JPRS ID: 10644 USSR REPORT EARTH SCIENCES
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JPRS L/ 10644
S July 1982
U SS R Re ort
p
EARTH SCIENCES
CFOUO /82)
.
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~ JPRS ~,/1p644
- 8 July 1982
- USSR REPORT
EARTH $CIENCES
(~'OUO 4/82~
. CONTENI`S
- oCEANOGRAPHY
. Nonlinear Interaction Between Internal Waves and
Near-Surface Shear Cu~rent ..........o 1
Multielement Four-Dimensional.Ana],ysis of Principal
;~dropl~Ysical Fields in Ocean .........o 11
Correlation Between Traina of Short-Period Internal
T~Taves ead Thermocline Relie~ f~n Ocean 21
Effect of Self-F~hancement of aravitational Anoma~.i~s
in Gradient Media 34
Seismic Noise at Ocean Floor 38
Influence of Turbul~nce Intermi.ttence on Forming of
Ocean 8urface Structure 43
F~ndamental Problems in Marine Blectro magr~etic Reaeareh...... 49
7~eory of Observation of IIndervater db3ects Through
W8V8-Cov~red 3ea Surfa~e �~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~� 67
' Seminar on t~eophysicai I~rdrodynamics of Concnisaion on
_ idorld Ocean Problems, II33~R Acadenqr of 3o3.ences (Chairman:
- A.. S. Monin, Corresponding Member, OSSR AcadeiYqr of
3ciences) ?5
Polar Northeastern Bapedition of Institute of taceanoYogy
Imeni P. P. ~irahov, U3:~i~ Acade~r of 3ciences (1978-
1981) 83
- a- ~SII - USSR - 21K 3&T FOUO]
cna ~c~~�.� t TcF n~ v
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Oscillations of Current Recorders at Self-Contained Buoy ~
Stations and Their $~fect on Measurements of Current
Parameters 86
T~T'ide Angle Seismic Profiling in Ocean.Using Towed Radio
Buoy 96
, Measurements of Volume Sound Scattering in Ocean Using
Abyssal Acoustic 9ystem 101
I,aboratory Investigation of Inf].uence of Internal Wave
on kegular Surface Waves 10l~
Model of Climatic Spectrwn of Internal Wave4 in Ocean........ 112
Gravitational-Capillary Solitons at SurFace of Fluid 117
Mean Component of Infrared Sea Radiance 123
TERRESTRTAL GEOP~iYSICS
Prospects for Ueveloping,New Methods in ~eismic Prospecting.. 130
~ - b -
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OCEANO~RAPHY
UDC 551.466.81:551.465.5
NONLINEAR Ih'TERACTION BETWEEN INTERNAL WAVES ANb NEAR-SURFACE SHEAR CURRENT
Moscow IZVESTIYA AKADEMII NAUR SSSR: FIZIRA ATtiOSPERY I OREANA in Russian
Vol 18, No 4, Apr 82 (manuscript received 26 Feb 81) pp 383-390
[Article by V. P. Reutov, Inatitute of Applied Phqsics, USSR ~Academy of Sci-
ences] ~ ~ ~
[Text] Abstract: A study is made of the ab~orption
(instability) of iat~rnal waves~in a two-layer
model of a stratified fluid with a~current near
the free surface. Absorption is determined by
the critical layer in which the phase velocity
of the wane is clbse to the ~current velocity.
Currents submerged at a depth small in comparison
with the thiclaiess of the upper layer ~re ezam-
ined. An expression is derived for the incre~ent
in a linesr approximettion ~ad the nonlinear de-
velopment of a wave With t~e is;de'scribed.
A great number of studies have now been published on the linear theory of in~
stability in a stratifi~d medium [1-3]. In very simple cases the nonlinear de--
velopment of internal waves can be described ~on the basis of the general ap-
proach employe~ for systems with slight nonlinearity [4, 5]. When the in-
. stability is detera~ined by the presence of laqers of coincidence (Miles in-
- stability mechanism [6-8]) it becomes possible td make an analytical study of
highly nonlinear processes of eaergy exchange between the current and a wave.
In this caee the analysis is eimplified because atrong nonlinearity is mani- ~
fested only in the narrow regiop of the critical layer (CL) [9-12J. .
In this article we solve the problem of the noizllnear stage of instabil.ity
(or absorption of a wave with a finite amplitude) in a two-layer model of a
stratif~ed fluid of infinite depth iia the presenae of a horizontal shear cur-
rent near the aurface. The orig~n of euch a current can be, in partfcular,
related to the directed movement of air over the boundary of the upper layer
(wind over the sea surface). An analyei~ is g~ven fos the vertical scales
of the velocity profile small in comparieon w~th th~ thickness of the less
dense upper layer. The Miles mechaniam of in~etasification and abaorption of
, internal waves is considered. Within the framework of tne theory o!c a crit- .
, ical layer formulated in [9-12], a study ie made of the linear and nonlinear
stages in the development of a wave with time: ~
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1. We will take the equations describing the two-dimensional interaction of
internal waves with a hor3zontal current in the near-surface layer of a
stratified fluid. We will examine currents penetrating to the depth , small
in compari~on with ths thickaesa h of the,upper layer, characterizing a glight
submergence of the current with the sma11 parameter E~,Q /h~ 1. We take flrna
turbulence into account phenomenologically through the constant coeff3cient of
turbulenr viscosity . We will use a dimensionless form of writing of the
equation for the stream function, as the unit length employing the thickness h
' of the upper layer, as the velocity unit the current ve.~ocity at the surface
u~, as the time unit h/u~; we normalize the stream fu,^tion to the value
hu~. The equation with dimensionless variables in this case coincides in form
with the initial equation if ~V is replaced by 1/R~, where Rk = u~h/i/ is the
Reynolds number. The axes x, z of the coordinate sqstem and records of th~
dimensionless velocity profile u(z) are ahown in Fig. l.
. t' ~ , ~ya1'.
D 1 , ~
~a
_
gP/p~~
Fig. 1. Illustration of relative positioning of region of current and fluid �
layers with differ~nt density; 1) velocity profile of shear current without
flexure point, 2) profile with flexure point.
We will examine sinusoidal waves with an amplitude slowly changing with time.
The nonstatioi~arity of the wave, viscosity and nonlinearity cannot be neglect-
ed simultaneously in the region of the critical layer situated in the immedi-
ate neighborhood of th~ resonance potnt z' z~ (u(z~) _ c is the phase velo-
city of the wave). The characteriatic dimensiona of the peak of puleations of
vorticity arising wich allowance for each of these factors separately, have,
accordingly, the form _ _ .
1 ~r~
~~-i~l/k~: ~ ku'R~~ ' (1)
w~:,~ tBl~.')u,
where k is the wave number, B is the ampli:ude of oscillations of the stream
function with z= z~, = B'1dB/dt is the wave increment; u' = du/dz, the sub-
script c here and in the text which followa means that lthe variable is taken
with z= z~. I~ a general case the scale of the critical layer wi13. he deter-
mined by the expressicn d~ m m:3k (dt, d~, dn). Then we will assume that in the
flow there ~.s one critical layer~ isola~ed from the boundary z~ 0:
_ : . . _ ~~j,~ ~ s~ ~ ,,,r, `2 ~
WiLhout limiting g~eater univer~ality of the examination, we will assume that
u'~ 0. As limits of. the critical layer the w~ak non~tacionarity of the wave,
v~iscosity and nonlinearity in the flow can be regsrded as amall disturbancea.
2
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Neglectiri~ viscosity and nonline~rity,~we will write an equation for pulsations
of the stream function wfth Iz-z~l~ d~ in the form
_ _ . _
Ia a ~~p +~e`'a ~.,~Q (3)
l a: a~~~ a~ : .a~`~
, .
Since u~ 0 only at distances N E from the st~rf~ce z= 0, the linearized con-
ditions at Che density ~ump aseume the form .
~ ~ _ --s
. . =~~a"'~,
. (4 )
_ a
; c~'~-s~.-~'r-,~.)+~~ a~'~ ~-~~.-~o,
where g= hg/u02 is a dfinenaionless aralogue of th~ acceleration of. free fall-
_ ing g. For oscillations of ti~e stream function.~at;the boundary..we w~ll use the
"hard cap" approximation. ~
,p~.~�-0. - (5,
When the wind flow createa thp shearing atreas p,~ at the water su.rface, the
boundary conditions for the mean current will be satisfied with Rh ldu/dzl s0
pti . Stipulation of the arbitrary profiles u(z) assumes, as usual, a paral~el-
ism and stationarity of the current for the considered~procesaes.
_ ' 2. In the absence of a current (u ~:t?) the system (3)~(5) describes internal
waves propagating with the phase,velocity [13]
. . . .
th k jy~
c~c,~[ k(i+thk) J ' (6)
where cm ~(gsP/~O )1~2 is the velocity of inf~.nitely long waves (cm>c). A so-
lution of the problem of weak interaction of aii internal wave with a near-sur-
face shear current will be sought uaing the method of spliced asymptotic expan- ~
sions [14]. The stream functian in the region Iz~~ E will be represented in the
form
~~*af(:,)~"'~-�'?*t.+~.-~~I~tf?+ . . . , (7)
where c~ c+~ c~1~ ( S c~l phase vel.ocitq increment caused by a current
a(E t) is the alowly changing coniplPx amplitude of the wave, f(z) describes
~ the form of the profile of an internal wave having the phaee velocity c:
. ~,~?1ks, . . ~ ~ - -,~1dr~. (22)
u,."B~
-s
As can be seen from (19), (22), the wave increment "Y(t)~ E~.
3. In order to describe the development of a wave with a linear critical layer
(dt ~~dn) in (20) we must assume here that T' u~"rt+ ~T,,., and linearize rhe
derived equation relative to A and Z,r . It can be shown [11, 12] that the re-
sults of the solution of such a linearized problem agree with the conclusions
from the linear theory of instability of shear currents. In accordance with the
- linear theory, the phase ~ump ~ of the logarithm, found for neutral waves in
the presence of viscosity, and from solution of the problem with initial con-
ditions for an ideal fluid, is equal to -?Z [2, 16]. Assuming in (22) that
-~1, from (19) we immediately obtain an expreasion for the linear wave incre-
ment:
. ~ - . .
n -
- ~ A 6C~~ ~
~.~.k..,( c 1 .
2 u,. ah k l cM 1 (23)
6 .
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As follows from (1) and (23), the scale of the nonatationary critical lay~r
is d~ E 2 and accordingly, with E~ 1 and a sufficiently low viscosity there
is satisfaction of the assumption of isolation of the critical layer.
Expression (23) shows that waves with a resonance point situated in the region
u" (z) ~ 0 attenuate (')' a R ~ ~ >
q ~
q ~
~
~z� ~ ~ ~ '
0
, N
h~
~Q
- Q7 .
16
Fo~ o~[c~~c usE or~.v
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(al8t)P�(x, x', t)-L,P,~(x, x', t)+ ~
' +L:~PM~x'. si t)+Qoo.~x. t).
~=~a+~ca~~a~--fa~ t.)a~~~t~,.t~)ala~-~"w(:, c),~ia:. (22)
At the me~surement time tt the covariations~l function PpP (x, x', tl'), found
at this time from solution of equation ('GZ), is corrected_ us~~ the formula
~ 2 ~ . ,x . � -
P~(x,x',t~'')�Pp(Y,s',t~'~)-~~ ~~.'P(~,t~')Pv.(x'.z.~t~ )-t'
(23)
_ _.--+e,;,p(~, t~-)p~.(=', f,-j+e,~�(x, ~~-)p~(~', t~-) l �
The authors of [2] proposed an approximate method for computing the covaria-
. tional functions puu~ Puv~ Pvu~ Pw through the covariation function P~op. In
order to obtain formulae for computing the cross-covariational functions PuP ,
PvP , Pp u and Pf,~ through the function PPP we will use geostrophic expres-
sions and a fo~mula for the approximate determination of the ocean level by
the dynamic method [10]. Then the croas~covari~tional function of the errors
of the u-component of velocity and the density anomaly is determined as fol-
~
.
lows . Pro `x, x,, t~ _E {au (~'t, aP (~~'.t, } 8 ~ a [aP (x' t) ~ X
~l fp� s ~8y ' (24)
- ' x
~xd�aP ~x~' t~ } ~ f~. a~ ~ P~ (x, ~ , t) d�� .
.
Similarly we obtain formuias for eomputing the remaining cross-variational
functions
- .
