circuit ensures three regimes
of analog processing and registry of the recorded information. This includes the
construction of the vertical p=of=le of depth in the water, curves of change of the
reflection coefficient and the integral characteristic curve of the echo signal.
- In the regime for construction of the ver.tical profile from the "depth measurement"
signal there is triggering of the depth integrator, which t ransforms the time into
+ a voltage in conformity to a linear law. Using the "bottom reading" signal the cir-
cuit for shaping the control signals stops the depth integrator and transmits the
state of the integrator to the circuit for storage of the s ample, which stores the
depth value to the next cycle of ineasurements. After transmitting a par.*_icular depth
value the depth integxator is discharged.
The acoustic stiffness of the bottom sediments is determined using the circuit for
measurement of the reflection coefficient, which consists of a time automatic vo1-
une c,untral (TAVC) and a neak detector.
A low-frequency echo signal in a reproduction regime is fed through a blocki.ng cir-
cuit to the TAVC circuit and then to a peak detector, where there is determination
of the amplitude value of the envelope of an echo signal, discriminated from the
totality of the echo signals. This includes a blocking circuiC and a circuit for
the shaping o� control signals.
In the regime for computing the integral characteristic curves the echo signals
from the TAVC are fed to an integrator with an integration time constant of 100
- msec. Here the positive half-waves of the echo signal are integrated in stipulated
registry limits. Then the state of the pe3k detector or the integrator is fed to
' the circuit for storage of the sample and from there, throu gh a LF filter (LFF),
~ it is fed to the amplifier of the curve plotter "U" coordinate.
The results of processing of analog magnetic records, obtained when carrying out
acoustic investigations along profile No 26 of the experimental lithological poly-
gon, are presented in Fig. 4. The figure also shows an echo gram and geological sec-
tion constructed using drilling data. The curves of change o� the reflection coef-
ficient along the profile were normalized using the maximum value of the envelope
of the sounding pulse, whereas the integral characteristic curves were normalized
using the value of the integral determined for positive half-waves of the sounding
pulse.
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On the curve of changes of the reflection coefficient it is possible to discrimin-
ate regions with increased values of the reflection coefficient (0.4-0.45) charac-
teri.stic of sandy-gravelly deposits, for example, in the region of points 1 and 2,
_ and also regions with values of the refleetion coefficient 0.15-0o2, characteristic
for silty-clayey deposits. For fine and pulverized sands the values of the reflec-
tion coefficients fall in the range 0.25-0.3a
1
KEY;
1.
Blocking circuit
11.
Horizontal scanning circuit
2.
Shaper
12.
Express recorder amplifier
3.
Synchronization circuit
13.
TAVC circuit
4.
Synchronization generator
14.
Depth integrator
5.
Measuring amplifier
15.
Peak detector
6.
Amplifier for registry and repro-
16.
Integrator
duction in 2d track
17.
Storage c:ircuit
7.
Amplifier for regastry and repro-
18.
Low-frequency circuit
duction in lst track
19.
Stabilizing pulse from auto-
8.
High-frequency filter
matic recorder
9.
Timer
10.
Circuit for shaping control sig-
nals
It should be noted that in the sectors of the profile lying to the left and right
of point 3 there are reduced values of the reflection coefficient, evidence of the
development of silty-clayey deposits in these sectors.
Thus, the determined distribution of the coefficients makes it possible to deter-
mine the geological section more precisely and increase the reliability of deter-
mination of the lithological type of sediment.
The intebral characteristics of echo signals along the profile were obtained for
the two intervals 0-2 msec and 2-36 msec. The appearance of the first echo signals
was used as the beginning of the reading. The changes in the integral characteris-
tic curve obtained for an integration time of the order of a prolonged sounding
pulse coincide with the changes in the reflection coefficient. The integral charac-
teristics for the second interval give some idea concerning the intensity of the
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echo signals received frcm the lower-lying layers or arising as a result of mul-
tiple reflections. Fcr examplP, in places of clayey deposits there are increased
values of the integral characteristic curve; for sands of ineditun grain size their
vglues are greater in comparison with fine-grained sands due to a change in the in-
tensity of the multiple wave.
a) aM
~ . _ . ~

~p
'4C . . .
= b ) 6 0.
--5
-f0
-J5
- -20
.
4 . ~ 6:.J..._ .f7i
- =/Ipo97una N926
3 ~ _ - 6 Ti~
- - - - _ - _ ~"!y~.;;.,: rMi�.:.`?.:
4 5
Profile No 26
C) B
0,4
- 0,2
i
0
d) 2
. 0,4
0,3
L
e) a
0,2 �
0,>
a f 2 3 4 5 6 17
0 200 400 M
Fig. 4. Results of analo g processing of magnetic records: 1) gravelly-pebbly depos-
its; 2) morainal deposits; 3) sands with medium grain size; 4) varved clays; 5)
- L-ine sands, pulverized; 6) sandy loams
In conclusion it should be noted that the use of analog magnetic recording in the
solution of mapping problems on the sheif ensures registry and storage of great
volumes of acoustic information, creates prerequisites for the analog processing
- of echo signals and affords a possibiiity of obtaining data for identification of
bottom deposits not only on the basis of records of echograms, but with allowance
fo r such objective data as the impedance and integral characteristics of bottom
- sediments.
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In additian, analog magnetic recording makes possibie rather simpls changeover to
the digital processing cf acoustic information with the use of highl; productive
digital computers using devices for thz input of analog information, which to a
considerable degree will broaden the range of procedures and processing methoda
and will facilitate a changeover to the automa*ed p rocessing of the results of
- acaustic invest:igations on the shelf.
Without question, digital re&istry of the results of acoustic measurements at a
real time scale has indisputable advantages both with respect to the accuracy of
registry and convenience in the exchange of information with the digital compu�er,
but the great velocity of receipt of acoustic information (100-200 kbyte/sec) and
its considerable volumes (15-20 kbyte/sec) create definite difficulties in the de-
velopment and creation of digital magnetic recorders of hydroacoustic informa.tion.
BIBLIOGRAPHY
1. Aksenov, V. A., Viches, A. I., Gitlits, M. V., TOCHNAYA MAGNITNAYA ZAPIS' (Pre-
c:ise MagnEtic Recording), Moscow, Energiya, 19730
2. Muzylev, V. S., Svechnikov, A. I., "Use of Acoustic Sounding for Lithological
Mapping of Bottom Deposits," GEOFIZICHESKIYE ISSLEDOVANIYA PRI RESHENIZ STRUK-
TURNYKH I POISKO-RAZVEDOCHNYKH ZADACH (Geophysical Investigations for Solving
Structural and Reconnaissance-Exploration Problems), Leningrad, ZAPISKI LGI
im. G. V. PLEKHANOVA (Notes of Leningrad Geolog ical Institute imeni G. V.
Plekhanov), Vol XIX, No 2, 1976.
3. Nigul, U. K., EKHO-SIGNALY OT UPRUGIKH OB"YEKTOV (Echo Signals From Elastic
Objec*_s), Tallin, Valgus, 1976.
4. Rokotov, S. P., Titov, M. S., OBRABOTKA GIDROAKUSTICHESKOY INFORMATSII NA SUD-
OVYKH TsVM (Processing of Hydroacoustic Information on Shipboard Digital Com-
puters), Leningrad, Sudostroyeniye, 1979.
5. Travnikov, Ye. N., MEKHANIZMY APPARATURY MAGNITNOY ZAPISI (Mechanisms of Mag-
netic Recording Equipment), Kiev, Tekhnika, 1976.
6. liampton, L., AKUSTIKA MORSKII:H OSADKOV (Acoustics of Sea Sediments), Moscow,
Mir, 1977.
COPYRIGHT: Izdatel'stvo "Nedra", "Geodeziya i kartografiya", 1980
5303
CSO: 1865/108
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_ UDC 532.58
EMISSION OF INTERNAL 14AVES FROM RAPIDLY MOVING SOURCES IN AN EXPONENTIALLY 'STRATIFIED FLUID
Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 256, No 6, 1980 pp 1375-1378 -
[Article by V. A. Gorodtsov, Institute of Mechanical Problems USSR Academy of Sci-
ences, manuscript submitted 30 Jun 801
jText] Computations of the field of internal waves in a density-stratified fluid
generated by moving bodies are considerably simplified if one knows the volumetric '
or surface sources equivalent to the bodies in their hydrodynamic effect. The find-
ing of such sources is a difficult problem, in a general case soluble approximately -
or numerically. However, for great velocities of movement the integral characteris- '
tics of the wave field are slightly dependent on the specific form of the sources ;
and universal asymptotic dependences are correct. ~
Small perturbations of the field of pressure p in an exponentially stratified (case !
of a constant Vaisala-Brent frequency N) ideal incompressible fluid, caused by a
mass source m(r,t), in the Boussinesq approximafiion are described by the equation
[1,2] . .
= 3
a^
( ( + l,. p
+ h'2 - mpO.
' } !4''?'~r (1)
[\,at= ax2 3y=1 ar23_=
~
Ilere t is time, x, y, z are the horizontal and vertical coordinates, PO is the den- ~
sity of the fluid in an unperturbed state, assumed henceforth to be constant.
_ i
For a uniformly moving source m(r, t) = mpf(r - vot) the energy of emission of in- -
ternal waves per unit time is equal to the value
W = jd'rp(r, t)m(r, t). (2)
Due to the linear homogoneous correlation (1) between p and m it is possible to ~
- give W a form of exnression wYcich is quadratic relative to the amplitude of the ~
source. Using the Fourier transform for the variables r, t, from (1), (2) we ob-
2 '
L'ain _ Poino I
W J3
kJwlwll.l' w215(w-
+
Sn,
L = wa kl wZ )(k< ~ V, ) . ~
~ Here k=(kX, ky, kZ), uJ are Fourier variables conjugate to the variabl2s r=(x, I
Y. z), t, and S (x) is the Dirac delta function. ~
This formula can also be rewritten in another convenient form ~
i
20
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W= po mo f d'r J3r'1(r) l i r'wlr - r'.
(3)
w(r) = gI Jd'kdw!wII.V~ w'I-iI~:~ -kvol,N(1.1~�~~'` (4)
As a simplification we will limit ourselves to the cases of horizontal and ver-
tical moqing sources. In the second case after performing integrations for the
components of the wave vector k we obtain a representation of w(r) in the form of
a single integral of the Bessel function
:
.v '
w(r) = - j dw wcos~ ~Jo (5)
4au,) o l i o ~!n ~ N=
for which, in the case of great velocities (v0-woo) an asymptotic expansion is cor-
rect (ln y is the Euler constant) '
3. iru Nz 2 .`.'1(.,C =.+t~�)
w(r)
'o 1 1 N2 . _o 7 L,o.. 7 `V.rF-+ i 4)
In accordance with this expansion and the general formula (3), for the energy loss-
es of a vertically moving source at great velocities we will have the asymptotic
farmula
w ~ Po8;ruN2 1Jd3rf(r)I7� (6)
0
if the integral entering into it does not becomes equal to zero. Otherwise, when
there is a compensation of the "receipts" and "losses" it is necessary to keep
the next terms of the expansion. For a source for which jr dzf (r) = 0, f d3rf (r) z~
0, we obtain 2 ~4
W M. ~MOI lfd'r=. (7)
! 6AU;;
Formulas (6) and (7) become precise in the case of a point source and a vertical
doublet respectively; the integral factor in (6) is then equal to unity, but in (7)
d2/4 (d is the dipole moment of the doublet).
In the case of liorizontal movement of the source, from formula (4) it is also pos-
sible to obtain a representation of the function w(r) through siagle inte&rals of
the cylindrical functions: 2m 3Vn ' /~~T /~Vx~ 'rY711
jV 2 x'(f.) a j'1~.V 1'Y~-l'VS1 u0~K/1~ v J_
Q ~ ~ 0 /
- ~ v~~,~'~ cus(NxQ\
` o ~ Uo / ~ 70).