_ u
pp~'~,x~,t)~-'-g a f
~~oo~x,x~~t)dW~ (25)
iPo ax
, t
' r
p.�(~x`,t)-~ g a, f p~(X,~,t)d�, (a6>
. tP. ab . .
Pn. ' . g a a
~x' x' t~ f
po 8x' J P�� x~, t) d�� (27 )
In the derlvation of formulas (24)-(27) the density anomaly at the bottom was
neglected.
Thus, all the elements of the covariation matrix P(x, x', t) can be computed,
which makes it possible to carry out a four-dimensional analysis of the main
fielda in the ocean with the presence of their measurement data at diacrete
moments in time t
2. Model computations were made in a grid region mea.suring 13 x 15 x 9 points
with a apatial interval L1x = d q� 17 miles, G z= 200 m. The principal para-
meters in the numerical model used ~rere as follows [9, 11]: ~GX =-0.00547;
0.03648 N/m2; A= 10; J~ = 10- , y= 10'3 m2/9ec, 0.2�10'10 m l.BeC-1~
Yi = 0.712�10-5 m/sec, y2 ~ 0.735�10-1 kg/R, Q t s 8.64�104 sec, Ta = 29�C.
~ 17
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� . .
�O.O�G�O.O.O�
.o.:o.o.o.~~.o..
,o�o 0 0 � �
.~.~,.~.~..~,.~.t
- ' 0' ~ �
' Q ' O ' Q � O � O '.O ' ~
0 ~ . C] ~
O i aymoK day ! .
Fig. 1. Sequence and number of observation etations for density and current
velocity fields on eaeh day of model time.
As the true fields we used the hydrophqsical fields computed in an inertial
forecast (with constant lateral boundary values~o~ for five days of model time.
We used equations (6)-(10) with the boundary conditiona (11)-(13). As the in-
itial equations we took the fields corresponding to the initial density field,
obtained on the basis of observational data from the second density survey
carried out in the POLYMODE polygon [11]. Observati.onal data were generated
- from this true state each 24 houre (see Fig. 1).
In subsequent computations as,the initial density field we used the initial
field f~ averaged on the 3asis of the nearest four points within the region and
two at the lateral boundaries. At the lateral boundaries the density ch~nged
linearly from the smoothed value on the firat day to the true value on the last
day. The following variants of computations for five days of model time were
used.
In the preliminary experiment (PE~ a purely hydrodynamic prediction of field
evaluations was made. In the first experiment (I), in addition to a predic-
tion of evaluations of the fields for each day there was assimilation of data
from observations of the u, v components of current velocity. In this procedure
in formulas (15), (16) beneath the aummat�ion symbol we keep the firat two terms
and in formula (17) the last term on the right-han,d side is neglected. In the
second experiment (II) the density evaluation was corrected using observational
data on velocity in explicit form (the indicated term was taken ~nto account in
(17)). In variants I, II there wae a two-element four-dimensional analysis of
- oceanic fields. In the third (IIY) and fourth (IV) experiments there was a
single-element four-dimensional analysis using measurement data only for the
density field. ~ ~
The fifth experiment (V) was carried out with simultaneous allowance for ob-
servational data on the velocity and deneity fields. The covariation matrix
PpP (x, x', t) was computed as in [2J.
18
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We will introduce th~ following notatioae:
a(z)~-~~, f ~rp~-~o~dS~
[ N = true; ~ = exp] - 1 -__,i~
aM.KOtz)~ max I~.-~.I, o(s)-{ ~f [I~.-~.I-a(z)~saZ} ,
~=.r~.~ E
8
- S is the surface of the polygon, ~ is the surfuce area, ~true is the true val-
ue of the field on the fifth day of model time; ~exp is the field value ob-
tained in the course of an experiment in this same time period. The table
gives the results of the numerical eaperiments. The figures in the parentheses
indicated by what percent the considered valnes of the errors ~X and
were improved relative to the similar errors in the PE.
It can be aeen that the assimilation of ineasurement data only for the velocity
field leads to an insignificant improvement in the results of four-dimensional
analysis of the velocity and density fie~ds. At the same time experiment III
shows that with the assimilation of information on the density field the
errors S~X and d for the velocity and density fields decrease signif-
icantly. This is also confirmed by experiments IV and V. The conclusion can
be drawn that the principal factor in the procesa o~ reconstruction of the
principal hydrophysical fielda in the ocean in the case of their four-dimen-
sional analysis is zhe density field. Within the framework of the conducted
model experiments the correction to a field, informati~~n on whose measure-
ments is lacking, by measurement data for other fieldf3 in explicit form on
the average is insignificant (see experiments II, IV}. In individual regions
of the polygon, as indicated by an analyeis of the results of computations,
it can be substantial. Minimum values of the errors ~~X and d are ob-
served with the simultaneous assimilation of ineasurement data for the density
and velocity fields (experiment V).
BIBLIOGRAPHY
1. Knysh, V. V., Nelepo, B. A., Sarkisyan, A. S. and Timchenko, I. Ye., "Dy-
namic-Stochastic Approach to Analyais of Observations of the Density
Field in Hydrophysical Polygons," IZV. AN SSSR: FAO (News of the USSR
Academy of Sciences: Phqsics of the Atmosph~re and Ocean), Vol 14, No 10,
pp 1079-1093, 1978.
2. Rnysh, V. V., Moiseyenkc*, V. A., Sarkisqan, A. S. and Timchenko, I. Ye.,
"Multisided Use of Measurements in Hydrophysical Polygons in the Ocean
in Four-Dimensional Analyais," DORL. AN SSSR (Reports of the USSR Academy
of Sciences), Vol 252, No 4, pp 832-836, 1980.
3. Mashkovich, S. A., "Multiel~ment Ob~ective.Analysis of Meteorological
Fields," METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrology), No 5,
pp 5-14, 1980.
4. Sa~iceva, Y., "Optimal Filtering in Linear Distributed Parameter Systems,"
INT. J. CONTROL., Vol 16, No 1, pp 115-127, 1972.
19
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5. Brayson, A. and Kho Yu Shi, PRIKT~ADNAY~'. '~EORIYA OPTII~,AL'NOGO UPRAVLENIYA
(Applied Theory of Optimum Control), Moscow, Mir, 1972, 544 pages.
6. Colantuoni, G. and Padmanabhan, L., "Optimal Sensor Selection in Sequen-
tial Estimation Problems," INT. J. CONTROL, Vo1 28, No 6, pp 827.-845,
1978.
7. Paramonov, A. N., Kushnir, V. M. and Zaburdayev, V. I., SOVREMENNYYE
METODY I SREDSTVA IZMERENIYA GIDROLOGICHESRIKH PARAMETROV OKEANA (Modern
Methods and Instrumentation for Measuring Hydrological Parameters in the
Ocean), Kiev, Naukova Dumka, 1979, 246 pages.
8. Knysh, V. V. and Demyshev, S. G., "Hydrothermodynamic Model for Investig-
ating Synoptic Variability and Energetics of the Ocean," MORSKIYE GIDRO-
FIZICHESKIYE ISSLEDOVANIYA (Marine Hyd~ophyeical Research), No 3, pp 97-
- 109, 1980.
9. Demyshev, S. G. and Knysh, V. V., "Numerical Modeling of Synoptic and
Macroscale Currents in lthe Ocean," STRUKTURA, RINEMATIKA I DINAMIKA SIN-
OPTICHESKIIQi VIKHREY (Struc*ure, Kinematics and Dynamics of Synoptic
Eddies), Sevastopol', MGI Art UkSSR, vp 46-58, 1980.
10. Perederey, A. I., "Computation of Surface and Deep Currents in the South-
ern Part of the Pacific Ocean," MORSRIYE GTDROFIZICHESKIYE 'ISSLEDOVANIYA,
No l, pp 76-87, 1972.
11. Nelepo, B. A., Bulgakov, N. P., et al., SINOPTICHESKIYE VII~iRI V OKEANE
(Synoptic Eddies in the Ocean), Kiev, Naukova Dumka, pp 223-248, 1980.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizika atmosfery i
okeana", 1982
5303.
CSO: 1865/152
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UDC 551.446.82
CORRELATION BETWEEN TRAINS OF SHORT-PERIOD INTERNAL WAVES AND THERMOCLINE
RELIEF IN OCEAN
Moscow IZVESTIYA AKADEMII NAUR SSSR: FI~IKA ATM03FERY I OREANA in Russian
Vol 18, No 4, Apr 82 (manuscript rec~ived 3~Apr 81, after revision 14 Jul 81)
pp 416-425 .
[Article by R. D~. Sabinin, A. A. Nazarov and A. N. Serikov, Acoustics Inati-
tute, US,SR Academy of Sciences]
- [Text] Abstract: Measureme~ts of internal waves by
means of drifting and towed arrays of dis-
tributed temperature sensors~are described.
The work was canied out in the POLYMODE
polygon in September 1977.:The correlation
between the directions of waves in trains
of short-period wavea and thermocline slopes
is indicated. It is postulated that the re-
. fraction of internal waves and notil.inear
effects arising dur3ng the propagation of
_ waves over the sloping thermocline play an
important role in the generation of trains
of short waves similar to those appearing
during the nonlinear decay of an internal
~ tidal wave arriving in ahallow waters.
Arrays of distributed temperature sensora in drifting [1] and towed variants
have been used in studying the apatial structure of trains of short-period
internal waves frequently encountered in the upper thermocline and their
correlation with synoptic variability of the ocean. The studies were carried
out in the POLYMODE polygon during the period 6-9 September 1977 simultaneous-
ly on the acientiEic research ehipe "Petr Lebedev" (drifting array) and "Ser-
, gey Vavilov" (towed arraq).
The principal element of the array the distributed temperature sensor
was made of a cable with steel strands whose resistance varied proportionally
to the mean temperature of the water layer intercepted by the sensor. As a
result of such averaging properties the distiributed temperature sensor is in-
sensitive to the distorting influence of the fine structure of the vertical
distribution of temperature in the ocean [2] and this makes it possible
21
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to carry out both phafe and amplitude comparisons of the readinge of spa-
~ tially separated sensors, that is, to use array methods for evaluating
the spatial-temporal spectrum of waves [3]. The readings of the distributed
temperature sensors were converted into the vertical displacements relative
to the thermocline by means of the experimentally evaluated response of the
distributed temperature sensors.to the known vertical displacement, as a rule
~ stable during the entire course of the measurements.
Tk?e drifting array, consisting of four 100-m distributed temperature sensors,
spaced horizontally, was supplemented by a"stepped" sensor of four 20-m dis~
tributed temperature sensors for evaluating the~vertical variability of the �
waves and three BPV-2 current metere for determining movements of the array
relative to the water (Fig. 1).
The towed array included three 40-m distributed temperature sensors, at whose
ends there were hydrodynamic deepeners of the lattice type. One sensor (C)
was submerged from the stern, and the other two were deflected by means of
torpedo-shaped fioats along the wake (K) and in a direction away from the
ship (B) (Fig. 2). In the latter case the float was supplied with a special
line ensuring deflection under the influence of the oncoming flow.
Figure 3 ahows the position of the runs which were carried out against the
background of relief of the 15� ieotherm, characterizing the positian of the
synoptic eddies during the course of the experiment (the map was compiled on
the basis of data from a temperature survey carried out during the period
9-11 September 1977). The track of the scientific research ship "Petr Lebed-
ev" with a drifting array is also shown here. Figure 3 shows that the region
of the measurements was situated for the most part in a transition region
between cyclonic and anticyclonic eddies and only run V intercented an anti-
cyclonic formation. The discreteness of the meaeurements was 30 sec and was
equal to the time constant of the distributed temperature sensor at the 0.7
Tevel. The basic information on the towing runs is given in Table 1.
Pressure sensors of the vibrotron tqpe with a sensitivity of ~ 10 cm were
mounted at the ends of the distributed pressure sensor. These made possible
a reliable checking of the change in depth and choice of sectors with small
depth variations. Substantial changes in depth (up to 5 m) during towing
were observ~d only during changing of the runs, but aome increase in coher~
ence between the readings of the distributed temperature detectors and the
- depth of its lower end at frequencies of 12-15 cycles/hour made it necessary
to use caution in examining data for this frequency range (in the subsequent
processing the data were smoothed by moving averaging in six ordinates, that
is, with a smoothing interval of 3 min). At frequencies from 0.51 to 10-12
cycles/hour the coherence was close to zero and the spectral density of os-
cillations of the end of the distributed temperature sensor was 1-1.5 orders
of magnitude less than the spectral density of readings of the distributed
temperature sensor.
The situation is different with respect to fluctuations in the depth of the
drifting array, when sporadic aqualls have led to sharp intensifications
of drift and a decrease in the depth of the distributed temperature senscr.
22
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FOR OF'FlCIAL U3E ONI.Y ~
. PA .DTS
n ~ .
- ia
. P~ IJTS
_ ,
"I~tok" SD BPV ,
NeroK CII 6nb
DTS* P * ~ pA DTS
- - ~
9e '
*
Diatributed temperature senaor
Direction finder �
D S !0 1S YO 15 30 N, uuKn/y cycles/hour
0 !J ZD 2 Z8 T�C
20
k0 . ,
60 ~ DT~JI I .
eo I '
~oo .
I
_ I
t00 ~
N T
J00
, , 400
M ~ .
Fig. 1. Drifting array of distributed temper'ature sensors; a) appearanee from
above; b) position of sensors relative to theratocline (T is temperature, N is ~
buoyancy frequency). .
2~
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. . . _ . . .
r
Q a 6 ~ ' 2Z t4 26 te T�C
0
~ x f0 d c '
20 ~
~ ~ ; '
-1 ~ ~
JG t ~ ~
'
, ,
6 '~'0 i
~ Pd Dist~ributed.
~
b b ~ tempeiature
1IO,r SQ ; sensor
. ~ K ~ ~ I~
ti ~ ~
~BOM . . t0 60 y,w
Fig. 2. Towed array of diatributed temperature senaora: a) general view, b)
appearance from above, c) position of seneors relative to thermocline (posi-
tions of the thermocline close to extremal are indicated: 1) STD atation No
25, 7 September 1977, 2) KhVT atation No 61, 9 September 1977).
. \SZ~
,H
n.,..wi Y ~ ~o
\ 6~ .
4~ 6~ . 29�
/600
4
640
28�
/660~
71� 70� 69�W
Fig. 3. Thermal trawling runa (1) and drift of scientific research ship "Petr
Lebedev" (2) againet background.of isobaths of 15' isotherm. The deptha of the
isobaths are given in meters.
The exclusion of the corresponding parta of the record from processing, as
well as sectors with a changing direction of drift and relative positioning
of array elements in space, resulted in a marked reduction in the information-
al material; from'the en~ire 2.5-day record it was possible to select only one
one-hour (I) and four two-hour segment~ (II-IV) reproachless in all respects.
- Samples of the corresponding records and frequency apectra are shown in
2~
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Fig. 4,a and b. The spectra were computed on the basis of segments (overlapp-
ing by 98X) of 256 (for the first segment ~ 128) ordinates with subsequent
aqerc,~~ing for all segmeats and 5 freguengcies. "PreWhiteni~g" was used (filter
o~ the f~rst differences with subaequent reconstruction of the apectrum bq
means of dividing the resulting evaluation by the filter transmission func- ~
tion). ~ .
. - ~ sr,"~ �h urt+ � .
f0i~ ,
a ~ ~
,a , (
- ,
. , _ . ~ l
;
a .
. ~ ~
I fUa ~ ~
I~M''U~~ll ~ N ~
, ~V ~ ~ t
. 18 ~ 19''~ 6 .77
I ~M d ~o~ ~
~
~ z2�� oo~ zg.n
1 M ~ '~l ~ ~ + (
j ~ ~
~
02~0 ~ 04J57.a77~~_p ~
I ~M - Y '
~
~ i
� ~ oe~s p � ~ z8 ,
~oY'
I1M .
~ ' ~
13~s 15~O7.g77 ,
I
~
. ~~Y
. ~N as
1 2 J4 Bd10/3?0 50 ;'quR~/r cycles/hour
Fig. 4. Samples of records (a) and frequency spectra (b) of drifting array.
The scale along the y-axis is given for aegment V(lower spectrum). For other
segments the scales are given with Eucceasive displacements by one order of
magnitude. The arrows indicate aegmeata of the spectra eub~ected to spatial
� and temporal analysis.
25
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f,u~~/y cycles/hour ~
S ~ .a ` ~
.o
`0
a
Z
w ~ 3
~ 4
Z ~ vIOIY � .
oa oY
/ n~
0 / Z J 4 S k,uuK~/~M~cycles/km
Fig. 5. Position of peaks of evaluations of spatial-temporal spectrum in plane
of frequencies f and wave numbers k agair~at background of dispersion curves.
(The figures indicate the numbera of the mod'es.) The arrowa indicate the di-
rection of the waves (Of coincides with a direction to the north, Ok to the
east) . \ - - _ . _ . _ _ __N _ ~
YD ~ _ ~ ~
~ ~ CyC1e8IkiR
' A F D 6
. ~~t i 1
~ irV~ . ~j ~
A
. =,M ' I .
r~ ~
~I~u~''~
E D
?.'~~y
. ~ e c a s ~
- , ~ ~ ~ ~ ~ ~ ~ ~ ~ L., ~ ~ ~ ~ ~ ~ ~
-m o m ~o se w~ o e~ ~o so eo~
t' ~ ~ ~S� ~ t hour
, u~?~ ~ M3? n s. :~rn ~
o~rn .
Fig. 6. Smoothed change in depth of thermocline on runs II, IV (solid curves)
and III (daehed curve) and trains of internal waves. The arrows on the symbols
for the ship indicate the wave vectora of the traine.
Figure 4 showa that only in the first segment was there a train of quasisinus-
oidal oscillations with a period of 15 m; nevertheleas the remaining segments
do not exhibit an appreciable predominance of any one periodicity. However,
against the general decreasing background of the corresponding spectra it is
possible to discriminate individual insignificant plateaus and peaks for which
we obtain~~ evaluations of the apatial-temporal apectrum by the traditional
method and by the maximum similarity method [3]; these usuallq agree well with
one another and are characterized by a single-peak structure. The determined
valu~e of the wave vector of waves predominating at a given frequency fg
26
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r
k tk,x, ~~~~(k , ky, are the etipulated coordinatea of the peak di the spectral
evaluation inXthe plane of wave numbers) was used for~finding the true.fre-
quency f on the basis of the known velocity of motion of the array relative
to the water v~ u, v~: -
~"~i-}-kv~
f
r-~uk,+vkr,
where u and v are the velocity components along OR and OY. �
' ^ ~I Y7 Z9'JO'N
~ .
. .
~
~ e
Y~
- JO �
3/ F
_ '
JP
E
u ~
29'
' 6
_ J4 ~ ~
33
~ D
, 3S. ~ ~
~ 31 ~
/ ~
/ /
~ 30
28�30'
70�30' ' 70'W ,
- Fig. 7. Isobaths of thermocline and direction of waves in trains on the basis
of data from towed (the arrows on the symbols for the ehip, placed at the
sites where the trains were encountered) and drifting arrays (arraw on the
wavy line deaoting the drif.t of the ecientific reaearch ship "Petr Lebedev").
The results are sumnarized in Fig. 5,,showi~ag the k, f- coordinates of the
peaks of the spatial-temporal spectrum of individual segments against the
background of the dispersion curves of the different modes, computed on the
. basis of~data from the "ISTOK" temperature and salinity meter. The d irection
of the corresponding waves is indicated by the"srrows at the k, f- po ints;
the direction to the north coincides with Of, to ~he east with Ok. Most of
the points are grouped near the curve of the lower mode, which a~rees well
with the readings of the stepped senaor, indicating the in-phase cliaracter of
27
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the osci].lations at different depths. The latter circumstance very convincingly
confirms the fact of a predominance of the lower mode becauae�a distributed
- temperature sensor with a length of 100 m, by virtue of averaging in a thick
layer, f ilters out oscillations of the higher~modes and creates the illusion
of a predominance of a lower mode in places where this is not actually the
_ case. However, the fact of a dominance of the first mode of high-frequency
oscillations in the upper thermocline is not new and is easily explaiY.ed,
since the higher modes attenuate rapidly due to the small thickness of the
waveguide.
Table 1
Information on Towing Runs
Run Time (zone -IV), 1977 Length, Means Mean depth
~ velocity*, course, end1ofeDTS,
_ Beginning End km/hour degrees m
I 1545, 6 Sep 1804, 6 Sep 5.1 2.3 86 61
II 1915, 6 Sep 0746, 7 Sep 97.3 7.9 196 47
III 0903, 7 Sep 1848, 7 Sep 69.0 7.3 18 49
IV 2300, 7 Sep 1209, 8 Sep 94.3 7.2 232 51
V 1231, 8 Sep 0549, 9 Sep 116.8 6.8 226 52
- Another fact.of interest is that in the entire analyzed frequehcy range and in
all the above-mentioned segments the observed directions of the indicated waves
waves are limited to the northwest quadrant. Such a unidirectionality of the
:vave spectrum, registered with a driftin~ array, is all the more meaningfui
in that it contrasts sharply with the broad scatter of directions of waves
in trains encountered during the towing of the diatributed temperature sensor.
In Fig. 6 we illustrate these trains; the smoothed change in depth of the �
thermocline on runs II, III and IV is illustrated; sectors with trains to
which the entire run I is related (train A) are shown at a somewhat enlarged
scale. Their position in time and space is represented by segments of a
straight line over the axis of time and distances in Fig. 6 and by the ship
symbols in Fig. 7. The smoothed curvea of change in the depth of the thermo-
cline along the ship's course oa the counterruns II and III were matched so
that the time axis of run III was directed from right to left (dashed line)
- and the distance zero corresponds to the point of intersection of runs II,
III and IV (see Figures 3 and 7). The absolute depth scale is related to the
smoothed curves and to the train A(run 1); only the vertical scale is indi-
cated for the remaining trains. On run V, being a continuation of run IV and
not shown in Fig. 6, there was a further deepening of the thermocline to 39 m
with some rising (to~35 m) toward the end of the run. A peculiarity of run V
was the absence of clearly e.cpressed trains and a general decrease in the dis-
. persion of the high-frequency oscillations.
A comparison of counterruns II and III makes it possible to evaluate the time
variability of the smoothed depth of the thermocline. The characteristic flex-
ure of the thermocline, observed on both runs, was displaced to the north
* The table gives the velocity of antenna motion relative to the water since
it, and not absolute velocity, is important for excluding the Doppler effect.
28
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~y ~ O+ O ~1 +-1 O ~ O t~ r-I u1 ~
. . � . . . . . . .
y rl ta N ~-i rl N rl ~-1 rl ~-1 N N ~ 00 N
H ~ y.i u.�C ~ a 3
O ~ ~
~ w ~O O N O 1A GC O M M O W r-I Ci
~ N M ~ N ri ~~-1 r~-I ~ r~-1 M ~ 0~1 Ct
~ p ~ ~
~ ~ w ~
~ ~n ~ ~o n o~ n s ~ o 3
c) .t v1 �:7 M c~'1 0~ ~o e+~ ~n M q b~
� � � . . r .
l d .
V ~ O O O O~O O O O O O ~ N
OD ~ ~
~ rl O '
~ � dl ~rl
. d
~ V ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ � � � � � � � � � � w
4.1 v.C c+1 M M N P'1 N N'1 e'1 N N u~~N
N '~C
m q
. ~
Ma~~
m
~ 3 .
~ oo a M ~ � ~ � ~ q ~
H ~ ~ ~
N ~ ~ ~
n 1~ GO ~t C~ ~O
W c+~D ~ 1 ~N-1 ~ ~ , e~-1 +~-1 Ca C7 N
,a a a? d
~ o ~ ~ q
~ ~ x ~ ao ac co ao 00 00 �D ebo oa m
~ ~p N Cd N N N N C) G) ~
~ r-I r-I ~-1 , rl rl ~ ~ O W N
d
kl G ~t ~O O ~O O r"I O 'r~l i3 ~ N
U O~ c~'1 ~7 N 1'~ rl ~D ~rl ia ~
~ ri r-1 ~-I N r-I N e-I 04 Q. I-~
~ ~ ~ ~ ~
A ~ ~ e~ ~
1+ M 1~+ N F+ N N `Lf J 1+ C!