Here amm Iz(/ y+ z, A='14 2y2 -(1 - ;2 I z2 11/2. For large velacities of move-
ment, using expansions of cylindrical functions and the cosine, we have
"rtv= u(r) ~ j ~/P~7Iln _ .YU.r~ t3 In ~ + (9)
t -n
: I +=i Zrv�
* :V 2
~
a ~%2 -vl)In 71vx .
21
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Iiecice follows an asymptocic formula for the energy loss per unit time by a source
- moving tiorizontally with a great velocity
( 4, In ~uo + 81 J,
W 8~'O 7N ~
(10)
- ~ ~ ;13 iJ3
r' I'(r)1(r) I dlInA,
- .ai = IfJ3r1'(r)I'. = Itt(}'-Y')= 11 -t2)(2-Z')21h,
if the total source ,f d3rf(r) is different from zero. For a source of the type
_ f dxf (r) = 0, i f d3rf (r)x I 2=A2 ~ 0 the following terms of expansion (9) become
fundamental: ~o~1 _~o
K~ _ -(4; 111 + B'~ ~11)
32 nua
B, lb j J'rd'r')'(r)I (r')xx' j d;.\/1 t' In,\.
T 0
- In the case of horizontal movement the simplest example of a point source loses
sense, since here, in contrast to the case of vertical movement w(0) is not a fin-
ite value (compare (S), (8)).
As can be seen from the written formulas (6), (7), (10), (11), the coefficients of
the higher terms of the expansions W for the inverse value of velocity of the
sources are dependent on the large details of the distributions of sources. Final-
ly, we note thaC by using these formulas it is possible to give the form of the ex-
pansions for the inverse value of the dimensionless Froude number vp/Nt , using some
characteristic dirnension of the source as t .
BIBLIOGRAPHY
1. Dokuchayev, V. P., Dolina, I. S., IZV. AN SSSR: FI.Z. OKEAIVA I ATMOSFERY (News
of the USSR Academy of Sciences: Physics of the Atmosphere and Ocean), Vol 13,
No 6, 655, 1977.
2. Gorodtsov, V. A., Teodorovich, E. V., Preprint of the Institute of Mechanical
Problems, No 114, 1978.
COPYRIGHT: Izdatel`stvo "Nauka", "Doklady Akademii nauk SSSR", 1980
5303
CSO: 8144 /0872
22
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UDC 910.2(261.3)
TNTERNATIONAL EXPEDITION IN THE BALTIC SEA ON THE SHIP 'GIDROMI:T'
Moscow OKEANOLOGIYA in Russian Vol 21, No 1, Jan-Feb 81 pp 187-190
[tlrticle by A. A. Aksenov, A. I. Blazhch{.shin, K. Vypikh, V. K. Gudelis and B. Rosa)
[Text] In accordance with a plan of the Coorclination Center of the Member Countries
of the Soviet Economic Bloc Under ~~he "World Ocean" Program, during the period 1-30
June 1979 specialists aboard the "Gidromer_" (Polish People's Republic) carried out
the first international expeditior for study o� Holocene shorelines and features
on the floor of the Baltic Sea. Participating in the expedition were Polish spec-
ialists of the Institute of Meteorology and Water Management (Gdynia) and the Gdansk
University and Soviet specialists from the Institute of Oceanology USSR Academy of
Sciences, the Geography Division Academy of Sciences Lithuanian SSR and the Geology
Tnstitute Academy of Sciences Estonian SSR.
The work was carried out in the southeastern part of the Baltic Sea in two standard
sectors of the Polish-Soviet economic zone (Fig. 1). A"Hantec" s eismop rof ilo graph
(Canada) was used in detecting the evidsnces of ancient shore levels and clarifying
the structural details of the Quaternary stratum. This apparatus operated in a
"boomer" regime. This apparatus makes it possible to regis ter the fine structure
of the Quaternary stratum with a high resolution (0.5-1 m). Using the "Hantec" pro-
filograph it was also possible then to select the sites for the taking of cores of
deposits at the sites of the surmised localization of ancient shore features.
The cores were obtained using a modernized oscillating piston corer of the Kudinov
design; the length of the cores was as great as 4.5 m. During the course of the ex-
pedition a total of 725 miles af seismic profiling work was done on 34 runs arid 22
cores were obtained.
~ These investigations yielded new data on Holocene shore levels and the structure
; of the Quaternary stratum in the southeastern Baltic. As became clear from a pre-
~ liminary analysis c,f the seismic profiles and data from vibrational drillin g carr-
ied out earlier, in the Quaternarv stratum, in tlie section south of the Slupslciy
~ trench, there is a predominance not of moraines, but fluvioglacial sands, in the
~ upper part reworked by the sea. The thickness of such sands on the land attains
~ 100 m. in this respect Slupskaya Bank di.ffers sharply from other shallow-water
sectors of the Baltic Sea where the Holocene bottom profile was developed in the
main moraine of the last glaciation. Ztao major antecedent valleys, oriented ap-
= proximately parallel to the present-day shore, are situated between the coast of
the Polish People's Republic and Slupskaya I3ank. The valleys are incised in the
' fluvioglacial sands and were filled, according to data from vibrational drilling,
by different continental formations, including peat bogs. The thickness of these
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deposits attains 20-30 mT the thickness of the covering marine sands attains 3-4 M.
Along the axis of the antecedent valleys there are several ancient lake basins
filled with varved clays. On the eastern flank of Slupskaya }iank, nmdc2!r a layer _
ol' recent sands, it j.s possible to trace cut-off glaciodynamic structures which
are the roots of pressure-created terminal moraine formations. Since the develop-
ment of the shore zone in the Holocene occurred in the considered region against
a background of an excess of sandy material, ancient shore levels are morphological-
ly poorly expressed.
� .
:cl~: '
. va '
72 e7
77 74
. 75 7e !
78 14
8 13
Q' 10� ~ 17 8 ~ ~19
ae 88 a ~1 20
ee
~ . e9
._..s.
00 00
~ 4 +4
bC b~ . 6T 43 . . . � . ' .
~ se . . " ' �
47 48 4~ 6R . :l`; 'O . 'AANMHMfAa
� . . . . . ' ' l1a
Gdyitia : _ '
. . Cdanslc ' � ~ � ~ ~ ~
. � ~ . ' � '
l~~ ~ � 3 1 `50~^ 3
rig. l. Map of seismic profiling runs and position of stations. 1) seismic profiling
r.uns; 2) posi' ion of vibrationally drilled hoies; 3) isobaths, m
Ancient shore levels are traced more cleerly on the southeastern slope of Yuzhnaya
5rednyaya I;anlc. Here there are scarps at depths of 16, 20, 27, 32, 40, 61-62.5 mo -
The last of the scarps is evidently structural. A core of deposits with a length of
about 3 m was obtained on the second scarp from aboveo Clearly represented in the
core are shore formations exhibiti.ng four major transgrecsive-regressive cycles and _
several lesser ones (Fig. 2). Each such cycle begins with a basal layer of gravelly-
24
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pebbly sediment and ends with medium- and fine-grained sand. The great thickness ot
the basal layers of the major cycles suggests the superposing (intersecting) of sev-
eral shorelines as a result of isostatic uplifting.
_ In the southwestern part of Gdansk Gulf there is an alluvial cone of the Vistula
River which extends in a northwesterly direction to a depth of 30-40 m, dropping
_ away in a steep scarp with a height of 30 m("Kamerun")o According to data from
seismic profiling, the cone consists of an obliquely layered stratum of sediments
with a thickness of 20-30 m, lying in unconformity on Pleistocene clays, revealed
by the cores in the deeper-water part of the gulf.
= stat ion em 9 c.n. 6 �cc,.i~7
deptlb aAZOSnt zn. 96,Snt 39,SM
_ ' "y' .
� � V y �
w !
� .ooe.oo �
~ ..o . o.o
,
�o o�� _ _ _
M - _ ~
- - -
_ . o. . ~':~:'i':':1`�~` _ '
� ' e .o�
~~:'.Z~.. � � � � _ ~
sLi.~;'Q ' ^ � � � u
2~--
� ' ~ - - _ � .
:J�
. ~�a.
3 '
a~ ~ ~6 e .s~h o~ ~ ~i ~7 o
03 08
L -19
.
- i
Fig. 2. Ancient shore formations in cores of Late Quaternary deposits (station 9--
_ Yuzhnaya Srednyaya 1iank, station 6-- underwater cone of Vistula River, station 20
southern side of Neman antecedent valley). 1) aleuritic silt; 2) coarse silt; 3)
medium- and fine-grained sand; 4) coarse-grained sand with gravel; 5) gravel; 6)
pebbles; 7) peat; 8) obliquely layered sands; 9) transgressive boundarieso -
As a result of vibrational drilling carried out at different bathymetric levels it
was found that the obliquely layered stratum is represented by sands of different
orain size and subordinate intercalations of gravels and silts. On the surface of
25
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rerraced areas silt depressions with depths of 30-34 m-- there are silts and
a"leuriti.c silts with a thickness up to 2 m or more, whereas in other sectors there
are only sands. At readings from -30 to -40 m in the core sections it is possible
to discriminate sev--ral peat intercalations, the thickest of which (40 cm) is at
the levels -(31.7-32.1) m. In all probability, the time of formation of the peat
deposits corresponds to the regression of Antsilovoye Lake. It was found that the
reflecting boundaries on the seismograms are caused by basal horizons of gravel and
pebbles forming as a result of the superposing of several transgressive-regressive
cycles in the delta of the Vistula, growing during the course of the Holocene.
Two such major cycles are represented in the core taken at a depth of 36.5 m(Fig.
in-
2, station 6). The lower cycle evidently corresponds to late boreal times
cludes both basin and subaerial sediments. Ancient shore formations (pebbles
gravels), associated with the first littorine transgression, are represented at
the base of the upper cycle. An intercalation of silts in the middle part of the
cycle possibly corresponds to the maximum level of the Littorine Sea.
M
40
ZO
,
 ~-1 _~j
0 f--- ~
_l
100 SD 0 100 200 M
Fig. 3. Remnants of ancient eolisn acLcumulations on the northern slope of the Kur-
shskoye Plateau (copied from seismogram, profile 72). For the location of the rro-
file sea Fig. 1.
In the northeastern part of Gdansk Basin and in the adjacent shallow waters a study
_ was made of slope discontinuities and planation surfaces. The most interesting data
were obtained on profile 72 (Kurshskaya Kosa - Gotland Depression) (see Fig. 1).
Here a number of scarps and profile discontinuities can be detected. In a number
of cases the good quality of the seismograms makes possible an unambiguous identif-
ication of these levels either as ancient shore formations or as structural or lith-
ological. For example, a scarp of 66-72 m on the western slope of the Liyepaya Rise
is caused by Devonian clint, whereas the eastern boundary of the Gdansk depression
is expressed by a gentle but distinct discontinuity of the bottom profile (64-72 m),
whose formation was evidently caused by incising of a glacial tongue iato the edge
of the Polish-Lithuanian syneclise. The ancient shore scarps and the abrasional ter-
raced surfaces, traced at depths from 66 to 63 m, are possibly Lower Holocene (Yoldi-
an), since in the paleontalogically studied cores from this region preboreal layers
_ are discovered at depths below 55 m. With respect to the Iower levels (62-66, 64-68,
26
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71-74 m), they cannot be regarded as Holocene shorelines. The highest of the
traced levels have absolute readings f rom -(32-35) to -(35-39) m and evidently
_ correspond to the shoreline of Antsilovoye Lake.