G! 4) C) d) N N 4) F+ O Gl O
~
~ d w~ a~
~ ~ ~ ~ w o, o ~r ~ o
i~� aai aai ~ o�'r a~'r d w m ~o
~0 ~ m v~ v~ tn a~ ~n m d,~ a? d
ae do~ . a ~
4~ ~.~j .~-I ~C ~C t~ 1~ 1~ I~ 00 ~ N
Q p V ~ w w ~w w w � ~ Q C) ld
~ rl N O ~7 O O ~ . N r-I ~~d U
_ E+ .G j N O ~-1 ~ ~ O a~.1 ~ W ~f
u1 ~ O~ ~ N ~ ~ ~ ~ ~ 00
u~1 O e'~rf O ~ N O .C m~'ri
~ N O ~-1 r-1 ~ ~
N W td
'I'~ ~ ~
~ ~ ~ ~
� Q~ .w
~~.1 N ~ 41
~
~ d oa c~ ca ~ w c~ z�~m~
~
29
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during the time between runs at a mean rate of 0.5 m/sec, which is too small
for i.nternal waves of such a length (100 km), which could be considered the
reason for the detected variability. Evidently here there are synoptic inhomo-
geneities of the thermocline tranaported by the current. Assuming that all the
other smoothed changes observed on runs I-V wer~.c~a~ssed by relatively slowly
moving synoptic inhomogeneities,we attempted to construct the pattern of depth
of the thermocline with time and at the place of towing, shown in Fig. 7.
We will now return to the trains of short waves A-G encountered during towing
and shown in Fig. 6. A common feature of these trains, consisting of several
waves, is the close affinity with a-marked deepening of the thermocline, which
resembles the situation arising during the nonlinear decay of waves over shal-
low water [4]. The highest waves (up to 3 m) were discovered on run I(train
A); the height of the waves in the remaining trains did not exceed 1.5-2 m.
(In a comparison of the apparent periods of the ~taves in different trains it
must be taken into account that the rate of towing on run I was 3-4 times
lower than on the ~~emaining runs.)
' General information on the trains and parameters of the waves, determined by
means of spatial-temporal spectral analysis by the maximum probability method,
is given in Table 2 and the correaponding wave vectors k are shown in the
form of arrows near the schematic representations of the ship in Fig. 6. As
a comparison, at the upper right we have shown a vector directed to the north
whose length corresponds to ~ k 0.5 cycle/l~. In those cases when the time
periodogram of the train contained not one, but two peaks close in value, as
was the case in trains D, E and F, two wave vectors have been shown, this re-
flecting the complex spatial-temporal atructure of the train.
The lengths of the waves in the trains for the moat part vary about 2 km; the
true periods on the average were close to a half-hour*. No direction can be
~ called predominant, in contradiction to the observations in ttie case of a
drifting array. The reason for such an inconsistency in the results must evi-
dently be sought in the spatial variability of the directions since the meas-
urements with the drifting arraq were carried out in a localized region,
whereas towing was carried out over a relatinely great area (see Fig. 7). In
particular, this is indicated by the good agreement between the directions of
the waves in trains B and F encountered during the time of towing near the
place of drift of the scientific research ship "Petr Lebedev" and measurement
data from the latter.
The d irections of the waves in different trains, registered with the towed
distributed temperature array, can be explained by a comparison of the ob-
served pattern with the relief of the thermocline (Fig. 7). In actuality, when
waves of any direction run onto a sloping thermocline their di.rection under
the influence of refraction will approach the normal to the thermocline iso-
baths, much as is the case with surface waves in the coastal zone. Refraction
* The high rate of towing (in comparison with the phase velocity of the waves)
is responsible for the low accuracy in evaluating the true frequency; this evi-
dently also explains the great scatter of the determined periods and phase vel-
ocities.
30
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occurs because the phase velocity C of the coneidered waves for all practical
purposes ie determined only by the depth of the thermocline, and not b the
total depth of the ocean. (In a two-layer case, for exam~le, C z~h dp/p,
where g is the acceleration of gravity, h is th~ depth o~ the imterface be-
tween layers with the densities /~l and p2, QP~ p2 - P~, f~~f~~, f~ 2� With
the observed differences in the depth of the ther.mocline the phase velocity
changes ~y 20X. This evidently also explains thg atable predominance of the
northwesterly moving wavea discovered by the acientific ~esearch ship "Petr
Lebedev,'~ which drifted near the steep slope~of~the thermocline, rising in this
direction.
If the height of the oncoming waves is not negl~g3t~le in comparison with the
depth of the thermocline the nonlinear eff~cte ~ietermined by the nonlinearity
- parameter a/h, where a is wave amplitude, ttecome important. This para-
meter, in essence, determines the.difference in velocities at the crest and ~
in the trough of an internal wave t:raveling along a shallow thern~ocline.
Since, in contrast to a.surface wa~~e in shallow waters, an internal wave is
not "braked" by the bottom, bu~ by, the ocean s~}r�face, its trough, more distant
from the surface, travels witti the velocity.C reater than the velocity of
the crest C~r, ~tr � 80p~h+a)/~D~ C~r i gQ,p (h-a)/~o , and overtakes the
crest, increasing the steepness of the rear slope of the wave. Finally, the
rear slope of the wave acquires the character of an internal front (bora),
accompanied by a singular train of short waves which are "released" by the
bora as it moves and graduallq lag behind it due to dispersion. A similar
phenomenon over~a sloping shallow bottom was ~xamined in [4] and has been ob- .
served repeatedly in nature (for example, see [5, 6]).
It is understandable that the described effecta are the ~tronger the shallower
the thermocline and possibly precisely for th~s reason the trains we~e not ob-
served on run V, where the thermocline depth$ w~re maximum (35-39 m) and the
slopes were minimum. Assuming the amplitude o~ the bora-forming waves to be
3 m, we obtain E = 3/22 = 0.14 (at the beginning of run I) and E~in = 3/39
= 0.08 (in the mi~~e of run V), that is~ the nonlinearity parameter changes by
almost a factor of 2 with a rather significant mean value. A definite role is
evidently also played by the decrease in the slopes of the thermocline because
the narrowing of the angular spectrum of waves, as a result of refraction, is
the weaker the lesser the slope of the thermocline and therefore whereas large
slopes of the thermocline lead to a refraction concentration of waves along
one direction (upslope) and thereby lead to an increase in the height of bora-
- forming waves, in the case of amall .slopes these effects are expressed to a
lesser degree, tha~ is, nonlinear phenomena a~.so attenuate.
In general, the following picture is obaerved: running onto a sloping thermo-
cline, the waves, under the influence of refraction, acquire a direction up-
slope and experience a nonlinear transformation, leading to the formation of
a bora and accompanying trains of ahort waves. Naturally, the direction of
the waves in these trains is close~to the dire~tion of the bora-forming waves
propagating up~lope. Such bora-forming waves can be pres~nt also in the back-
ground, possibly quasi-isotropic field of internal waves, which becomes ani-
sotropic, being refracted over irregularities of the thermocline. Precisely .
the anisotropization of the background field pv~er the thermocline, rising
31
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toward the northwest, evidently also explains the observed stable predominance
of northwesterly directions of the waves in a broad frequency range of a more
or less monotonically decreasing apectrum (see Figurea 4 and 5). The simultan-
eous existence of two systems of waves in some trains (D, E, F) agrees with
the earlier observed facts of a complex structure of the trains accompanying
the bora [5J.
The proposed hypothesis of a correlation of the trains of short-period inter-
nal waves frequently encountered in the upper layer of the ocean and the re-
lief of the thermocline finds indirect confirmation in the well-known facts of
intensification of such waves near fronts (for example, see [7]). It is inter-
esting that the considered mechaniam even explains such earlier-noted pecul-
iarities of short-period internal waves as the possibility of their quasi-
standing character, even under the conditiona prevailing in the open ocean
[1], to which must be added the refraction of ~ackground isotropic waves on
extended rises of the thermocline.
Thus, the phenomenon of formation of trains of powerful waves (related to the
shelf), in the case of nonlinear decay of an internal tidal wave in shallow ~
water, possibly has its analogy in the open ocean in the form of formation of
trains over the thermocline with a changing depth. Since synoptic nonuniform-
ities of depth of the upper thermocline occur widely, the development of more
or less significant trains of short-period internal waves, directed up the
slope of the thermocline, can be a frequently encountered phenomenon in the
ocean.
BIBLIOGRAPHY
1. Sabinin, K. D. and Serikov, A. N., "Spatial-Temporal Parameters of Short-
Period Internal Waves in the Indian Ocean~" GIDROFIZICHESKIYE I OPTICHESK-
IYE ISSLEDOVANIYA V INDIYSKOM OKEANE (Hydrophysical and Optical Investiga-
tions in the Indian Ocean), Moscow, Nauka, pp 13-27, 1975.
2. Sabinin, K. D., "Use of Distributed Temperature Sensors for Measuring In~
ternal Waves," POVERHIiNOSTNYYE I VNUTRENNIYE VOLNY (Surface and Internal
Waves), Sevastopol', MGI AN UkSSR, pp 134-145, 1978.
_ 3. Kozubskaya, G. I. and Konyayev, K. V., "Adaptive Spectral Analysis of Ran-
dom Processes and Fields," IZV. AN SSSR: FAO (News of the USSR Academy of
Sciences: Physics of the Atmosphere and Ocean), Vol 13, No 1, pp 61-71.,
1977.
4. Lee, C. Y. and Beardsley, R. C., "The Generation of Long Nonlinear Internal
Waves in a Weakly Stratified Shear Flow," J. GEOPFIYS. RES., Vol 79, No 3,
pp 453-462, 1974.
5. Ivanov, V. A. and Konyayev, K. V., "Bora in the Thermocline," IZV. AN SSSR:
FAO, Vol 12, No 4, pp 416-423, 1976.
32
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6. Apel, J. R., Bqrn, H. M., Proni, J. R. and Harnell~ R. L., "Observations
of Oceani,c Internal and Surface Wdvea ~rom F~arth Resources TechnolQgy
Satelllite," J. GEOPflYS. RES., Vol 80, No 6, pp 865~8$1, 1975.
7. Beckerlq, J. C., "Doppler 3hifted Internsl Waves Relative to a Tower Sen-
sor in a Thermal Front Region," DBEP SEA RE9., Vol 22, Na 3, pp 197-200,
1975.
COPYRIGHT: Izdatel'stvo "Naulca", "Iznsstiya AN 89SR, Fizika atmoafery i
okeana", 1982
5303 ~ '
CSO: 1865/152
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UDC 551.461
EFFECT OF SELF-ENHANCEMENT OF GRAVITATIONAL ANOMALIES IN GRADIENT MEDIA
Moscow DOKLADY AKADEMII NAUR SSSR in Ruasian Vol 263, No 5, Apx 82 (manuscript
received 22 Oct 81) pp 1092-1094 .
[Article by S. S. Ivanov, Institute of Oceanologq imeni P. P. Shirshov, USSR
Academy of Sciencea, MoscowJ
[Text] One of the promising directions in the development of marine geophysics
at the resent time is the atudy and allowance for the influence of aome fine
effects~~ising due to different proeessea in the water layer of the ocean.
This direction can also be traced in such methods as magnetometry [1] and
gravimetry [2, 3] which in the past have traditionally not taken the influence
of the water layer into account. Isi this article we wish to note one effect
not described earlier asaociated with the restructuring of the density atruc-
ture of the ocean water layer in the anomalous gravitational field.
We will visualize that in a homogeneous. gravitational field characterized by
a constant vertical potential gradient (a U/ d z= const = r) and, accordingly,
by parallel and equidistant equipotential surfaces,there is some inhomogeneous
medium of a low viscosity in which for some reasona (thermal factors, compres-
sibility in the gravity field, etc.) ther~ is a vertical density gradient whose
value will also be considered constant (d d/dz = conat). Surfaces of equal den-
sities (isopycnic surfaces) will coincide with the isopotential aurfaces, that
is, in this case will be represented by horizontal planes (Fig. 1). At some
poi~t in this medium we will place the origin of coordinates (the z-axia is
directed vertically down~~ard) and at this point we will place the valuea of
the gravitational potential and density respectivelq Up and 6"~. Then for each
point in the medium these values wi11 be expresaed as
U . (/o + 7s, o ~ ao + ~dv/dt) s. - - -
We will examine what will occur if at the origin of coordinates we place some
point mass M, which we call an ano~ealy. Its�~appearance givea riae to an anom-
alous gravitational field having the potential W= fM/r (where f is the gravi-
tational constant, r is the distance to the orig~n of coordinates) and the
gravitational acceleration G\ga =-fMz/r3. In turn. the appearance of anom-
alous potential leada to the vertical di~placement of isopotential surfaces by
the value ~ R= -Wa/(Y+ Q ga). The isopycnic surfaces are displaced by the same
value, due to the low viscosity of the medium following the isopotential aur-
faces. As a reault o~f this, at each point in the mrdium there will be an in-
crease in density cauaed by diaplacement of the isopycnic line by the value
~ 34 ~
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~d ~-~(dd/dz) and accordingly there will be an elementary additional mass
dm = ACfdv. The total additional maee will be determined by integration in a
_ volume bounded by a sphere of some finite radius R. Introducing the natural
assumption that d ga ~ we obtain
M. s I!I dz 1!! ~ du 2~rR~ ds . (1)
R 9' R 'Ir
Expression (1) shows that the appearance of the anomaloue mass M in the gradient
medium causes a restructuring of the density fie~.d and the formation because of
this of the additional mass m, whoae value is dependent on the M parameter, and
also on the extent of the region occupied by the medium, as well as the value
of its denaity gradient. The influence of this additional mass is expressed
in the appearance of an additional gravitational field, spherically sqaimetric
and concentric with the anomalous field of the mass M and having the potential
Wadd s fm/R and the acceleration a 8add '-fmz/R3.
d-LO?_..~....._._._~,.:. ~y-t1�
~ /P _ di
d r
t
~ i
l(r+dU ....r.. ~+/r
~+llr
~ r.