Interesting formations associated with the shoreline of this basin have been dis-
covered in the northeastern part of the Kurshskoye morainal plateau. These accum-
ulative bodies (horizontally measuring from 15 to 100 m and in height 1-2 m) were
precipitated onto the structural (cuesta) scarps of the Upper Cretaceous substrate
covered with a thin layering of coarse fragmented sediments remaining from erosion
of the moraine (Fig. 3). In all probability these bodies represent the remnants
of ancient dunes.
A core with a length of 3.6 m(see Fig. 2, station 20) was obtained from the
southern edge of the Neman antecedent valley. It contains accumulative formations
associated with the incising of this valley and its subsequent filling with Holo-
-i cene sediments. The upper basal horizon of coarse and fine gravel in this core
can be compared with the ancient shore formations of the first phase of the lit-
torine transgression. The obliquely laye:ed beds of sands and silts, which lie
underneath in places, evidently represent a delta facies. The sediments of this
facies along the uneven (but not basal) boundary 1ie on fine-grained sands and
silts of marine or eolian genesis. It is difficult to identify the lower-lying
layers. On the basis of a preliminary analysis of the materials obtained on the expedi-
tion it is clear that the position of the ancient shore levels detected in the
southeastern part of the Baltic does not fully correspond to that predict;zl
theoretically as a result of isostatic adjustments. In the region of the; Sambiy-
skiy Peninsula and Kurshskaya Kosa, on the one hand, and in the region of the
southern part of Gdansk Gulf, on the other hand, the position of the Holocene
levels is virtually identical. As can be seen from Fig. 2, the traizsgressive
boundary between the littorine and Antsilovskiye sediments in the cores from
these regions is at the levels -(38.5-39.9) m. At the same time, on the southern
slope of Yuzhnaya Srednyaya Bank (station 9) this level is at the reading -21.4
- m, that is, the relative value of the isostatic rise between the mentioned read-
ings is approximately 17-18 m.
Investigations by the member countries of the Socialist Economic Bloc on the prob-
lem of Holocene ancient shorelines and coastal formations in th- Baltic Sea will
~I be continued.
COPYRIGHT: Izdatel'stvo "Nauka", "Okeanologiya", 1981
- 5303
CSO: 1865/93
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UDC 910.2(261)
THIRTY-FIRST VOYAGE OF THE SCIENTIFIC RESEARCH SHiP 'AKADEMIK KURCHATOV'
- (PRINCIPAL SCIENTIFIC RESUL'rS)
Moscow OKEANOLOGIYA in Russian Vo1 21, No 1, Jan-Feb 81 pp 183-187
[Article by V. G. Kort]
[Text] The principal objective of the expeditian during the 31st voyage of the sci-
entific research ship "Akademik Kurchatov" was a study of the mesoscale (synoptic)
spatial-temporal variability of hydrophysical fields (currents, temperature, den-
sity) in the regions of the eastern part of the subtropical zone of the Atlantic
Ocean. The investigations were planned as a development of the studies carried out
under the Soviet-American POLIMODE program. In accordance with this program, during
the period 1977-1978 Soviet scientists, working in the southwestern part of the
rlorth Atlantic, carried out investigations of the dynamics of ocean currents in a
long-term (more than one year) hydrophysical polygon; during this same time Amer-
ican expeditions carried out investigations in the central part of the North Atlan-
tic. As a result of investigations under the POLIMaDE program (USSR, United States),
Poiigon-70 (USSR) and MODE (United States), it was possible to obtain unique data
on the dynamics of inesoscale movements ta the ocean and study the dynamics of synop-
tic eddies in the western half of the subtropical zone of the North Atlantic. It
was established that the synoptic eddies, having a great kinetic energy, are prop-
agated from the eastern half of the ocean.
The implementation of investigations in the eastern part of the North Atlantic
should clarify the regions of generation of eddy systems of a synoptic scale and
- supplement our knowledge concerning the dynamics of ocean currents in this poorly
studied region.
The general region of the investigations was bounded by the meri3ians 20 and 40�W
and the latitudes 20 and 40�N. The expedition lasted 105 days. The track followed
by the expedition is shown in Fig. 1. The expedition worked from 17 April to 31
July 1980. The expedition was headed by Corresponding Member USSR Academy of Sci-
ences V. G. Kort. The scientific research ship "Akademik Kurchatov" was commanded
by captain of distant navigation K. V. Sokolov.
- The scientific program of the expedition included: investigatians of evolution of
eddies in the open ocean under the influence of the mean current, atmospherlc pro-
cesses and topogenic factors; study of the dynamic, energy and biohydrochemical
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characteristics of eddy disturbances in the ocean; study of the geographical dis-
tribution of eddies in the ocean; investigation of the spatial-temporal variabil-
ity of primary hydrooptical characteristics of the ocean in dependence on hydro-
logical conditions and other factors; a complex of studies on heat exchange be-
tween the ocean and the atmosphere; aerological observations.
During the voyage three quasisynchronous hydrological surveys were ma.de of regions
of the passage of the anticyclonic eddy discovered at the beginning of the work;
seven self-contained autonomous oceanographic buoy stations with automatic current
recorders and automa.tic water temperature recorders operated in the field of the
investigated eddy for a total of 30-35 days. Temperature sounding of the upper
layer in the ocean (0-500 m) was carried out each 20-30 miles on 30 runs with a
total extent of more than 20,000 km. Along the entire track of the vessel there
was aerological sounding (once a day), meteorological and actinometric observations.
tlbout 9,000 hydrochemical determinations were made in water samples. Measurements
were made at 85 hydrooptical stations. More than 200 biological samples were col-
lected.
The primary processing of observational data and PreZiininary pr.ocessing were carried
out during the course of the voyage. The principal results of this analysis are
given below for different aspects of the program.
1. Meteorology. With transition from spring to summer two periods can be discrimin-
ated in the formation of the Azores High: during the first pericd the weather ma.p
does not show the Azores High as a unified pressure formation and in most cases
the pressure field has two or three centers. This period is asoigned to spring. The
second period, summer, is a time when the Azores High is well formed and constitutes
a single-center pressure formation. In spring there are winds from all eight direc-
tions, whereas in summer onZy from the NE, E and SE, with a predominance of
winds of a purely eastPrly direction. The center of the Azores High experiences a
looping movement in a counterclockwise direc*ion. On the northern periphery of the
Azores High there is usually no air temperature inversion in the lower troposphere
(1-3 l:m; 1ue to the cyclonic activity in the temperate latitudes. In the southern
half of the anticyclone, facing the equator, a temperature inversion is observed
everywhere, both near tlie center of the anticyclone and on its periphery. Changing
its thickne.ss and intensity, the inversion exists daily.
The stratocumulus clouds beneath inversions have a very strong va-iability: in the
course of 15-20 minutes the clouds can scatter or cover the entire 5lk,�_ The albedo
of the ocean surface was low -15% and therefore a great part of the heat reaches
the ocean surface and is absorbed by it. The mean daily values of total solar radia-
tion are as follows: 578, 668, 512 cal.cm 2�day 1 for periods I, II, III respective-
1y. The interaction between the ocean and the atmosphere leads to the following
values 4f the heat balance components for the ocean surface by periods:
R
P
LE
E
I 9-16 May 477
2.2
85
0.145
II 6-21 Jun 555
8.6
154
0.264
III 5-15 Jul 422
8.6
144
0.247
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where it is the radiation balance; I' is turbulent heat exchange; LE is the expendi-
eure of heat on evaporation (all ttiree parameters are expressed in cal�cm 2�day-1);
E ie evaporation from the ocean, cm�day'1.
p 20 o w
60
� .0 ~ ::;i 0
~ . .
y;:.: Q i:
40 40
0
i0siiu
.
C~al-Upt ~i .
~ ]0
�
YII1u1
' � .
\
40 ~p 0 p
Fig. 1. Map of track and work on 31st voyage of scientific research vessel "Akadem-
ik Kurchatov." The solid lines represent temperature runs made with the T30-1. The
~ shaded polygon represents the region of successive hydrological surveys of the anti-
cyclonic eddy.
2. Hydrology. Three quasisynchronous liydrological surveys made it possible to trace
the evol.ution of the mesoscale anticyclonic eddy discovered early in May to the
southwest of the Azores (at a distance of 300 miles) (Fig. 2). In the first stage
(11-15 May) the anticyclonic eddy had a mean diameter for the 15� isotherm of 250-
300 km and a depth of displacement of this isotherm 75-100 m. The eddy was traced
to the horizon 1,500 m. The central region of ttte eddy had the coordinates 32�30'N,
31�30'W.
The second hydrological survey (13-21 June) indicated some weakening of the eddy.
- Its mean diameter decreased to 200 km and the displacement of the 15� isotherm at-
tained 50-60 m. The coordinates of the central regton of the eddy were 30�30'N,
33�40'W. Thus, after approximately 30 days the eddy had moved 370 km in a southwest-
erly direction with a mean velocity 10-12 km�day-1.
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36 H 32 30
I
u' 
, ~
34 u
~
~ A n
32 ~1 j ; ~ xi
ai
~oo-~ ~ ~ �

30 30
A
~ �
u
A
:
x x a x
Fig. 2. Topography of isothermic surface 15�C according to data from hydrological
surveys. The solid isolines represent depths of the 15�C isotherm in m according
to data from the first and third surveys; the dashed isolines same for the sec-
ond survey. 111,2 cyclonic eddies; A-- anticyclonic eddy whose evolution was
investigated.
At the time of the third survey (9-13 July) the core of the eddy had divided into
three parts of different intensity and the eddy itself had essentially decayed.
The entire region of individual eddy cores was pressed between two cyclonic eddies
which had followed the anticyclone from the first stage of its investigation. The
central region of the breaking-up anticyclone had the coordinates 28�00'N, 35�30'W.
During the period between the second and third surveys the eddy moved a distance
of 320 km to the southwest with a mean velocity 11 km�day-1 or 13 cm�sec'1. The
identity of the anticyclonic eddy in all three stages of the survey is confirmed
both by the general character of the eddy field in the polygons of the hydrological
surveys and by the distribution of the hydrological and hydrochemical character-
istics in the eddy region.
Prior to completion of the total processing oi the observational data and their an-
alysis it is difficult to determine the nature of the investigated anticyclonic
_ eddy. However, the uistribution and structure of the hydrological and hydrochem-
ical citaracteristics quite definitely indicate the capture and transport of dif-
ferent water masses by this eddy. It can be assumed that the investigated eddy is
31
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a mesoscale topographic eddy. The complex and sharply changing bottom relief and
the hydrological regime in the region of eclciy propagation to a certain degree
confirm this hypothesis.
Instrumental measurements of currents with three autonomous buoy stations during
- the first period of the investigations indicated the existence of rather strong
ebb-and-flow and inertial currents in the region.
'i'he orbital velocities in the investigated anticyclonic eddy on the average at-
tained: at the horizon 200 m-- 20 cm�sec-1, at 400 m-- 23-25, at 700-800 m-- 15-
20 and at 1,500 m-- 6-8 cm�sec'l.
The geographical distribution of inesoscale eddies in tiie eastern part of the North
Atlantic was investi;.;ated on 15 transoceariic temperature runs (in the layer 0-500
m) with a total length of 16,500 km. A total of 26 clearly express e d cyclonic and
anticyclonic mesoscale eddies c,rere registered. These had a mean diameter of 200-
250 km and a mean movement of the 15� isotherm of 100-150 m. Most�of the discovered
eddies were concentrated around the Azores region, especially to the southwest of
these islands. The ocean region bounded by the western shore of Africa on the east,
the Mid-Atlantic Ridge on the west and 16-28�N, was poorest in mesoscale eddies. In
mst cases the discovered mesoscale eddies correlate with sharp rises of the ocean
floor. This correlation is closest in the regions of passage of zhe Canaries, North
_ Trades and North Atlantic Currents over sea rises and ridges. It can be asserted
that the Azores Islands region is the site of the most intensive generation of ineso-
scale eddies in the eastern Atlantic.
Hydrochemistry. A very detailed study was made of the chemical structure and evolu-
tion of the anticyclonic eddy in time and space on the basis of five quasiconserva-
- tive chemical indices dissolved oxygen, silicon, phosphorus, pH and alkalinity
to depths of 1,700-2,000 m.
_ Maps of the distribution of dissolved oxygen and silicon made it possible to judge
the evolution of the anticyclonic eddy in time and space, especially at moderate
and great depths. The combination of the five chemical parameters and salinity give
basis for asserting that one and the same anticyclonic eddy was investigated in the
three surveys.
The entire investigated region is characterized by an oxygen supersaturation of the
_ entire surface layer with a thickness of 70-140 m on the average by 4% (per 0.2
ml). With respect to C02 the picture is the opposite at the ocean surface the
C02 content is less than in the near-water layer of the atmosphere and the ocean
absorbs C02 from it proportional to the wind velocity and the difference in the
partial pressures of COZ in the water and atmosphere.
Much material was collected on the content of organic carbon in the water (more than
200 determinations). It was experimentally established that fihe results of the de-
terminations of Corg with the S. V. Lyutsarev instrument must be modified by a cor-
rection of 1 mg C/liter, which is not less than 30-50% of the measured values.
32
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4. I{ydrooptics. More than 80 hydrooptical stations were occupied during the voyage.
- Tttese investigations reveuled the high purity and spatial homogeneity of the waters
in the investigated region. This applies, in particular, to the spectral absorption
values, which are close to the values adopted for pure distilled water. The spec-
- tral attenuation vaiues in the surface layer experience appreciable fluctuations,
_ but for the most part they are in the limits characteristic for very pure surface
- waters.
A great volume of information was collected on the variability of the vertical pro-
files of small-angle scattering (about 400 vertical profiles were measured) and in-
vestigations were also carried out in processing the results of remote methods for
determining the optical properties of sea water, the content of chlorophyll and
suspensions in the surface layer of the ocean.
Data from measurements made using a spectral instrument for determining irradiance
' from above, sea and sky brightness, installed at the ship's prow, agree well with
data fmm direct measurements of optical properties; the chlorophyll concentrations
computed on the basis of these data fall in the range 0.06--0.10 mg�m'3, characteris- -
tic for biologically very impoverished regions of the ocean.
5. Hydrobiology. In the course of the voyage there were 31 successful trawlings
with the trawl at different depths from 75 to 700 m and as a result of the first
- sorting of material there were 248 samples of different groups of macroplankton
organisms. A11 the samples were weighed for subsequent computations of biomass. All
the fish were determined; it was established that the collection included 117 -
species. _
Phytoplankton collections were made at 106 stations. Thirty-five full bathometric
series were run in the layer 100-0 m and 202 catches were taken with a large net in
this same layer; the total number of samples was 590. During the voyage 130 batho-
metric samples and 10 net samples were processed; 188 forms of phytoplankton were
deCermined down to the species level.
The region to the northeast of the Cape Verde Islands was the richest with respect
- to the biomass of inesopelagic fish (15 g/104 m3); this was followed by the regions
. to the south of the Azores Islands (10 g/104 m3) and the central part of the ocean
(6 g/104 m 3). The poorest4region was that between the Madeira Islands and the -
coast of Morocco 5 g/10 m3), which contradicts the general op-nion that there
! is a high biological productivity of these waters and this merits special analysis.
: We should note the presence of several equatorial species of inesopelagic fish in
_ the zone of the Canaries Current, near the Cape Verde Islands. This is appaxently
evidence of the penetration here of waters of equatorial origin. In this same re-
gion there was found to be a species of fluorescent anchovies which is new for the
region.
The phytoplankton of the investigated regions was extremely impoverished (less than
1,000 cells per liter), but the region to the east of the Madeira Islands (less
than 300 cells per liter) stands out as being especially impoverished, as it is
with respect to the biomass of abyssal fish. The general impoverishment of plank-
ton flora is attributable both to the fact that a great part of the work was carried
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out in oligotrsph~ier oftthe population of phytoplanktoniand biogenoushe
period of the
elements. gives
The finding of aeveralSr~eii n�asatheo outhern partuof thetzoneZOfemixingnof trope
basis for regarding thi 8
ical and arctic-boreal plankton f lora.
It was established as a result of use of a new method for the proces.sing of phyto-
- plankton samples reverse method) popuanlatorderion
plankton algae in the oli8otroPhic waters
magnitude greater than was assumed earlier.
COPYRIGHT: Izdstelistvo "Nauka", "Okesnologiya", 1981
5303
CSO: 1855/93
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UDC 551.466.81
LINEAR MECHANISri OF FORMATION OF THE SPECTRUM OF INTERNAL WAVES IN THE OCEAN
Moscow IZVESTIYA AKADEMII NAUK SSSR: FIZIKA ATMOSFERY I OKEANA in Russian VoI 16,
rdo 9, Sep 80 pp 992-996
[Article by V. A. Sokolov, L. M. Fomin and A. D. Yampol'skiy, Institute of Ocean-
ology USSR Academy of Sciences, manuscript submitted 12 Dec 78, resubmitted after
revision 22 Aug 79]
[Text] As indicated by measurements, movements of the internal waves type are al-
wa;s present in the ocean [1J; they can have greater or lesser energy and have
a different distribution of amplitudes of oscillation in the vertical profile,
which is probably associated with 1o ca1 conditions of stratification and the in-
tensity and spectral structure of the external effect, exciting internal waves.
[2]. High-frequency internal waves are observed most clearly in the thermocline
region, where the vertical density gradient is not small. Another peculiarity of
internal waves is their temporal intermittEnce: usually the record of fluctuation
of water temperature or the vertical velocity component at a point resembles the
record of a signal with amplitude modulation; the predominant value of the carrier
frequency of the fluctuations will be less than the local value of the Vksala
frequency [3].
On the basis of general considerations the mechanism of the formation of internal
waves can be represented in the followi.ng way. If some force (fluctuations of at-
mospheric pressure or wind velocity) acts on the water layer or at the ocean sur-
face, leading to vertical displacements of water particYes in the thermocline re-
gion, in addition to the forced osci3.lations there should be free oscillations at
the local Vaisala frequency. The latter will have the greater enc.tgy the greater
the set of spatial scales of the external effeGt which will cover the range of
wave number values satisfying the dispersion relationship for internal waves.
In the real ocean the VAisalg frequency changes with depth; there should be a
cou:bining of the fluctuations at closely spaced levels due to the continuity of
moverment of the water. In the simplest case this is similar to the addition of
sinusoidal signals at close frequencies and the appearance of an amplitude-modul-
ated oscillation with a carrier frequency (W 1+ 4)2)/2. In the case of a contin-
uous sr.ratification of water the mechanism of linear interaction of fluctuations
at dif.ferent horizons will be more complex, leading to the formation of a whole
sYe;:trum of internal waves with the properties noted above.
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'fhus, we will exantine how the spectrum of internal waves changes with depth in
dependence on stratification conditions with an identical external effect. Such
a fnrmulat3on is in some sense a special case of a more general formulation of
*_he problem by A. I. Leonov and Yu. Z. MiropoZ'skiy [2], who investigated the
mechanism of generation of internal waves in dependence on the type of external _
effect spectrum.
In our examination of the vertical and temporal structure of higY�.�-frequency in-
ternal waves in a layer of a nonrotating stratified fluid we wi11 write the fol-
lowing system of equations : aw g i aP au i aP _ o~
-p+--=0, +
at pu Pc as 8t po 8i -
_ aP aP, au aw
-+w-=o, -+-=o,
_ at a: ax aZ
(1)
where u, w are the horizontal and vertical velocity components; P is pressure;
P=/>(x, z, t); p0 = pp(z) is water density; g is the acceleration of gravity;
the z-axis is directed downward; the x-axis is directed horizontallyo It is pos-
tulated that the sought-for functions are not dependent on the second horizontal
coordinate.
The system of equations (1) is easily reduced to one equation for the stream func-
tion g: a=+~
- O=t + N' (s) 0,
a~= a= (2)
a= a1 .
v=m-+-.
az, a=3
Here NO x= -W, aVia Z= u, N2(z) = gd ln/�p/dz is the Vaisala frequency.
We will also use the boundary conditions: V = 0 at the initial moment in time (with
t= 0) and at the bottom (with z= H); at the free surface of the ocean with z= 0
EArsin(k.t--Wn4 with 0ns were reduced to the
space (x, z, t) by an inverse Fourier transform. The rap id Fourier transform was
_ used for direct and inverse transforms.
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The region for the solution is a rectangle in the space (x, z), 0< xjv/N. (16)
- For a transverse vertical direction the precise formula for pressure follows from
(11) �
"(~'s
4nv ,idasin`aN,(2Zsin~~)= (17)
�
m�m {Jo (Z) No (Z) -I, (Z) Ns (Z) Zm Nlzl
~ 16v 2v
and in the distant zone is reduced to the simple result
p(mo..~/4nlal)ein( N Izl} , Iz>v/N. ' (ls)
The pressure field oscillates vertically with a linearly decreasing amplitude; the
wavelength of the osci.llations in the distant zone is equal to 2jlN/v.
In order to determine the pressure change along the axis of movement it is conven-
ient instead of formulas (10), (11) to use formula (2), substituting into it a
simple expression of Green's function for horizontal directions (see [121)
acr (T, r) et) ~o (Nt) .
^ at I _ ( s_, 4nYz'-I-y:
In the case of a horizontally moving point source we obtain
10 1V'[
m ( a --1V'} f dT- (19)
4 n ~ at~ v yz+ (x,+at) s� .
� o
In the special case xl = 0 from this formula we obtain (14)..,At the limit y-0 dif-
ferent results follow in dependence on the sign on xl.
Ahead of the moving source (xl > 0) for the pressure distribution we obtain the for-
mula
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:
P 1 V-1=0= 4nv Gde- + 1V' )5,,, (1Vx' m�N �Nx' ,
~ v 1 4nx, S ~ v ~ (20)
in which by S~,~ ~(X) is meant the Lommel function. In the distant zone, with X; 1>
using the asymptotic form S1, 1(X)N 1+ X-z we find that the pressure field
- has an attenuating character (compare (16), (18))
Pjv-,-o=-,naN/4nx,, a,>u. (21)
- On the "wake" axis behind the point source (x1Nl.
8nv N1
From this result follows an important conclusion concerning the logarithmic diverg-
ence of energy ) osses at the limit of the point source (t--> 0). The infinity of
the energy losses is typical in problems of wave generation by amving point
so urce. In particular, as is well known [13, 15], for the Cerenkov radiation of
light waves by a moving point charge, if the dispersion of properties of the
_ medium is not taken into account, this will be observed. In the case of internal
 waves considered here they have a strong dispersion also when N= const, However,
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as can be seen from (25), the dispersion of waves during horizontal movement leads
- to the suppression of the contribution of long waves and does not change the log-
arithmic divergence of losses for a point source due to the contribution of shfl rt
waves.
4. Generation Fressure for Splierically Symmetric Source
- For an evaluation of the part of the pressure pW which is associated with the field
of waves generated by a moving source (gives a contribution to the energy loss on
wave generation) it is necessary, as is clear from the preceding text, that in the
general formulas the Gr(k,W) be replaced by 1/2D(k, W). Then from (5) we obtain
im,
pW = 16W f d'k dwuo.(N'-W)D(k, co) f (k) e{'",8 ((u-kv), (29)
wtiich for a horizontally moving spherically symmetric source after introduction of
_ spherical coo rdinates, integration for angles and replacement of the variables ul=
N cos oC , k= (N/v) ch f3 assumes the form
m,N= "/s ` N
pw = Z~Zv J da f dP� ( v ch p) C(a, P) sinZ a,
0 0 (30)
IVx, Ny Na
C(a, P) -cos ( U cos a j cos ( v cos a sh P) cos ~ v sin a ch .