Fig. 1. Vertical section of gradient density medinm in gravitational field. The
dot-dash lines represent isopotential (and isopycnic) surfaces corresponding
to a homogeneous field; the solid lines represent the same in the presence of
' an anomaloua mass M; the dashed linea represent isolines of anomalous poten-
tial.
Thus, it appeara that the gravitational field of an anomalous mass (potential
and its derivatives) in a gradient medium aomewhat exceeds in its intensity a
field of the same mass in a medium homogeneoua in density. Since this effect
arises due to a corresponding organization of the medium occurring under the
influence of the anomalous mass itself~ we called it the effect of self.-en-
hancement of gravitational anomalies in gradient media.
Two circumatances should be emphasized. First, the noted affect arises in both
gradient and in density-stratified media, in a limiting case in a two-layer
medium. The sole condition for the appearance of the effect in this case is
that the viacoaity of matter muet be sufficiently small that the deneity boun-
daries will adhere to the equipotential surfaces of the gravity field. Second,
this effect also arises in a case when the anomalous mass is situated outside
the gradient medium. In other words, the additional masa in the gradient or
stratified medium arises under the influence of any gravitating ob~ect dis-
rupting the homogeneity of the field in this medium.
35
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It followa from the cited computations that the following expression will be
- correct at the boundary of the spherical region
_ . _ _ _ - ------r--------------... - -
~ [ n 0 TC = add ] Wnoe s 4~-,
~�n ~?n s~aj d� Rs
_ W~ t~~ '~I( 7 dz
This expression makes it posaible to evaluate the described effect in some
specif ic cases. In particular, we w9.11 examine ita possible manifestation in
an ocean whose water thickness can be represented as a gradient medium in den-
sity respects.
Assuming for d d/dz a value 1�10-6 g�cm 4(frequently observed in the ocean,
although somewhat exaggerated for the water layer as a whole) [4], we find
that for R= 5 km the relative self-enhancemsnt of gravitational anomalies at '
the ocean surface should be about 1�10'4, that is, O.Oly (an anomaly of 100
mgal is intensified by 0.01 mgal). This value, to be aure, is too small to be
of importance for experimental gravimetric investigations in the ocean. How-
ever, for oceanological practice another aspect of the deacribed effect can
be important, specifically, the increase in the denaity of sea water horizon-
tally in the direction of.greater values of the anomalous gravitational field
necessary for its appearance.
Elementary computations show that the free-air anomalies observed at the ocean
surface with a characteristic amplitude of 50 mgal [5] correspond to an incre-
ment of gravity potential in the water layer of about 1�105�s~c-2, that is, the
magnitude of displacement of the isopotential (and isopycnic) surfaces is about
10~ cm. With the above-mentioned sea water density gradient (~ertically) th'_s
gives a density increment (horizontally) of about 1�10'4 g�cm3 or in the first
_ place after the decimal point in the so~called nominal density of sea water
(a parameter adopted in oceanologq and equal to Q'q =(Or= 1)�103 g�cm 3).
Such changes are extremely significant and without question can be detected
during hydrophysical measurements in the ocean and taken into account in com-
puting currents by the dqnamic method [6, 7]. It should be noted that there
are some still unpublished data on the preaence of a quite close correlation
between the density values for sea water at different horizons and gravity
anomalies (A. M. Boyarinov, S. V. Protsay,enko~ personal communication); these
can serve as unques.tianable. .su~g.o~t.~n...favflr of the existence of 'the- self-en-
hancement effect for gravitational anomalies in the ocean.
An important feature in the appearance of the deacribed effect in the ocean is
that gravitating objects, including those situated deep beneath the ocean
floor, lead to the forming of an inhomogeneous structure of isopycnic (and ac-
cordingly, isobaric) surfacea in the water layer, as a result of which there
are unequal conditiona for the passage of water masses associated with gravi-
tational anomalies. It is easy to see that more favorable conditions for this
prevail in regions where the distance between these surfaces is maximwn, that
is, in places where the additional gravitational potential is minimum. In this
connection it can be expected that ocean currents in princinle 'should ~ravitate
toward regions of negative gravitational anomalies. This effect probably should
be manifested more atrongly for weak cu-rents having a relatively small kin-
etic energy and most strongly for the tra3ectories of movements of isolated
36
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water massea, such as individual ocean eddiea.
It follows fram what has been said that the eff~ct of s~~f-enhancement of grav-
itational anomalies must be a~nifested most clesrly in the oce&n, A atudy of
this effect and its corollaries by hgdrophysical methods will be o~ great im--
~ portance for dynamic oceanalogy.
BIBLIOGRAPAY
1. Sochel'nikov, V. V., OSNOVY TEORII YESTESTVFNNOGO ELEKTROMAGNITNOGO POLYA ,
V MORE (Principles of the Theor�q af .the Natural Electromagaetic Field in
_ the Sea), Leningrad, Gidromet~oizdat~ 1979.
2. Ivanov, S. S., DAN (Reports of the USSR Aaademy of 3ciences), Vol 253, No
2, p 312, 1980. ~
3. Demenitskaya, P. M., Ivanov, S. S. and Litvinov, E. M., YESTESTVENNYYE FIZ-
ICHESKIYE POLYA OKEANA (NatuY'al Phyeical Fi~lds in the Ocean), Leningrad,
Ned~'a, 1981.
4. OKEANOLOGIYA. FI ZIKA OKEANA. GIDROFIZIKA OREANA (Oceanology. Ocean Phys-
ics. Ocean Hydrophysics), Moscow, Nauka, 1978.
5. Dehlinger, P., MARINE GRAVITY, Amaterdam, Oxford, N. Y., 1978.
6. Zubov, H. H. and Mamaev, 0. DINAMICHE9~IY METOD VYCHISLENIYA ELII~ENTOV
MORSKIKH TECHENIY (Dynamic Method for Computing the Elements Qf Sea Cur-
rents), Leningrad, Gidrometeoizdat, 1956.
7. .Burkov, V.A., OB SHCHAYA TSIRKULYATSIYA MIROVOGO OREANA (General Circula-
tion of the Warld Ocean), Leningrad, Gidrometeoizdat, 1980.
~ COPYRIGHT: Izdatel ~ Stvo "Nauka~~~ "Dokl,ady Alcademii nauk SSSR", 1982
5303
CSO: 1865/147
37
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- . UDC 550.348.432
SEISMIC NOISE AT OCEAN FLOOR
Moscow DOKI,ADY AXADII~SII NAUK SSSR in Rusaian Vol 263, No 5, Apr.82 (manuscript
received 14 Dec 81) pp 1098-1],O1
[Article by Yu. P. Neprochnov, V. V. Sedov and A. A. Oetrovskiy, Institute of
Oceanology imen3 P. P. Shirshov, USSR Academy of Sciences, Moscow]
[Text] Recently seismic investigations in the ocean have been requiring use of
increasingly more complex observation sqstems, including up to 10 or more bot-
tom seismographs. The rational planning of these extremely costly experiments
requires information on the level and ~pectral compoaition of bottom seismic
noise, limiting the effective reaponse of receiving-recording apparatus situ-
ated at the ocean floor or near it. The vigorous development of technology and
the method for aeismic investigationa with bottom seismographs during the last
20 years has favored the registry of bottom noise phenomena in the USSR
and abroad [1-5]. However, this information, obtained by the scientists of
different countries with the use of various kinda of apparatus, with the use of
different processing methods and forms of representation of the noise spectra,
is difficult to compare and is frequently contradictory.
At the Institute of Oceanology, USSR Academy of Sciences, seismic investigations
with bottom seismographs have been carried out since 1965. Although the prin-
cipal purpose of theae studies was deep seismic sounding of the earth's crust .
and upper mantle, incidentally extensive material on bottom noiae was obtained
in the frequency range 2-20 Hz. The investigations covered all the principal
tectonic structures of the floor of t4~e world ocean internal and marginal
seas, ocean basins and major rises within their limits, mid-oceanic ridges and
the areas surrounding them, and block ranges. The observations were made under
the most diversif ied hydrometeorological conditions. Noise was registered using
instrumerits of the same type (bottom seismographs designed at the Physics Fac.-
ulty of Moscow State University and the Inatitute of Oceanology, USSR Academy
of Sciences) and procesaed by the same method, making it possible to carry out
- a~oint analysis and statistical processing of the experimental spectra.
The analysis was made using the 59 most representative magnetic records of seis-
mic noise obtained on expeditions of the Institute of Oceanology, USSR Academy
of Sciences, during the period from 1973 through 1979. The distribution of these
records by research regions is ahown in-Table 1. The bottom seismographs were
placed at depths from 210 to 6520 m. The duration of the continuous registry at'
the bottom varied from 1 to l0 days, depending on the purpose of the experiment
. 38
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~ i
c~ .cr ~o ~c ~a ~o ~n r� ~ ~ oo v~ eo o~ o+ o~ ao
a? t~ n ~~r~ ~t~ t~ ~nnnt~t~~ ~
~ a~ o+ o~ a~ o~ o~ a~ c~ o? c? o~ o, c~ o~ a~ a~ o~ v+
~ a+ ~ ~ ~.1~ ~ ~ ~
H ,
~
c~
,a ~
~
ai
p i+. ~ ~ ~ ~ r. in
a ' M 1~ O ~t ri M ~'r1 e-I
N rl N e-I N N N N N
y~ ~ v v ~ v vv v v
dJ ~
~ 3 - - - - - - - - -
N u~ ' O d O O d d d d d
,~~1 c~d 0~0 O ~q~ W ~ ~e~ C~! d CA1 N d
O N d! r-I .C ~-1 ~ .C .-1 e-1 r-1 e-1 ~-1
bl rl U 4l t~ C~ ' d N C) Gl Gl
W O 9 1~+ '17 OO F~ 1+ 'H 'iC 'd 'C!
~ ~ q d G~l
~ ~J W ~ ~ ~i ~ ~ ~ ~ ~"i r~'
O 4~-~ ~ ~ ~ ~~rl p~ r~l i+~ 'i+ D+ D~ P+
ca p ,a N ,a ~ r~ ,i
N ~ ~ d 1~+ RI ~ N 1~+ N H F+
W Fi ..O 'C) '!i ~�1 D+'d 'C7 i.~ 1.~ 1.~
~ ~ ~ ~ ~ 'f~ ~ ~ ~ 'P~ '1"~ ~ y'~ Q)
~ ~v ~ ~ p~ ~ ~ ~~~~v~~ ~
~ -
0
u
a~
04
~
u
~ .
`3 0 .
a~
r~l N~ e-1 N1 r-1 r-i ~i r-1 r-I rl Crf N1 N N N 1~ ~7 ~/1 ~t N ri
.C O r1
o z ~
~
~
ti-~I OQ? ~7 v1~O~O N
q ~t e'~'1 ~t ~O v'1 N ~r1 u1
~ ~ ~o^~ooooao a o0 00 ~,o 0
.G' 0000~1~OOe-1000 N 00 ~oC~O MO O
H a ~1 N N~~ ~-1 N c~~1 M ~S ~T ~1 Crf ~ N u~1 ~ ~'~1 e'~~1
N
~ig A
~
bD ~
N Cy
V1 N ~0 d
00 i~ i~ ' OJ
� a~ ~ ~ a ~
~ o�~o`~o�~o`~a�~oa ~
o a? b d v~ a~ ao a? `a~
a~i o ~ oa"~ ~~~a.o c~ ~ ~o ~a~o ~
a,~ ~ a~a+ u u uao um ~u.~~u~
00 /b t0 t/~ O rl W rl 4~1 ~rl Gl rl H YI ~ 1+ ~1 rl
CI Cl N i~ O~�1 O 1.~ H W P4 Cl 4~ t0 Ol W rl
~ a v~ ~ a~ a a a a~ w~,~ o
~ G ~p e0 CS ~0 C7 td ~ CJ m OQ u o~ u~+
t/~ q a~ ~ fJ .-I O rl O~-I i~ cd rl r1 N ed H etl ~~d
co eo r~ ,i a+ ~ a.~ r~4 3 a o a? w c~
aa a a3? o d oo ~ oo d o~ oo .c H.c
~ ap'i ~c~ 1+ m~oaba~4b ~w a~'o" o ag?~+ o a~i
~ V P~1?~. ~ ~ ~ W~.~dZ ~
- 39
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- and the method used. The seismic noise was analyzed on segments of the records
of bottom seismographa with an extent of about 3 minutes, free of seismic
waves caused by known artificial and natural sourcea (shots, pneumatic radia-
tions and ship's noise during deep aeismic sounding in the region of the exper-
iment, earthquakes).