� Hence, in special cases along the y-, z-axes for a point source we will have pre-
, cisely the same results as in (14), (17), that is, the generation pressure coin-
cides with the total pressure. Such a coincidence will also be observed in a more
general case. The difference between the total pressure and the generation pressure
~ can be repres ented in an integral form, similar to (29), with the replacement of
_ 1/2D(k, w ) by the even (with respect to frequency) part of the function Gr(k, uj).
~ If the source has a"fo rward-backward" syIInnetry, then with xl = 0 the integrand is
odd (with respect to frequency) and the integral disappears. Accordingly, in the
transverse plane of symmetry of the source the total pressure coincides with the
,;eneration pressure.
On the axis of movement there is no such coincidence of total pressure and genera-
tion pressure. As can b e seen from (30), for a spherically symmetric source pW(-xl,
y,z) = pW(x1,y,z),,0 and in particular,
m,N Nx, " N (31)
pW (xf, o, o) ~ 4nx, 1 v/ J d~� ` U ~h
o .
- whereas the total press ure on the axis of movement of the point source, according
to (20), is infinite wheii xl< 0 and assumes �inite values when xl> 0.
We note in conclusion that the change from a point source to a combination of
point sources in ttie fo rm of a dipole does not do away with divergences and at
- the limit of a point so urce intensifies them. Moreover, i.he generation energy
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remains infinite and for a source distributed along the axis of movement f(r) _
'v (x) S (Y) b (z) ,
� � " " dk
W= m0 f dWl'N'-cAv((61u) f � (32)
2n= ykYv'-Nt .
- � � 0 x/.
In this case, as for a point source, there is a logarithmic divergence of the sec-
ond integral in the case of large wave numbers (for short waves).
BIBLIOGRAPHY
l. Mei, C. C., Wu, T. Y., "Gravity Waves Due to a Point Disturbance in a P1ane
Free Surface Flow of Stratified Fluids," PHYS. FLUIDS, 7, No 8, pp 1117-1133,
1964.
2. Wu, T. Y., "Three-Dimensional Internal Gravity Waves in a Stratified Free-
Surface Flow," ZANM, 45, T194-T195, 1965.
3. Wu, T. Y., Mei, C. C., "Two-Dimensional Gravity Waves in a Stratified Ocean,"
PHYS. FLTJIDS, 10, No 3, pp 482-486, 1967.
_ 4. Miles, J. W., "Internal Waves Generated by a Horizontal?y Moving Source,"
GEOPHYS. FLUID DYNAMICS, 2, No l, pp 63-87, 1971.
5. Sturova, I. V., "Plane Problem of Wave Movements Arising in a Stratified Fluid
During Flow Around a Submerged Dipole," DINAMIKA SPLOSHNOY SRED'i (Dynamics of a
= Continuous Medium), Izd. IG SO AN SSSR, No 15, pp 157-169, 1973.
6. Sturova, I. V., "Wave Movements Arising in a Stratified Fluid During Flow
Around a Submerged Body," PMTF (Applied Mathematics and Technical Physics), No
6, pp 80-91, 1974.
7. Nikishov, V. I., Stetsenko, A. G., "Plane Internal Waves Aris ing in a Stratif-
ied Fluid During Flow Around a Source-Loss System," GIDROMEKI',ANIKA (Hydromech-
anics), Kiev, "Naukova Dumka," No 36, pp 66-70, 1977.
80 Sturova, I. V., "Internal Waves Generated by Local Disturbances in a Stratif-
ied Fluid," DINAMICHESKIYE ZADACHI MEKHANIKI SPLOSHNYKH SPYD (Dynamic Problems
of the Mechanics of Continuous Media), Izd. IG SO AN SSSR, No 35, pp 122-140,
1978.
9. Sturova, I. V., "Internal Waves Generated by Local Disturbances in a Linearly
' Stratified Fluid of Finite Depth," PMTF, No 3, pp 61-69, 1978.
10. Sturova, I. V., "Internal Waves Generated by Local Disturbances in a nao-Layer
Stratified Fluid," IZV. AN SSSR, FAO (News of the USSR Academy of Sciences:
Physics of the Atmosphere and Ocean), 14, No 11, pp 1222-1228, 1978.
50
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11. Sturova, I. V., Sukharev, V. A., "Plane Problem of jJave Movements Arising in -
a Continuously Stratified Fluid During Flow Around a Submerged Body," IZV.
AICAD. NAUK SSSR, MZhG (News of the USSR Academy of Sciences: Piechanics of F].u-
ids and Gases), Pdo 4, pp 148-152, 1978.
12. Gorodtsov, V. A., Teodorovich, E. V., LINEYNYYE VNUTRENNIYE VOLNY V EKSPONEN-
TSIAL'NO STRATIFITSIROVANNOY IDEAL'NOY NESZHIMAYEMOY ZHIDKOSTI (Linear Inter-
nal Waves in an Exponentially Stratified Ideal Incompressible Fluid), Pre-
print No 114, Institute of Mechanical Problems USSR Acadeiuy of Sciences, 1978.
13. Ivanenko, D. D., Sokolov, A. A., KLASSICHESKAYA TEORIYA POLYA (Classical Field
Theory), Gostekhteoretizdat, 1951.
, 14. Dokuchayev, V. P., Dolina, I. S., "Generation of Internal Waves by Sources in
an Exponentially Stratified Fludd," IZV. AN SSSR, FAO (News of the USSR Acad-
; emy of Sciences: Physics of the Atmosphere and Ocean), 13, No 6, pp 655-663,
1977.
! 15. Tamm, I. Ye., SOBRANIYE NAUQiNYKH TRUDOV (Collection of Scientific Works), Vol
i 1, Moscow, "Nauka," 1975.
~
i COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika atmosfery i nkeana",
1980
~
~ 5303 ~
; CSO: 1865/63
~
i
~
-i
'
~
~ -
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_ UDC 551.46
GENERAL CIRC'ULATION OF THE WORLD OCEAN
Leningrad OBSHCF.AYA TSIRKULYATSIYA MIROVOGO OKEANA in Russian 1980 (signed to press ;
_ 17 Jan 80) pp 2-5, 252-253
[Annotation, fareword and table of contents from book "General Circulation of the ~
World Ocean", by V. A. Burkov, Gidrometeoizdat, 1800 copies, 254 pages ]
[Text] Annotation. The book gives a description of general circulatio*.z in the
world ocean. The author presents the physiographic canditions for development of
genera]. circulatio:l of the world ocean, defines it, examines the mechanical and
thermohaline factors exciting general circulation, gives a brief overview of water
masses and their tracers, describes the field of masses in the world ocean, and
sets forth the method for formulating schemes of rnovement from the surface to the
bottom of the ocean. The materials used in the work are characterized.
Macroscale schemes of general horizontal circulation of surface, subsurface inter-
mediate, intermediate, deep and bottom waters are analyzed and the vertical struc-
ture of currents and elements of vertical movements are considered.
- The book characterizes individual links in the general circulation ocean cur-
rents of different types : equatorial and tropical, monsoonal, eas terly and' west-
erly boundary currents in subtropical anticyclonic circulationsa
The book is intended for scientific workers, graduate students and undergraduateso
~ Foreword. This book, "General Circulation of the World Ocean," is an attempt at
- formulztion and physical interpretation of the rhree-dimensional macroscale field
of movement in the world ocean.
Systematic descriptions of general circulat3.on of the world ocean in nionographs and
textbooks on oceanology [24, 44, 75, 106, 114, 143] have been incomplete with re-
spect to coverage of regions of the world ocean and to a considerable degree are
outdated. Since the time of writing of these mnographs the number of observa-
tions of the main oceanological characteristics (temperature, salinity, oxygen con-
- tent, currents) has increased by several times, although their distribution over
the surface of the world ocean and in time sti11 remains nonuniformo The over-
whelming number of observations are concentrated in the northern parts of the At-
lantic and Pacifj.c Oceans and within these sectors *he observations are concen-
trated in the coastal regions. The central parts of the oceans and the antarctic
waters are still poor in obseriations.
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In order to form a picture of general circuiation of the world oceqn it is pos-
- sible to use direct or indirect methods. The direct methods ir,' ae a generaliz-
ation of instrumental measurements of currents. However, thera are still. so few
such measurements t.hat in the coraing decades there will b. no possibility of re-
creating the pattern of movement of ocean waters on their basis: An exception in
this respect is the surface layer of the world ocean, the scheme of currents for
which can be constructed using data on drift and deflection of ships. Such maps
have also been constructed before [132] and are included in the oceanographic
manuals mentioned above. A map of surface currents based on data on the drift and
- deflection of vessels is also given in our monograph on the basis of the results
of modern computations made by Steed [136]. The ciLaracterizations of movements in
the water layer are given nn the basis of indirect methods, that is, on the basis
of the results of one of the diagnosCic models developed by the author [14, 151,
not using direct measurements of currents, but data on the wind and density of
ocean water related to the components of current velociiies by hydrodynamic equa-
tions.
But for the time being even indirect data are limited. And they are by no means
adequate for constructing even one synoptic model of the world ocean, as is done
, for the atmosphere. At present indirect data can be used only in constructing the
stationary circulation of the world ocean, generalizing all the observations
_ made in t;he history of oceanology in the form of the mean long-term annual values
' of the characteristics, related to unit areas, which are selected in dependence
' on the scales of movement. Exactly this is done in this monograph. For circula-
tion schemes at the scale of the entire ocean we used the mean long-term annual
values of the characteristics averaged for 5� spherical trapezia. For individual
regions of the world ocean it was possible to employ the mean long-term seasonal
values, related to 1� "squares."
' i-n the critical evaluation of the results, in this monograph extensive use is made
' of a comparison of the constructad circulation schemes and the distribution of
, oceanological characteristics, primarily temperature, salinity and the oxygen con-
tent, using as a point of departure the concept of a close relationship between
the fields of these characteristics and the field of movement in a baroclinic
ocean.
The first five introductory chapters give the principal parameters of the world
ocean as a physiographic component of the planet, give some idea concerning station-
ary and nonstationary forms of movement of ocean waters an3 a detailed description
_ of the external factors exciting circulation, their relative contribution to the
resultant circulation, as well as an exposition of the method for computing gen-
eral. circulation and a brief description of the initial datao
Ttiree large chapters give a systematic description, c:.itical analysis and the basic
results for the three-dimen5ional field of movement ln the world ocean: horizontal
circulation of surface, subsurface intermediate, intermediate, deep and bottom
; waters, elements of vertical movements and the vertical structure.
As a result of rather rough averaging the pattern of general circulation of the
world ocean obtained by computations naturally has a schematic character, although
~ it satisfiss the perception of its principal characteristics. However, in order to
53
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collate it with the real pattern the book is supplemented by a large special
chapter entitled "Currents in the World Ocean." In this chapter, insofar as pos-
sible, a description is given of indivldual currents on the basis of unaveraged
observations of one or more expeditions or on the basis of inean data, but matched
- with the spatial scale of a particular currento This chapter also gives instru-
mental observations in order to characterize, unfortunately, those few currents
for which they have been made. Thus, the reader wi11 find material on how to pro-
ceed from the generalized pattern of general circulation to really existing flows
- in the world ocean.
In conclusion, the principal conclusions from the work are presented.
This book continues and generalizes studies made earlier devoted to the general
circulation of individual oceans: Atlantic [8], Indian [17, 661, Pacific [13, 141
and even the world ocean [20]. The latter study of the macroscale characteristics
of circulation of waters in the world ocean was presented in a preliminary and
concise form. Thus, our monograph reflects the sequence of the entire direction -
of investigation and generalization of general circulation in the world ocean.