_ _ _ _ _ _ -
_ .
W,c~�c'~�fu"Nt c~�sec'~..gZ-1/2 _ .
10"f
2 w~~M.~-1.~u-t~t , -1. ~i/2
'~_6 ~~-f ~ W,cw�~ f4 cro sec FIz
� ~
ti
~o- : a ~o-~ r ~
_ ...r~ k ,
. Z 2
e
~o- ~ ro~,ra ~~Z 10 ~ io f r� xZ ~~0~ r ~?o f rv
~ Fig. 1. Fig. 2. Fig. 3. ~
Fig. 1. Statistically mean (1), maximum (2) and minimum (3) spectra of bottom
seismic noise in frequency range 2-20 Hz; 4) spectrum of bottom seismograph
amplifier noise.
Fig. 2. Dependence of inean level of bottom seismic noise on thickness of uncom-
pacted sediments in neighborhood of placement of bottom seismograph. 1) thick-
ness greater than 300 m; 2) thicknesa leas than 300 m.
Fig. 3. Dependence of inean level of bottom seismic noise on measurement season;
1) spring and autumn; 2) su~er.
The spectra of bottom seismic noise were obtained uaing an analog 1/3-octave
spectrum analyzer, type NR-8054A, which makea it possible to obtain the square
' root of the spectral denaity of intenaity of the inveatigated signal W in the
frequency range 1-60 Hz. The relative error in computing W averaged ~ 30X with
a reliability coefficient 0.95, which wae adequ~~te for the purposes of this
study.
Most of the registry pointa constituted a group of bottom seismographs situat-
ed in a particular research region, but the groups ~themselves were spaced quite
widely, which makes it possible to ~udge the characteristics of bottom noise
40
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not only of individual na.rts, Lut also of the entire world ocean.
Figure 1 shows the statistically mean spectrum generalized for all the deter-
- mined values. The spectral density values at frequencies of 2, 3, 4, 6, 8, 10
and 20 Hz were computed as the mean arithmetical value of 59 individual spec-
tra. Also shown are the envelopes of the minimum and maximum spectral density
values at the mentioned frequencies and the noise spectrum of the mentioned bot-
tom seismograph amplif ier. The mean spectrum has a minimum at a frequency of
10 Hz, where the spectral density is 4.5�10'~ cm�sec'1�Hz-1/2. In the direc-
- tion of the low frequencies the noise level increases sharply and at a fre-
quency of 2 Hz its mean spectral density is 7.5�10'6 cm�sec"1�Hz"1~2; there
is also a relatively small rise in the level of bottom reoise in the direction
of the high frequencies. The mean curve agrees well with the apectra obtained
by T. Asada and H. Shimamura [5].
Figure 1 shows that the deviations of the spectra of real noise from the stat-
istical mean can be significant (for the limiting case by a factor of 6), tak-
ing in a range of 1-1.5 orders of magnitude. The lower curve is at the level
of weakest bottom noise registered earlier and analyzed by D. D. Prentiss and
J. Ewing [2]; the ~ange of change of spectral density for it was from 10-6 to
5�10-8 cm�sec'1�Hz`1~2 at frequencies of 2 and 10 Hz respectively. The upper
curve passes.near the spectra obtained by L. N. Rykunov and V. V. Sedov [1]
and the lowest spectra in level, obtained by H. Bradner [3].
The results of observations in regiona with different seismogeological condi-
tions made it possible to analyze the dependence ef the level of bottom noise
on the thickness of the sedimentary cover at the registry points. ~ao mean
spectra were computed for this purpose: one of these was obtained using data
from the registry of noise in regions with a thickness of sediments less than
300 m(0-300 m)~ whereas the other was based on data for regions with a thick-
ness of sediments greater than 300 m(300~4000 m). Information on the thick-
ness of sediments in the regions of placement of bottom seismographs was ob-
tained using materials from continuous seismic profiling and deep seismic
sounding on corresponding expeditions; the sedimentarq stratum includes rocks
with velocities of propagation of longitudinal waves not greater than 2.5-3.0
km/sec. The limiting value for the thickness.of sediments of 300 m was select-
ed because it divided the available archlves of 59 spectra approximately in
' half. This made it possible to compute the mean spectra with a greater accur-
_ acy than each individual spectrum, thereby making it possible to consider the
difference in the resulting mean apectra to surpass the errors in measuring
them. Figure 2 shows that the mean level of bottom seismic nvise increases
with an increase in the thickness of the sedimenta at the registry point;
this dependence becomes clearer for the high~frequency noise components. The
dependence of the level of bottom noise on the thickness of sediments agrees
with the results of a study by G. V. Latham and C. H. Sutton [4J, where it
was noted that the presence of unconsolidated aediments on the ocean floor
leads to a concentration of seiamic energy in this layer and a considerable
increase in the level of bottom noise.
We also analyzed the dependence of the mean level of bottom seismic noise on
hydrometeorological conditions. As a point of departure we used the well-known
fact of an intensification of cyclonic activity in the oceans in autumn 4nd
41
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spring in comparison with the summer period. A study of the experimental data
indicated that in many cases more intense but briefer changes in the noise
level caused by other factors (bottom currents, sea transport, etc.) are super-
posed on seasonal fluctuations of the mean noiae level. Thus, the averaging of
the 59 spectra at our disposition ~nade it possible for each frequency to dis-
criminate "long-period" fluctuatic~ns of bottom nois~ (period of about 3 months)
of a low intensity against a backp,round ~f its more intense and briefer varia-
tions. Figure 3 shows the mean spe,:tra for spring and autumn (averaging for
24 spe~tra), and also for summer (a~~eraging for 35 spectra). It can be seen
that during periods of intensif icatic.~ of cyclonic activity in the oceans the
mean level of the bo~.tom seismic noise i~zcreases by a factor of approximately
_ 1.5 in the investigated frequency range. The influence of a local cyclone on
the level of bottom seismic noise directly in the region affected by a cyclone
was examined in a separate study [6].
In order to refine and supplement the dependences between bottom seismic noise
on seismogeological and hydrometeorological conditions which have now been
clarif ied it is necessary to recommend the formulation of planned expedition- ~
ary investigations of this problem, preferably in a broader frequency range
(from 0.1 to 100 Hz).
BIBLIOGRAPHY
1. Rykunov, L. N. and Sedov, V. V., IZV. AN SSSR: FIZIKA ZII~I (News of the
USSR Academy of Sciences: Physics of the Earth), No 7, pp 30-39, 1965.
2. Prentiss, D. D. and Ewing, J., BULL. SEISMOL. SOC. AMER., Vol 53, No 4,
pp 765-781, 1963.
~3. Bradner, H., Dodds, J. G. and Foulks, R. E., GEOP~IYSICS, Vol 30, No 4, pp
511-526, 1965.
4. Latham, G. V. and Sutton, C. H., J. GEOPHYS. RES., Vol 71, No 10, pp 2545-
2573, 1966.
5. Asada, T. and Shimamura, H., "The Geophysics of thz Pacific Ocean Basin and
Its Margin," AMER. GEOPHYS. UNION, GEOPHYS. MONOGRAPH, Vol 1~, p 286, 1976.
6. Ostrovskiy, A. A., Manuscript deposited at the All-Union Institute of Sci-
entific and Technical Information, No 3056-80, 1980, 14 pages.
COPYRIGHT: Izdatel'stvo "Nauka", "Doklady Akademii nauk SSSR", 1982
5303
CSO: 1865/147
!~2
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~ UDC 551.465
INFLUENCE OF TURBULENCE INTERMITTENCE ON FORMING OF OCEAN SURFACE STRUCTURE
Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 263, No 5, Apr 82 (manuscript
received 3 Aug 81) pp 1225-1229
[Article by V. S. Belyayev and R. V. Ozmidov, Institute of Oceanology imeni
P. P. Shirshov, US SR Academy of Sciences, Moscow]
[Text] Ocean turbulence, together with other factora, plays an important role
in forming of ocean surface characteristics. Turbulent heat con~uctivity of
water is one of the important parametera determining ocean surface tempera~
ture. Turbulent velocity fluctexationa, interacting with wave monements of
fluid, exert an influence on roughness of the water'surface. However, the con-
cepts concerning the discontinuous distribution of turbulence in the ocean pre-
vailing only recentlq should lead to~the conclusion that there is a uniformity
- of these manifestations of turbuleace over great expanses of the ocean.'But ex-
tensive obaervations of ocean turbulence carried out during recent years have
shown that it is characterized by a strcng intermittenee: zones of turbulent
fluid alternate in the ocean with eect:ors in which the observed ~regi~e of water
motion is close to laminar [1]. In this coanection, manifestations of turbu-
lence at the ocean surface should have a"spotty" structure which, in general,
can be detected by both contact and remote methods.,
In [2] the author proposed a model of ve~tical turbulent exchange in the ocean
in the presence of turbulence intermittent with depth. According to this model
the mean value of the coefficient of vertical exchange K is described by the
expresaion ~
f f ~z A P~h. v) dhd#~'~ ~1)
, o: 'o . -
where h is the thickness of the turbuleat layer of fluid, d is the intensity
of turbulence in the layer, p(h,Cf) is the ~oint 'probat~il:ity dfstribution func-
"tion of the parameters h and d, nl ia the mean number of the turbulent layers
in a unit interval of depths (the Poiason 1aw parameter for the distribution
of turbulent layers in the ocean), c is.a dimensionless universal constant of
the order of 0.1.~Usin~, th~ presently availa:ble experfinental data on the '
function p(h, d) and the parameter nl ia [2] the authors obtained evaluations
of the K yalues varying for different regions of the ocean from a few to sev-
eral tens of cm2/sec. Fle note that expression .(1) for.K was obtained in [2],
in essence under the condition of smallness of the lifetime of the turbulent
43
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layers in comparison with the characteristic time of propagation of passive
impurities in the upper layer of the ocean. '
We will evaluate the possible statistical scatter of the K values caused by
the turbulence intermittence effect. In the case of a Poisson distribution of
turbulent layers with depth the dispersion of the coeff icient of vertical tur-
bulent exchange . _ _
D~(K) = c~n~ j j hso1 poh (o. h) dvdh
0 0 ~2~
and evaluations of the mean square scatter of K values in accordance with
formula (2) with the use of the experimental data enumerated in [2] in order of
- magnitude constitute K.
We will examine how variationa of the coefficient of vertical turbulent exchange
are manifested in the temperature field of the ocean surface. We will consider
the coefficient of turbulent thermal diffusivity K,r to be proportional to the
coe~f icient of turbuTent exchange of momentum K with the proportionality fac- '
tor oc- (of the order of 0.1) and we will examine the nonstationary problem of
the propagation of heat from the surface into the depths of the ocean, describ~
ed by the equation
aT � ' a~T � ~
: ~ ~ .�x ,
ar az' t3>
where T is water temperature, z is the vertical coordinate with the origin of
coordinates at the ocean surface, t is time, reckoned from some initial time
t~ = 0.
= As the boundary conditions for equation (3) we will assume that
0 .�~~.ar~; . t < to = 0
aK aT = ' ; T(z, t) =.0, (4)
aZ Z=o _~~cpp ~~~~r a r, =o x~_
here q is the heat flow through the ocean surface, P is water density and CP
is its heat capacity at a constant pressure.
Since we are interested in the deviations of temperature from some equilibrium
distribution, then, without reducing the universality of the problem, we will
assume an initial temperature distribution in the form
_
T(s, 0) = 0. (5)
The solution of equation (3) with the boundary conditions (4) and the initial
_ condition (S) has the form
. _ -
~ ?Q ~ 1 ~
. T z, t) = exp ) - 3' I 1 - ~erf ~I ~ , ~ 6 )
Cp P~ V n 1
where
~1
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2 3' , z
~ erf = j e-~ d~; _ .
. ~ 0 2 aKt
and for the ocean surface
_ 29 ~ .
T(O,t) _ '
Cp p iraK '
Figure 1 shows curves of dependence of ocean surface temperature on time with
several values of the coefficient K,r + a K, T1~e values of the determining para-
meters for the computations were: q= 10-3; 10-4 cal/cm2�sec (the left and right
scales along the y-axis),p = 1 g/cm3, Cp = 1 cal/g��C. With the course of time
the range of temperature change of the acean surface with different KT values
exnands~ for example, with t= 1 hour it is 0.02-1.81�C, and with t= 10 hours
it is already 0.07-5.72�C.
The depth of penetration of disturbances of the temperature f ield z~ is deter-
mined from the condition
T(~o.
T~O~ l~ = 0,01. ~ 8 )
It follo~as from (6) and (7) that
T~~D~f~ = exP~-fo)- 1~~'o II -erf3'o)� ~9~
From (8) and (9) we find the solution
zo = 3,21 aKt. - - - - (1~>
i
't ~ T; C
~4�10~~
5 0,5
~ O,d
10'Z
1 0,1
as --10-~ 0,05
q~ O,UJ
!0�
at 10~ a01
0 1 4 6 L t,v hours
Fig. 1. Anticipated deviation of the ocean surface temperature from an equil--
ibrium distribution for different coefficients of turbulent thermal diffusivity
_ ICZ, = OC. K.
45
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In accordance with (10), with a variation of KT and t in the ranges from 1.4�
10-3 to 101 cm2/sec and from 1 minute to 10 hours the z0 value varies in the
range from 0.9 cm to 19 m, as a result of which the adopted boundary condition
(4) with z--?oo must be co~sidered justified.
Thus, the scatter of values of the coefficient of vertical turbulent exchange
caused by the intermittence of turbulence can lead to substantial variations
of ocean surface temperature (the model considered above, not taking the hori-
- zontal nonuniformity of the temperature field and horizontal turbulent heat
exchange into account, can be used because the horizontal dimensions of indi-
vidual turbulent zones in the ocean are usually much greater than their thick-
ness). And since there will alternately be more and then less turbulent layers
of fluid in different regions of the ocean near its surface, the temperature
f ield of the ocean surface acquires a"mosaiced" structure. Accardingly,
the temperature drops between adjacent spots in such a structure will be de-
pendent on the differences in the turbulence levels in the surface layers of
the ocean and on the lifetime of ~the turbulent layers. Evidently, 1 hour can
be used as the characteristic (in order of magnitude) lifetime of the approx-
imately constant turbulence level in individual layers. Then with molecular
vertical heat exchange in one of the ocean zones and with a value KT = 10 cm2/
sec in the adjacent zone the drop in surface temperature between these zones
Q T attains 1.8�C. However, if in one zone ICT = 1 cm~/sec, and in the other KT
= 10 cm2/se:c, ~ T after the elapsing of 1 hour will be only 0.046�C. With quite
typical values KT = 0.1 cm2/sec in one zone and KT = 1 cm2/sec in the other ~ T
attains values 0.15�C. According to [3], the typical dimensions of spatial in-
homogeneities of ocean surface temperature in the ocean in calm weather are
1-10 km, whereas the temperature between adjacent spots can differ by 1-2�C.
However, according to observations made in a number of regions in the North
Atlantic under different weather conditions, the typical L~ T values at dis-
- tances of about 1 km were ,d T= 0.04-0.20�C [4].
The different turbulence of the upper layer of the ocean must also exert an in-
fluence on the characteristics of surface waves. True, in most cases the waves
themselves are the principal factor in the turbulence of this layer and there-
fore they must be in some dynamic equilibrium with the turbulence generated by
them. However, if turbulence is generated by other factors (such as shear in-
stability of the current) or the boundary of some turbulent l~yer under the
influence of diffusional or advective processes advances into the zone occupied
by wave motion, there will be a process of interaction between waves and such
"external" turbulence. If there is a gradient grad E in the layer of wave move-
ment,in the density distribution of the energy of potential wave movement E a
tloca of ~~ave energy arises which is directed against the gradient and is equal
to [5]
j = -K~ grad E, (11)
where KE is the coefficient of exchange of wave energy, which can be considered
equal to the coefficient of turbulent exchange of momentum K.
Thus, "external" turbulence causes an outflow of wave energy in a downward di-
rection, which should lead to an attenuation of surface wave amplitude. Such
an effect of extinction of gravitational waves due to strong interaction with
l~6
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"external" turbulence wae noted for the firet time by G. I. Barenblatt [6, 7].
'P~IE: (�hange in the F parameter with time can be described by the equation
aG _ . 82E
ar ~s x a~~ ' (iz~
With the boundary conditions
8E I - - -
8z :=o - ~ I:~� - ~ ~13~
- and the initial density distribution of wave energy with de_:rth
E (z, 0) = Eo exp (-az) ~14 ~
the solution of equation (12) has the form
(z. t) = 1
E Eo. j eXp - (2 - + exp - ~z + exp ~15)
2 n t a [ 4Kt, 4Kt
and with z= 0 from (15) we obtain
I:'(U, t~ = Eo exp (~2 Kt) [ 1- erf Kt) (16)
Table 1
K, cm2 � sec-1 , m
10 5 1 0.5 0.1 0.05
102 43.8 min 10.9 min 26.3 sec 6.57 sec 0.263 sec 0.0657 sec
1Q1 7.30 hrs 1.82 hr 4.38 min 1.09 min 2.63 sec 0.657 sec
.10~ 73.0 hrs 18.2 hrs 43.8 min 10.9 min 26.3 sec 6.57 sec
10'1 7.30 hrs 1.82 hr 4.38 min 1.09 min
_ 10'2 73.0 hrs 18.2 hrs 7.30 hrs 10.9 min
- It can be assumed approximately that a decrease in the amplitude of a wave with
the length _L occurs at a depth equal to ~./2; in this case the energy decreas-
es by a factor of e at the de~;~~ 1./4. On the basis of expression (16), Table 1
gives estimates of the time intervals T during which the energy density of sur-
face waves is reduced to one-quarter of the initial energy density Ep. Depend-
ing on the value~of the K coefficient and the ~ parameter (Table 1 gives the
corresponding values 4/~1) the time interval ~ changes in a wide range;
the attenuation of the short-wave part of the wind wave spectrum occurs most
rapidly in this case. Such an effect should lead to the "spottiness" of the
wave field at the ocean surface.
There are a number of assumptions and simplifications in the constructions cited
above. In particular, in a model of vertically intermittent turbulence the as-
sumption was made that there is a statistical uniformity of the process, al-
though the upper layer of the ocean is usually more turbulent than the under-
lying water masses. The schemes for computing the influence of intermittent
47
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turbulence on surface temperature and sea wavea are also simplified.
We note in conclusion that the determined orders of magnitude graphically il-
lustrate the important role of the turbulence intermittence factor not taken
into account up to the present time in the forming of the structural features
of hydrophysical fields in the surface layer of the ocean.
BIBLIOGRAPHY
1. Monin, A. S. and Ozmidov, R. V., OKEANSKAYA TURBULENTNOST' (Ocean Tur-
~ bulence), Leningrad, Gidrometeoizdat, 1981, 320 pages.
2. Belyayev, V. S. and Ozmidov, R. A., DAN (Reports of the USSR Academy of
Sciences), Vol 254, No 4, p 995, 1980.
3. Fedorov, K. N., Ginzburg, A. I. and Piterbarg, L. I., OKEANOLOGIYA (Ocean-
ology), Vol 21, No 2, p 203, 1981.
4. Karabasheva, E. I. and Pozdynin, V. D., IBID., Vol I8, No 4, p 614, 1978.
5. Benilov, A. Yu., IZV. AN SSSR: FIZ. ATM. I OKEANA (News of the USSR Academy
of Sciences: Physics of the Atmospliere and Ocean), Vol 9, No 3, p 293,
1973.
- 6. Bareriblatt, G. I., IBID., Vo1 13, No 6, p 845, 1977.
7. Barenblatt, G. I., PODOBIYE, AVTOMODEL'NOST', PROMEZHUTOCHNAYA ASIMPTOTIKA
(Similarity, Self-Similarity, Intermediate Asymptotic Behavior), Lenin-
grad, Gidrometeoizdat, 1978, 208 pages.
COPYRIGHT: Izdatel'stvo "Nauka", "Doklady Akademii nauk SSSR", 1982
5303
CSO: 1865/147
48
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_ UDC 550.38:550.37
FUNDAMENTAL PROBLEMS IN MARINE ELECTROMAGNETIC RESEARCH
Moscow FUNDAMENTAL'NYYE PROBLEMY MORSKIKH ELEKTROMAGNITNYKH ISSLEDOVANIY
in Russian 1980 (signed to press 19 Nov 79) pp~2-5, 25~-271
[Annotation, table of contents and abstracts from collection of articles
"Fundamental Problems in Marine Electromagnetic Research", responsible edi-
tor A. N. Pushkov, doctor of physical and mathematical sciences, Institut zemnogo
magnetizma, ionosfery i rasprostraneniya radiovoln, 300 copies, 272 pag~^]
[Text] Annotation. This collection of articles contains papers presented at
the 2d A11-Union Seminar on Fundamental Problems~in Marine Electromagnetic
Research held at the Institute of Terrestrial Magnetism, Ionosphere an~ Radio
Wave Propagation, USSR Academy of Sciences, in 1978. The collection includes
articles devoted to the development and use of marine magnetometric instru-
mentation, investigations of the permanent geomagnetic field related to ~he
compilation of a catalogue of magnetic surveys, creation of a bank of magneto-
metric data, and also work in the field of a geohistorical analysis of the
earth's anomalous f ield. In addition, the collection contains a number of ar-
ticles on the theory and practice of marine electromagnetic sounding and pro-
filing, including the development of inethods for the numerieal and physical
modeling of the electromagnetic field in ocean areas. One of the sections in
the collection is devoted to theoretical and experimental investigations of
electromagnetic fields caused by the movement of water masses. The collec-
tion is of interest to specialists concerned with study of the geomagnetic
field and also for a wide group of geophysicists working in the field of inves~
tigations of the earth's deep structure.
Contents ~ .