Due to the limited volume of the book, except for the chapter "Currents in the
World Ocean," preference is given to original text and original illustrations. Re-
views of the literature on the development of concepts concerning general circul-
ation of the world ocean have been omitted. The first five introductory chapters -
- deal only with those problems which are necessary for exposition of the main ~
theme. In the remaining chapters, devoted to general circvlation, comparisons of
the newly obtained results with those obtained earlier are aZsr limiteda The auth-
or hopes that the book will come into the hands of an adequately t;..kined reader
capable of comparing the information obtained earlier with the results in this book
and will evaluate them successfully. Along the lines of emphasis on the exposition
of new results the bibliography is kept relatively modesto However, it contains all
the main sources relating to general circulation, although it makes no pretense to
completeness with respect to ocean physics and dynamics. On the other hand, the
chapter Currents in the World Ocean" makes extensive use of the sources in the -
literature, drawing upon fresh and reliable observational data,
This work on general circulation of the world ocean did not begin from scratcho In
this monograph the author uses accumulated knowledge both on the actual pattern of
circulation and on its physical natureo A generalization of this information is ac-
complished in part in the first five chapters of the monograph, which also contain
some original results obtained by the 3uttior. Accordingly, the conclusion of the
book must be regarded as a brief summary of our ideas concerning general circula-
tion of the world ocean as interpreted by the authoro
1fie descriptiun of general circulation is limited to three large oceans: Atlantic, ~
Indian and Pacific, although, to be sure, their antarctic sectors are includedo ~
The Arctic Ocean is not included in the book because the author has not investigated -
it himself and did not wish to present a compilatien. However, the Arctic Ocean can
be regarded as a mediterranean sea, not formally, but from an oceanological point ~
of view. And there are four such large meaiterranean seas in the world ocean: the ~
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Mcdlterranean Sea, Caribbean Sea, seas of the Sunda Archipelago and the Arctic
Ucean. Tn the author's opinion, physical oceanography of these mediterranean
seas can be the subject of a separate book.
To be sure, without the assistance of the staff of the Institute of Uceanology
imeni P. P. Shirshov USSR Academy of Sciences the author would not have been able
- to handle such an enormous volume of material as was necessary for describing and
analyzing the general circulation of the world ocean. The collection, systematic
arrangement and processing of data on Cemperature, salinity and currents is b ut a
small part of the work, in which many specialists participated. The author ex-
presses deep appreciation to them. Among them, the author especially wishes to
not-7 the direct and constant assistance of V. S. Fedorov, A. I. Kharlamov, I. G.
Usychenko and Ye. G. Morozov, who assisted with computations on an electronic com-
puter.
The author is also deeply appreciative to Corresponding Member USSR Academy of Sci-
ences A. S. Monin and Corresponding Member USSR Academy of Sciences V. G. Kort for
valuable comments on the work.
CONTENTS
l; I'oreword 3
i
; Chapter 1. World Ocean in the Geographic Envelope of the Planet 6
' 1.1. World Ocean as the Water Envelope of the Planet......................... 6
-I 1.2. Interaction Between the Zdorld Ocean and the Atmosphere 8
; Chapter 2. Spatial-Temporal Structure of Movement of Ocean Waters 10
! 2.1. Micro-, Maso- and Macroscale Spatial and Temporal Elements of Movement
of Ocean Waters 10
2.2. Determination of General Circulation of jJorld Ocean 12
2.3. Choice of Spatial and Temporal Scales for Describing General Circulation
of the World Ocean and Its Individual Links Using Observational Data.. 15
Chapter 3. Mechanical Factors in Circulation of Waters 17
3.1. Wind Stress at Surface of World Ocean 17
- 3.2. Models of jJind Circulations 21
Chapter 4. Thermohaline Factors in Water Circulation 34
4.1,, Distributian of Receipt and Release of Heat, Precipitation and Evapora-
tion at the Surface of the World Ocean................................ 34
4.2. Three-Dimensional Thermohaline and Density Stratification of the World
Ocean 39
4.3. Models of 'fhermohaline Circulations in the World Ocean 50
(:hapter 5. Field of riasses in the Wor1d Ocean 53
5.1. Interaction Between riechanical and Thermohaline Factors in Formation of
the Resultant Field of Masses in the World Ocean 53
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5.2. Geostrophic Model Dynamic Piethod as the Simplest Model for Reproduc-
ing the Pattern o� Ilorizontal Circulation in the Worlri Ocean at Iso-
baric Surfaces 56
5.3. Potential Energy of the World Ocean 59
Chapter 6. Method and Initial Data for Constructing Models of General Circula-
- tion of the World Ocean 62
6.1. Model of Transport of Water in an Inhomogeneous Ocean................... 62
6.2. Initial Data and Formulas for Computing General Circulation of the
World Ocean 67
6.3. Use of Tracers in the Analysis and Evaluation of Formulated Circulation
Schemes 73
Chapter 7. Circulation of Surface, Subsurface Intemiediate and Intermediate
Waters of the World Ocean 75
7.1. Circulation of Surface Waters.............o....������������������������� 75
7.2. Circulation of Subsurface Intermediate Waters 86
- 7.3. Circulation of Intermediate Waters 93
7.4. Circulation of Upper Sphere of World Ocean 106
Chapter 8. Circulation of Deep and Bottom Waters of the World Ocean........... 110
8.1. Circulation of Deep Waters ......a............. 110
8.2. Circulation of Bottom ~aaters 125
8.3. Circulation of Lower Sphere of World Ocean 134
8.4. Interaction Between the Upper and Lower Circulation Spheres and Role of
Vertical Movements................................................... 137
Chapter 9. Vertical Structure of Currents in the World Ocean 146
9.1. Structure of Zonal Currents............................................ 146
9.2. Structure of Meridional Currents 150
9.3. Meridional Circulation in Oceans 155
Chapter 10. Currents in the World Ocean 165
10.1. Currents in the Tropical Zone of the World Ocean...................... 166
a) Tropical and Equatorial Currents of the Pacific Ocean.............. 167
b) Tropical and Equatorial Currents of the Atlantic Ocean 192
10.2. Monsoonal Currents of the Indian Ocean................................ 201
- 10.3. Easterly Boundary Currents 217
10.4. Westerly Boundary Currents................. 226
(:onclusion.... . . . . . . 239
Bibliography . 244
COPYRIGHT: Gidrometeoizdat, 1980
5303
- CSO: 1865/103
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TERRESTRIAL GEOPHYSICS
COLLECTION OF ARTICLES ON GEOPHYSICAL PROBLEMS
Leningrad UCHENYYE ZAPISKI LENINGRADSKOGO ORDENA LENINA I ORDENA TRUDOVOGO KRAS-
NOGO ZNAMENI GOSUDARSTVENNOGO UIVIVERSITETA IMENI A. A. ZHDANOVA: VOPROSY GEOFIZIKI
~ in Russian No 404, Issue 28, 1980 (signed to press 6 Feb 80) pp 2, 338-247
~ [Annotation and selected abstrac.ts from collection "Problems in Geophysics", edited
by G. V. IKolochnov, professor, and A. S.. Semenov, professor, Izdatel'stvo Lenin-
I gradskogo universiteta, 714 copies, 248 pages] -
-I
i [Text] Annotation. The collection contains articles written by specialists of the
i Department of Physics of the Ear.*.h of the Physics Faculty of Leningrad State Uni-
versity and specialists of the geophysical departments and laboratories of the
Geology Faculty of Leningrad State University. The pliblished articles give a
thorough review of the status of the problem of tidal phenomena a.-id it is shown
that the latter can be used in obtaining information on the internal structure of
; the earth; a physical mechanism of change in the magnetic states of rocks is pro-
posed; a number of problems involved in the analysis of models of the earth's con-
; ductivity, solution of the direct and inverse problems in magnetotelluric sounding -
~ in inhomogeneous media, solution of the inverse problem in magnetometry, use.of
i variable electromagnetic fields in study of the sea, and also detection of the
noise arising during the registry of long--period oscillations of the earth are
, considered.
- ~ The collection is intended for scientific specialists, graduate students, students
~ in advanced courses concerned with study of physics of 14--he earth and engineers
i specializing in geophysics.
SELECTED ABSTRACTS
UDC 660.38.550.8
MEASUREMENTS OF MAGNETIC SUSCEPTIBILITY OF ROCKS UNDER NATURAL CONDITIONS
[Abstract of article by Kudryavtsev, Yu. I., and Miklyayev, Yu. V.)
[Text] The authors examine examples of application of the method for measuring ma.g- _
netic susceptibility of rocks under natural bedding conditions. The results of
profile measurements of magnetic susceptibility are used in increasing the effect-
iveness of interpretation of magnetic field curves. On the basis of the distribu- _
tion of magnetic susceptibility values at the surface of an intrusive formation it
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is possible to discriminate individual mineral facies and zones of mylonitization,
evaluate the degree and depth of near-contact changes, and establish the charac-
teristics of the internal structure of intrusive bodies. 4 figures, 8 references.
UDC 550.832.8.08
VALIDATION OF APPARATUS FOR INDUCTION MEASUREMENTS OF MAGNETIC SUSCEPTIBILITY AND
CONDUCTIVITY OF A MEDIUM
[Abstz'act of article by Kudryavtsev, Yu. I.]
[Text] The article gives a blocli, diagram of an instrument for measuring magnetic
susceptibility and conductivity of a medium and a circuit diagram of the probe.
In the instrument provision is made for stabilizing the amplitude of the magnetic
moment of the generating coil, the reference and compensating voltages, regardless
of the effect of ttie investigated medium. In addition, a constant phase ratio is
raaintained between the magnetic moment and the reference and compensating voltages,
as well as the measured emf. As a result, there is an increase in accuracy, phase
selectivity and response of the measurements. 2 figures, 9 references.
UDC 550.835.002.56
ROENTGENORADIOMETRIC SENSORS WITH TWO-STAGE EXCITATION FOR THE TESTING OF ORES IN
MINE WORKINGS AND IN BOREHOLES
jAbstract of article by Meyer, V. A., Nakhabtsev, V. S., Ivanyukovich, G. A., and
ICrotkov, M. I. ]
[Text] The autho�rs describe the design and characteristics of sensors for the test-
ing of ores developed at Leningrad State University. In the sensors for the excita-
tion of fluorescence of the elements to be determined use is made of the secondarv
emiasion of the target, which, in turn, is excited by a radioisotope source. Pro-
vision is also ;nade for the use of the primary emission of the source for irra~~a-
tion of the investigated medium. The use of two-stage excitation makes it possible
_ to enhance the response and selectivity of roentgenoradiometric analysis. 4 figures,
5 re fe rences .
UDC 550.831(075.8)
DETERMINATION OF THE, PARAMETERS OF AN OBLIQUE THIN'STRATUM FROM GRAVITY ANOMALIES
jAbstract of article by Mironov, V. S.]
[Text] A geometrical method is proposed for determining the parameters of an ob-
lique material band from its gravity anomalies. This method can also be used in
dPtermiiiing the parameters of strata with an infinite extent in depth on the basis
of anomalies of the gravity gradient.
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UDC 550.834.24
Y,OW-VELOCITY INTEFcFERENCE WAVES IN SEISMIC PROSPECTING. I. SURFACE WAVES
- [Abstract of article by Rudakov, A. G.]
[Text] The article gives an analysis of the problem and methods far studying low-
- velocity interference waves in different stages of 3evelopment of seismic pros-
pecting by the reflected waves method. The author gives a substantiation of the
need for a new approach to study of waves of this class in connection with a uni-
versal changeover to modif ications of multiple overlappings in the cor-mon deep
_ Point method. In the first (pub lished) part of the article tlie emphasis is on sur-
, face waves: their characteristic properties (range of apparent velocities, appar-
; ent periods, positions in the plane of the travel-time curve), the patterns of cor-
re?ation of these properties with the properties of high-frequency registry, and
also existing concepts concerning the nature of waves of this type. 4 figures, 45
j references.
UDC 550.312;528.27;528.56
TIDAL PHENOMENA
[Abstract of article by Lin'kov, Ye. M.]
! [Text] An investigation of tida.l phenomena, such as earth and ocean tides, tidal
i changes of the rate of the earth's rotation, tidal friction, etc., is a vigorous-
ly developing field of terrestrial physics. The article reflects virtually all as-
~ pects of this interesting and important problem. Russian and Soviet geophysicists
; have made a major contribution to soYution of this problem. The article gives a
- description of tidal phenomena and farmulates the basic principles in the statis-
tical theory of tides. The Laplace method i3 examined and the characteristics of
~ the principal tidal waves and the dependence of their theoretical amplitudes on
latitude are considered. The bas ic principles of the Love theory are given, illus-
trating the possib:ility of determining Love numbers from tidal phenomena. Experi-
mental results of determination of Love numbers are also given. A-lso considered
is. a method for taking into account the influence of ocean tides on earth tides.
_ The influence of inertial accele rations on gravimeter readings is also evaluated.
The nature of tidal friction and its role in secular slowing of the earth's rota-
tion is described. The influence of earth and ocean tides on secular slowing of
the earth's rotation is conside red. In conclusion, the resuZts of investigations
of tidal phenomena are summarize d. 12 A'igures, 3 tables, 40 references.
UDC 550.830:519
- INFORMATION CONTENT OF COMPONENTS OF THE MAIN COMBINATIONS OF SECONDARY CRITERIA IN
DISCRIMINANT PROBLCMS IN MAGNETOMETRY
- [Abstract of article by Zhezhel', N. F., and Zhezhel', Yu. N.]
[T.ext] The authors disc.uss metho ds for evaluating the information content of sec-
ondary criteria in interpretation probletas related to determination of the qualit-
ative state of the investigated object or medium. Tt is shown that for practical.
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purpuses tnstead ot evaluations of the information content of criteria considered
separately it is desirable to use evaluations of the probability of the occurrence
of the analyzed criteria in different effective groups, averaged for a series of
problems. 4 figures, 2 tables, 3 references.
UDC 550.837.6
DETERMIIIATION OF THE DEPTH OF A CONDUCTING LAYER FROM THE RESULTS OF
MAGNETOTELLURIC SOUNDING IN MEDIA C(3NTAINING SURFACE INHOMOGENEITIES
[Abstract of article by Porokhova, L. N., and Pogareva, 0. I.]
[Text] The paper gives the resulrs of interpretation of two model sections com-
plicated by inhomogeneities of the bench type and the graben-bench-horst type
with a hori2ontally polarized field using statistical interpretation algorithms de-
veloped for horizontally layered media. It is shok�n that the joint interpretation
of the complex of curves on the profile, camplicated by horizontal inhomogeneities
causiug the "S effect," makes possible a quite precise determination of the para-
meters of the conducting layer without recourse to complex solutions of the di-
rect problem. 4 figures, 1 table, 3 references.
UDC 550.837.61
ELECTROMAGNETIC FIELD OF THE VERTICAL HARMONIC MAGNETIC DIPOLE AT THE SEA-
BOTTOM DISCONTINUITY
[Abstract of article by Molochnov, G. V., Katkov, V. N., and Radionov, M. V.]
[Text] In this article numerical data are used in an analysis of the behavior of
the electromagnetic field of a harmonic magnetic dipole situated at the sea-bottom
discontinuity. Cases of different conductivity of the sea floor are examined.
1 figure, 1 reference.
UDC 550.34
SPECTRAL COMI'OSITION AND NOISE LEVEL ON RECORDS OF A LONG-PERIOD SEISMOMETER
[Abstract of article by Petrova, L. N., and Lepeshkin, F. G.]
[Text] 'fhe mean spectra of seismic noise and microvariations of atmospheric pres-
sure in the range 10-60 minutes are given. The authors give comparisons of the
spectra of seismic oscillations and magnetic field variations, as well as the
levels of spectral amplitudes of noise and long-period seismic oscillations (use-
- ful signal). The conclusion is drawn that in the absence of a useful signal the
seismic record to a considerable degiee is a result of changes in atmosnlieric pres-
sure on the instrument and soil. No influence of magnetic field variations on
- seismometer readings was discovered. Noise data make it possible to correct the
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spectra of long-period osci:llations, and accordingly, determine their parameters
more precisely. 2 figures, 4 references.
- iJnC 550.837.6
BEHAVIQR OF MAGNETOTELLURIC SOUNDING CURVES IN COASTAL REGIONS ON THE BASIS OF
THE RESULTS OF MODELING
[Abstract of article by Dobrovol'skaya, M. A., Kovttm, A. A., and Kokvina, Ye. D.]
[Text] Magnetotelluric sounding curves near several types of characteristic sea -
~ sections (in a model) are examined. The behavior of these curves is analyzed as
-a function of ttie distance of the sounding point to the boundary of the inhomo-
~ geneity and the depth of the sounding point. As a result of the analysis some
i recommendations are given oai carrying out magnetotelluric soundings in the coastal
~ regions. 3 figures, 5 references.
UDC 550.837
USE OF THE SLOPE OF THE MAJOR AXIS OF THE MAGNETIC FIELD POLARIZATION ELLIPSE IN
FREQUENCY SOUNDING
[Abstract of article by Molo chnov, G. V., Radionov, M. V., Seku, Konate]
[Text] The author examines the gossibilities of carrying out frequency soundings
with measurement of the slope of the major axis of the polarization ellipse of a
vertical magnetic dipole to Che horizon 0( . On the basis of an analqsis of the
computations a study was made of the behavior of the angie over two-lffer media
with poorly and well-conducting bases. 1'he effective characteristic ~0/p 1(h/hl)
is introduced. The dependence of effective resistivity on the effective depth of
penetration of the electroma gnetic field is given; it is simple and conve.nient to
use in interpretation. An investigation of the behavior of the /P/ )01(h/hl) curves
made i.t possible to develop isoparametric frequency-distance soundings in the zone
of inean parameters. 4 figures, 11 references. 4
BAROVARIATIONS AS NOISE IN LONG-PERIOD SEISMIC OBSERVATIONS
[Abstract of article by Kozhevnikova, E. G., Orlov, Yeo G., and Lin'kov, Ye. M.]
[Text] The article describes the design of a microbarograph with a magnetron con-
verter, methods for calculating the characteristics of the pressure eZements and
calibration of a concentrated load. The spectra of barovariations in the range of =
periods 200-5000 sec are given. 2 figures, 7 references.
COPYRIGHT: Izd3tel'stvo Leningradskogo universiteta, 1980
5303
CSO: 1865/104
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UDC 550.837
INTERPRETATION OF LOCAL GEOMAGNETIC ANOMALIES BY THE 'CONTRACTING SURFACES' METHOD
Novosibirsk GEOLOGIYA I GEOFIZIKA in Russian No 12, Dec 80 pp 106-117
[Article by M. S. Zhdanov and I. M. Varentsov, Institute of Terrestrial Magnetism,
Ionosphere and Radio Wave Propagation, Troitsk, Moscow Oblast, manuscript sub-
mitted 21 Sep 79]
[Text] Abstract: The author proposes an iteration
algorithm for determining the form of a
Iocal deep geoelectric inhomogeneity situ-
ated in a layered medium under the condition
that the parameters of the layers (their con-
ductivity and thiclcness), and also the excess
_ conductivity of the inhomogeneity are known.
The form of the inhomogeneity is determined
in the process of minimizing the functional
of the mean square deviation between the ob-
served and model fields. The minimizing prob-
Iem is solved by the gradient methoda The de-
- scribed algorithm is applied in the form of a
program in FORTRAN-IV language, intended for
the interpretation of two-dimensional E-polar-
ized fields.
The most important problem involved in modern nethods of geoelectric e:tploration
is a study of anomalies of the variable geomagnetic field cau:tcianomalies,
homogeneities of t}te geoelectric section. As is we11 known, geomaSnet
in accordance with the nature of the sources causing them, can be divided into
two groups: surface and deep [2, 9, 10, 15]o The first group includes anoIDalies
associated with snham�ed n bit inhomogeneitiesein the earth's,crustsandtupperc
ond are anomalie Y deep
mantle.
In most cases the inter.pretation of surface anomalies essentially involves a deter-
mination of the total longitudinal conductivity of the surface inhomogeneous layer
of the earth, which can be dotie using integral transforms of the observed field
[10, 11, 16, 20, 211.
The prflblem of interpretation of deep geamagnetic anomalies is more complex. The
- author of [9] proposes a method for its solution based on an analytical continua-
tion of the field into the lower half-space. An analysis of the vector lines of
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the analytically continued electromagnetiG fields in some situations of practical
importance makes it possiFile to determine the position and form of deep inhomo-
geneities [23]. '
For a more detailed determination of the configuration of deep geoelectric inhomo-
geneities it is des-Irable to employ the ideas of the trial and error method, wide-
ly employed in different geophysical investigations and making it possible to cor-
rect the configuration of the region with anomalous conductivity on the basis of a
comparison of the theoretically computed fields and the results of practical ob-
servations. This article is devoted to further development of these methods.
Farmulation of Problem
' We will examine a two-dimensional model of the geoelectric section consisting of a
' conducting horizontally layered earth with z= 0 in contact with a homogeneous non-
~ conducting atmosphere. The conductivitq (0'n, n= 1, N) and the thickness (hn, n
I = 1, N- 1, hN =00) of the layers in the model are assumed to be known. Assume
; that in the earth there is a geoelectric iahomogeneity Q characterizing a con-
� ductivity different from a normal distrihution:
i / Qn, r4 0- Y (l)
{orn + Ac 1T91, T4 o- Q.
Here rq is the radius-vector of the observation point and Qa(rq) is an arb3.trary
function des Cribing anomalous conductivity.
The field is excited by extraneous electrical currents distributed in the P region
of the atmospher�e. The dependence of the field on time is expressed by means of
~ the factor e iWt. The permeability in the entire space is constant and equal to
i � p= 4j1 �10-7 H/m. We will neglect displacement currents. We will assume that the
field and medium are homogeneous along the y-axis, that is, we will solve the prob-
H~ lem in a two-dimensional formulation. We will limit ourselves to examination of the
i most interesting case of E-polarization.

~ Assume that i:n this model we know the synchronous values of the magnetic field H
i on some profile L on the earth's surface in the range of �requencies a� the para-
meters of t:e normal geoelectric section (O'n, hn) and the form of the functional
~ dependence of anoma.lous conductivity by on the coordinates of the observation
point. The problem is to determine the boundary of the region Q c:iaracterizing
this anomalous conductivity.
_In formulating the problem the question naturally arises as to the uniqueness of
its solutio n. In the theory of potential fields the anawer to this question is
given tiy the Novikov theorem [13], guaranteeing uniqueness of solution of Che in-
verse problem for stellate bodies with a known distribution of excess density. In
the theory of electromagnetic fields there is no such thaorem and therefore the
problem, in essence, is to find one of the possible solutions (the inverse problem
is formulate d in a similar way in the method proposed by Weidelt [21]). In addi-
tion, unde r the condition that the electromagnetic fields are measiired on some
extensive p rofile on the earth's surface in some range of periods, there is every
- basis for assuming that this information is adequate for an unambiguous determina-
tion of deep inhomogeneities. In particular, P. Weidelt demonstrated the uniqueness
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of solution of the inverse problem for the case when the conductivity of the sec-
tion is described hy an analytical function [22].
In solving the formulated problem hy the trial and error method it is necessary to
A rigorous
compare the observed fields with the results of numerical computations.
solution of the direct problem for the region of any inhomogeneity of a quite arbi-
trary configuration requires an examination of rather complex systems of :integro-
differential (or finite difference) equations [6, 7, 18, 19, 21]. Accordingly, in
fo rmulating effective trial and error algorithms it is desirable to use simpler ap-
pro ximate approaches to solution of direct problems. In particular, in some situ-
ations with a relatively small extent of the region Q in comparison with the wave
length a sufficiently precise approximatiun can be obtained if in solution of the
integral equations liy the "contracting images" method we limit ourselves to the
fi.rst iteration [3, 5, 7, 121. Physically this means that we stipul.ate the excess
currents 3eX induced in the region of the inhomogeneity Q, proportional to the
no rmal eJectric field. In particular, with E-polarization
j eg =(09 Jgx g 0) a
and the scalar function feX can be approxi.mately determined using the formula
J ex - daEy �
(2)
where F., is the normal electric field.
The distrib ution of the normal electric field F.y in a layered earth is determined
by well-known methods [1, 8, 23] by analytical continuation of the normal compon-
ent of the electric field, discriminated from the observed field at the surface,
within the earth. Thus, the invPrse problem in the ana.lysis of deep anomalies is
rzduced to the finding of the boundary of the region Q characterizing the distrib-
ution of excess conductivity Acs. The excess currents flowing in the Q region can
b e considered as extraneous currents exciting the deep anomalous field. According-
ly, the problem involves determination of the configuration of the Q region filled
with extraneous currents of a known density.
lde note, f inally, that in a theoretical investigatiQn of the formulated problem it
is convenient to operate not with the magnetic field H itself, but its flux func-
tion V, which in the region of homogeneity of the medium unambiguously determines
the components of the electromagnetic field: H. = avtqzz, 11: -_Max, F.,, _-iw�uilr:
De termination of the Boundary of the Region Filled With Excess Currents
Assume that we know the flux function ~ of a deep anomalous field on some profile L
on the earth's surface in the range of frequencies J2. In addition, we know the den-
_ sity distribution of the "extraneous" excess currents jeX flowing in the xegion
q, whose boundary is to be determined.
Henceforth we will assume that this region is stellate relative to some internal
point 0, whose coordinates are stipulated. At the point 0 we place the origin of a
- po"Lar system of coordinates (P, ~O) and we describe the boundary of the Q region
in these coordinates by the equation_
.
� p = 7((P)
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~
The problem is as follows: on. the basis of the known function find the boundary
uf the anomalous region a, that is, determine the unknown fimction f(T).
A A
We will limit ourselves to Findyng the function � describing the baundary of Q it
the class of continuous functians F:
- F = {fc(p): fcT> > o, t((p+ 2n)= Aq)),
- Each function f from F in polar coordinates fixes the boundary )Qf of some region
Qf. The flux function of the corresponding magnetic field, excited by the currents
jex, flowing in the region Qf, is determined in the following way:
n f(ri) .
[ N36 = ex] T1 ~r~ 1na (r-) G. ~r, rM~ pdpdcp, (3)
-n o
where Gn(r, rm) ig the Green's fur.ction of a layered (normal) sectior., an.d rm is
the radius-vector of the current integration pc-Lnt m E Qf with the coordinates (P,

For effective solution of the direct problem we will examine a representation of
~ Green's f unction in the form of the Fourier inteRral
~ 00
~
- j G. (r r* Gn ( lX+ Zi rM 2a gn (
i,kzr Z; rM ~ e--{kx zdkx,
_ a,;
~ in which the spectral densiry gn (kX, z, 7) is expressed relatively simply through
; the elementary functions [21], and it can be computed using an economical FFT (fast
I Fourier transform) algorithm. After transposition of tha Fourier transform opera-
~ tion and integration in (3), we obtain a formula which is simpler from the computa-
~ tional point of view 00 . n 10m), .
; r} _ ~ x, 2) - e x lqa6 (Er) b'n (kx, z; pdpd~dkx.
~ c Zn f '-{k .x f f . .
036 = ex] , -�-n o . (3a)
' In the class F we will seek such a function f for which the corresponding flux
~ 2~1f is sufficiently close (in some metrics) to the flux function 1 of the fieZd
~ stipulated at the earth's surface. The measure of closeness of the observed and
' theoretically computed fields for simplicity will be taken in the metrics of the
~ complex space L21cJ, x]:
~ II IV' II =1/.f I T Isaxaw = 1[ ~ f T . T*axaW,
a i 0 L (4)
' where the asterisk denotes a complexly con3ugate value,a and L are the interval
; of f requencies and the observation profile, for which the af function is known.

Thus, ttie problem is to find such a function f for which
II~~-~II0.
(15)
, (16)
With such a determination of the function gfi the first variation of the functional
Ma, is equal Lo a _
[ff, 8J;] 2 f I hfi Il+sd(p C p, (17)
n
from which it follows that the inequality (14) is satisfied provided that hfiv6- 0
(and accordingly, gf i*0).
Fo r dstermining the tfi value we will examine the function
cb (t) = Ma [ft gi,]
and we will seek tf, from the minimum condition !~(t). For sufficiently small t a
minimum always exisis due to the negative value of the first variation of the
�unctional Ma and formula (11). The problem of one-dimensional minimizing is
solved by standard methods [14].
The formulas (10)-(15) make it possible, proceeding on the basis of some initial
approximation fp E F and the initial interval tf0, to construct a series of func-
tions {fi} minimizing the functional Ma . These functions in space describe cyl-
indrical surfaces contracting toward the surface of the anomalous region Q. Ac-
cordingly, the proposed method was given the name "contracting surfaces methodo"
The described iteration process with a fixed QC parameter is completed under the
condition
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111r- fi-~~~ < pli, (18)
where 91>'0 is some stipulated value. The optimum value of the regularizatich
parameter oC is selected from the series (oCp ) , converging to zero,
ap+1 = �ar, P= 1, 21 0< 1.
(19)
For each value of the parameter (X = aP there is a minimizing of the functional
Mtc Q[ f] by the described scheme. The result of the minimizing the fim.ction fa, P
is used as an initial approximation for minimizing the functional Mac. +l[f]
(for the functional My- l[f] the initial approx3mation is the function f03o As the
quasioptimum regularization narameter A:qo, for which the corresponding,, function
of the series [fo[P} is closest to the precise solution of the problem f, We
select, conforming to [4], the parameter o[qo, for which there is satisfaction of
the condition ,
or (axo, s~ = InIII I lap-1 - faP II[KO = qo = quasioptimum] P (20)
The function f= f vLqa, corresponding to the parameter oCQo, is a quasioptimum
approximation to the f solution.
~ Spectral Modification of Method
- The computation scheme for the "contracting surfaces method" can be simplified by
proceeding to an analysis of the spatial spectra of the observed electromagnetic
fields. Assume that in some range of space frequencies K=(k'X, k"X) we know the
function the Fourier transform along the x axis of the flux functiou
considered above,
~ (kx~ Z) = F. IT (x+ Z)l (x+ Z~ C{kx xdx.
_
The "spectral" direct problem Vg = F[Vf] is solved using a formula following
from (3), (3a): n ~(q)) - V1 (kx, Z) = J J 1a~ (r~`) b'n (kz, Z; r~`) PdPd~�� (21)
[N36 = ex] _n o
The latter formula no longer contains the Fourier transform ogeration; therefore,
the volume of the computations is substantially reduced.
We wi11 examine the quadratic functional
(22)
determining the measure of closeness of the Fourier transforms of the observed and
computed fields, in the metrics of the complex space L21 al, kX]:
I w I'dkxdw tpV*dkxdco.
~n V
x (23)
A comparison of expressions (22), (23) with (4), (6) reveals a great similarity
between tl~A :Fllr.-711:,nal l[f] and its spectral analogue &r[f]. Moreover, in the
special situation when L= (-oo, oo ) and K= (-00, oo ) these functionals are
equal due to the well-known Parseval equation. Therefore, for solving the problem
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of minimizing the �'J functional :Lt is natural to use the regularizing procedure
described above. In this case it is necessary only to replace I[f] in formulas
- (8)-(20) bY �~f If J, 4/bY V ~ X E L bY kEK, Gn 1':: 8n-
~ . p qo>
~ 0,02
. : � ~ .
' j � I
- i ,
_ Fig. 1. Determination of form of conducting circul.ar cylinder by the "contracting
surfaces method." l, 2) curves of real and fictitious parts of spectrinn of ver-
_ tical component of magnetic field hZ at earth's surface; 3) boundary of cylindrical
inclusion; 4) result of solution of inverse problem with regnlarization; 5) same,
without regularization; 6) initial approximation; 7) values Re hZ, Im hz, computed
for model 4; specific conductivities of ittclusion dI and surrounding medium OrE
(and so foxth in figures).
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k
- > Reo - Imq6
~ .
,
3 '
4
_ ~5 � ~
- � 6 , i
7
. 8 2 i . , . -
. . . . . . . g ~ . i~,,, .
~
~
� ' ~y-^~1~.
` ~1
' I 1 , ~ 1 1
. r� 10 v 20 / ~aZ
~ �
Air BosByx uo,=o o1 . 0,2

Ground 3eMnp 6e

o,
c
_ 60=1oo
zA . .
Fig. 2. Determination of configuxation of rectangular inclusion of anomalous con-
�
ductivity by "contracting surfaces method." 1, 3) curves of real and fictitious
parts of spectrum of flux function j( of magnetic field at earth's surface; 2, 4)
same curves, complicated by 10% error; 5) boundary of rectangular inclusion; re- ,
sults of solution of inverse problem; 6) according to precise data; 7) according
to approximate data; 8) initial approximation; 9) values Re V, Im couput
, for model 6; 10) same for model 7.
Examples of Interpretation of Deep Anomalies by "Coatracting Surfaces Method"
On the basis of a spectral modification of the "contracting surfaces method" the
INEMTA program, written in FORTRAN-IV language and applied on a YeS-1010 electron-
ic computer, was developed. It makes it possible to carry out an interpretation
- of anomalies of two-dimensional E-polarized fields (HX, HZ, Ey,IY) on the basis of
the correspondiag space spectra.
The program was tested in a number of models of deep electromagnetic anomalies.
_ The first example (Fig. 1) illustrates the need for using regularizing algorithms
in determining the configuration of deep geoelectric inhomogeneitiesa The model
consists of a homogeneous earth containing an anomalous region in the form of a
horizontal circular cylinder. The solution of the inverse problem, wirhout regular-
ization (OC= 0) leads to a result differing greatly from the true con�iguration of
the inhomogeneity. The standard deviation of the spectrun of the observed field
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from the theoretica].ly computed field for the model obtained in the course of solu-
tion of the inverse problem of the model is only 2%, which indicates a high degree
of instability of the problem. At the same time, the use of a regularizing algo- 4
rithm makes it possible to obtain entirely satisfactory results.
o 'i-

~
I =A
z41
(
i
i
~
Fig. 3. Solution of the inverse problem by the "contracting surfaces method" with
automatic correction of the posit.ion of the pole of the coordinate system. 1) cur-
rent position of pole of coordintite system; 2) boundary of conducting inclusion;
3) initial approxima.tions for each position of pole; 4) initial approximationr S)
indicator of initial approximation for each position of po1e; 6) indicator of fin-
al result; the numbers on the curves represent the relative error of the approx-
imation, -
Figure 2 shows a model in which the homogeneous conducting earth contains a rec-
tangular inclusion of anomalous conductivity. The inverse problem was solved by
the "contracting surfaces method," first using the precise values of the space
spectra of deep anomalous electromagnetic fields, and then using the values of
the spectra, complicated by a 10% random error. The results presented in Fig. 2
show that despite the presence of a great error in the initial data, the inter-
pretation in the second case, by means of the regularizing algorithm, makes it
possible to solve the inverse prot+lem almost with the same degree of accuracy as
in the first case (with precise stipulation of the space spectra).
In the examples considered above, in accordance with the general theory of the
method, the pole of the polar coordinate system (,P,