I. Instrumentation for Measuring the Electromagnetic Fields in the Seas and
Oceans and Experience in Its Use
l. Lovotov, L. L., Nikolayev, A. A. and Semevskiy, R. B. "MBM Sea Towed
Magnetometer" 6
2. Bobrov, V. N., Gaydash, S. P. and Kulikov, N. D. "~ao-Component Quartz
Bottom Magnetic Variation Station" 9
3. Belov, V. A., Burtsev, Yu. A., Murashov, V. P. and Gaqdash, S. P.
_ "Digital Three-Component Bottom Magne~ic Variation Station" 11
~9
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4. Krotevich, N. F., Panurovskiy, V. N. and Klekovkin, V. A. "Bottom Three-
Component Variometer With Magnetostatic Converters" 16
5. Pyatibrat, 0. M., Ignatov, I. I. and Ryabushkina, T. P. "Sea Bottom
Three-Component Ferrosonde Magnetic Variation Station MVS-ZK" Z4
6. Kozlov, A. N. and Abramov, Yu. M. "Magnetometric Complex for Measur-
ing Variations and Magnetic Field Gradient in the Frequency Range
0-400 Hz" ~ Zg
7. Karnaushenko, N. N. and Kukushkin, A. S. "Methods and Instrumenta-
tion for Investigating the Natural Electromagnetic Field in the
Ocean in the Frequency Range Above Several Hz" 30
8. Artamonov, L. V., Beresten', L. N. ~nd Popov, M. K. "Evaluation of the
Effectiveness of Vibrational Protection of a Towed Variable Magnetic
Field Transducer" 35
9. Gordin, V. M., Lyubimov, V. V. and Popov, A. G. "Experience in Work
With the~KM8 Quantum Differential Magnetometer Under Conditions
of a Sea Magnetic Survey" 40
10. Belyayev, I. I., Perfilov, V. I., Gorodnitskiy, A. M.~and Suzyumov,
A. Ye. "Component Geomagnetic Survey on 21st Voyage of the Sci-
entific Research Ship '1?mitriy Mendeleyev 48
11. Machinin, V. A., Tsvetkov, Yu. P., Pushkov, A. N. and Kharitonov,
A. L. "Buoy Differential Proton Magnetometer for Determining Tem-
poral Variatiores of Geomagnetic Field in Sea Magnetic Surveys" 51
12. Abramov, Yu. M. and Abramova, L. M., "Experience in Carrying Out Gradient
Magnetic Measurements in the Arctic Ocean" 59
13. Klekovkin, V. A., Selyatitskiy, V. G., Sypko, A. P. and Fedyunin,
S. G. "Electric Field Hydromodulation Transducer" 65
14. Bogorodskiy, M. M. "Bynamic Barosensitivity and Tribopolarization
Effects of Measurement Electrodes" 70
15. Bogorodskiy, M. M. "Static Barosensitivity of Measurement Electrodes
and Evaluation of Errors in Measurement of Electric Fields of
Waves" ~g
II. Methods for Representation and Analysis of Permanent Geomagnetic Field
16. Kolesova, V. I., Petrova, A. A. and Pushkov, A. N. "Problems in In-
vestigating the Geomagnetic Field of the World Ocean on the Basis
of a Specialized System for the Accumulation, Storage and Process-
ing of Data" ~ 92
- 50
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17. Tsipis, Ya. L. and Gubenko, N. D. "Feafures in Creating a Bank of
Magnetotelluric Data" 100
18. Zolotov, I. G, and Roze, Ye. N. "Analysis and Representation of tre
Earth's Magnetic Field by the Oprimum Interpolation Method" 106
19. Rc.ze, Ye. N. "Investigation of Methodological Errors in Gradiento-
metric Measurement Method" 119
,
20. Karasik, A. M., Desimon, A. I. (deceased), Pozdnyakova, R. A. and
Sochevanova, N. A. "Magnetic Anomalies in the Ocean on the World '
� Schematic *4ap of the Anomalous Magnetic Field" 129 '
. ~
21. Kolesova, V. I., Petrova, A. A. and Efendiyeva, M. A. "Investigation ~
of Structure of Geomagnetic Field Elements Along a Geotraverse in ~
the North Pacific Ocean" 138
22. Shreyder, A. A. and Trukhin, V. I. "Paleomagnetic Application of
- Data From Component Magnetic Investigations in Ocean" 146
23. Goroditskiy, A. M. , Litvinov, E. M, and Luk'yanov, S. V. "Magnetic
Characteristics of Ttao Major Transformal Dislocations in the
Southeastern Pacific Ocean" 151
24. Semenov, V. G. "Solution of the Inverse Problem of Determining the
Source of a Physical Field in a Dipole Model" 161
III. Theory and Practice of Marine Electromagnetic Soundings
25. Varentsov, I. M. and Golubev, N. G. "One Algorithm for Finite-Dif-
f erence Hodeling of Electromagnetic Fields" 169
26. Zhd anov, M. S., Varentsov, I. M. and Golubev, N. G. "Solution of
_ Inverse Problems in Geoelectrics by Iterative Trial-and-Error
Me thod" 186
27. Berd ichevskiy, M. N., Zhdanov, M. S., Trofimov, I. L. and P'onarev,
G. A. "Use of Modular Magnetometers in Sea Magnetic Variation
Research" 192
28. Kala shnikov, N. I. and Korepanov, V. Ye. "Promising I~ethods for E1-
ec tronagnetic Investigations of Structure of the Earth's Crust
in the Oceans" 196
29. Molo chnov, G. V., Radionov, M. V, and Rybakin, Yu. N. "Electromag-
ne tic Soundings With Measurement of the Elements of the Polar-
iz ation Ellipse in the Areas of Northern Seas" 203
- 30. Belyayev, I. I., Polonskiy, Yu. M., Svetov, B. S. and Khalizov,
A. L. "Experience in Measuring Variations of the Magnetic and
El ectric Fields at Great Depths in the Paci.fic O~ean" , 209
~l
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31. Finger, D. L., Filatov, 0. V. and Ignatov, I. I. "Experience in the
Registry of Variations in the Modulus of the Vector of the Earth's
Magnetic Field by the KM5 Sea Quantum Magnetic Variation Station
on the Sea Floor" 214
32. Shneyer, V. S., FinAer, D. L., Dubrovskiy, V. G., Pyatibrat, 0. i~i.,
Pukhomelin, A. r., Bobr.ov, V. N., Gaydash, S. P. and Ignatov,
I. I. "Preliminary Results of Magnetic Variation Measurements
in the Southern Caegian Area" 21~
33. Novysh, V. V. and Bogorodskiy, M. M. "Some Results of Measurements
of the Electric Field in the Coastal Zone of the Caspian Sea" 223
IV. Electromagnetic Fields of a Hydrodynamic Source
34. Korotayev, S. M. "Inveatigation of the Electric Field of Submarine
Sources in the Caspian Sea" 224
_ 35. Belokon', V. I., Rodkin, A. F. and Smal', N. A. "Computation of
Disturbances of the Earth's Magnetic Field by Long-Period Vari-
atione of Ocean" 230
36. Sma.gin, V. P. and Savchenko, V. N. "Geomagnetic Field Variations From
Sea Waves Along Shore With Sloping Bottom" 234
_ 37. Karnaushenko, N. N. and Kukushkin, A. S. "Experimental Investigations
of Vertical Structure of the Natural Electromagnetic Field in the
Ocean in the Frequency Range Above Several Hz" 241
38. Novysh, V. V., Smagin, V. P. and Fonarev, G. A. "Measurement of the
Electric Field of Waves by Towed Electrodes" 249
39. Kazakov, A. V., Medzhitov, R. D., Rutenko, A. N. and Shekhovtseva,
Ye. L. "Investigation of Statistical Characteristics in Magnetic
- Fields of Wind Waves" 252
UDC 550.380.8
MBM SEA TOWED MAGNETOMETER
[Abstract of article by Lavotov, L. L., Nikolayev, A. A. and Semevskiy, R. B.J
[Text] This article is devoted to a description of the design and construction
of the firs't Soviet-produced series-capable magnetometer developed and intro-
duced into standard production at the "Geofizika" Scientific-Production Com-
bine. It is intended for the measurement of weak tnagnetic fields in the seas
and oceans from aboard surface ships and submersibles. Experimental use of the
instrument under real navigational conditions confirmed its high technical and
operational qualities. The MBM apparatus has undergone expert metrological test--
/ ing by the USSR Gosstandart and has been included in the State Register of
Measurement Instruments.
52
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UDC 550.380.8
TWO-COMPONENT QUARTZ BOTTOM MAGNETIC VARIATION STATION
[Abstract of article by Bobrov, V. N., Gaydash, S. P. and Kulikov, N. D.]
[TextJ Four two-component magnetic variation stations have been developed and
have undergone tests in the Caspian Sea. A station is oriented on the magnetic
meridian by analogy with a sea compass using a special orienting magnet. The
station uses quartz antitilt z and H variometers and a special optical system
of mirrors making it possible to record the variations of two components on
photofilm with a sensitivity of 0.5 nT in the range f550 nT. The duration of
self-contained operation is 7 days. Figures l.
ULC 550.380.8
DIGITAL THREE-COMPONENT BOTTOM MAGNETIC VARIATION STATION
[Abstract of article by Belov, V. A., Burtsev, Yu. A., Murashov, V. P. an~i
Gaydash, S. P.]
- [Text) A digital three-component bottom magnetic variation station has lieen de-
veloped. Station operation is based on the inclusion of a quartz sensor in a
~weep conversion system. Two sensors are used in measuring three components.
Registry is with a cassette magnetic recorder employing an intermediate memory.
The registry range is f1000 nT with a sensitivity of 0.1 nT. The duration of
self-contained operation is 10 days. F`igures 2, references 3.
UDC 550.380.8
BOTTOM THREE-COMPONENT VARIOMETER WITH MAGNETOSTATIC CONVERTERS
[Abstract of article by Krotevich, N. F., Panurovskiy, V. N. and Klekovkin,
V. A.]
_ [Text] The article gives a description of a bottom three-component variometer,
based on the principle of an arbitrary orientation of primary magnetostatic
transducers. The authors give a functional diagram of the measurement channel
of this variometer and its technical specifications. Variometers with electronic
and electromechanical compensation are compared. Figures 3, references 5.
UDC 550.380.6
SF.A BOTTOM THREE-COMPONF.NT FERROSONDE MAGNETIC VARIATION STATION MVS-3K
[Abstract of article by Pyatibrat, 0. M., Ignatov, I~. I. and Ryabushkina, T. P.]
[Text] This paper reports on a bottom sea ferrosonde 3-component magnetovaria=
tion station, the MVS-3K, developed and constructed at the Institute of Terres-
trial Magnetism, Ionosphere and Radio Wave Propagation. The authors give the
53
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principal schematic solutions and station parameters. On the basis of the re-
sults of in situ tests the conclusion is drawn that the new instrument is
highly promising. Figures 1, references 2.
UDC 550.380.$
- MAGNETOMETRIC COMPLEX FOR MEASURING VARIATIONS AND MAGNETIC FIELD GRADIENT
IN THE FREQUENCY RANGE 0-400 Hz
_ [Abstract of article by Kozlov, A. N. and Abramov, Yu. M.]
[Text] This report describes the development of a measurement complex for reg-
istering variations and the gradient of the earth's magnetic field on the
basis of the recording apparatus of the KMV magnetumeter-gradient meter in
the range 0-1 Hz with a resolution of 0.1 nT and variations of electromag-
_ netic processes in the frequency range 1-400 Hz with a resolution of about
1 nT�Hz-1~2 under sea conditions. References 4.
UDC 55~.46.083:621.317.7
- METHODS AND INSTRUMENTATION FOR INVESTIGATING THE NATURAL ELECTROMAGNETIC
FIELD IN THE OCEAN IN THE FREQUENCY RANGE ABOVE SEVERAL Hz
[Abstract of article by Karnaushenko, N. N. and Kukushkin, A. 5.]
[Text] The authors describe measurement methods and give the makeup and prin-
cipal technical specifications of specialized measurement apparatus for inves-
tigating the natural electromagnetic field in the ocean in the frequency range
above several Hz developed taking into account the principal requirements and
specifics of ineasurements of such fields. The elements for the input of data
into an electronic computer are described. Figures 1, references 7.
UDC 550.370
EVALUATION OF THE EFFECTIVENESS OF VIBRATIONAL PROTECTION OF A TOWED VARIABLE
MAGNETIC FIELD TRANSDUCER ~
[Abstract of article by Artamonov, L. V., Beresten', L. N. and Popov, M. K.]
[Text] This is an analysis of the technical possibilities of vibrational pro-
tection of the primary transducers for measuring a variable, extremely low-
frequency magnetic field at sea using apparatus towed behind a ship. The re-
sults of an experimental investigation (on a vibrating stand) of a unit for
measuring the horizontal field component, protected against vibration by the
- inertial shock-absorbing suspension method, are described. It was established
that suppression by not less than 40 db in comparison with vibration of the
body of the towed "f ish" is technically attainable. Figures 2, references 1.
51~
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UDC 550.389
EXPERIENCE IN WORK WITH THE KMS QUANTUM DIFFERENTIAL MAGNETOMETER UNDER
CONDITIONS OF A SEA MAGNETIC SURVEY
[Abstract of article by Gordin, V. M., Lyubimov, V. V. and Popov, A. G.J
[Text] The results of an experimental determination of the horizontal gradi-
ents of the geomagnetic f ield in the southern part of the Atlantic Ocean with
the KM8 quantum differential magnetometer are given. The authors analyze the
results of a number of inethodological experiments related to an investigation
of the influence of the cable and towing ship on the gradient meter read ings.
The~optimum regime for registering the gradient of the earth's magnetic field
was determined. Figures 5, tables 2, references 4.
UDC 550.838
COMPONENT GEOMAGNETIC SURVEY ON 21st VOYAGE OF THE SCIENTIFIC RESEARCH SHIP
'DMITRIY MENDELEYEV'
[Abstract of article by Belyayev, I. I., Perfilov, V. I., Gorodnitskiy, A. M.
and Suzyumov, A. Ye.]
, [Text] The concise technical specifications are given for a model of the KMZ-4
component magnetometer developed by the Special Design Burea~ for Physical In-
strument Making, USSR Academy of Sciences. The article describes the method
for the processing of data obtained during the voyage using a"Minsk-22" el-
ectronic computer. Also given are the results of a hydromagnetic survey of
individual regions of the Pacific Ocean. The error in a component survey of a
polygon in the region of the central part of the Shatskiy Rise was determined.
References 2.
UDC 550.3$0.8
BUOY DIFFERENTIAL PROTON MAGNETOMETER FOR DETERMINING TEMPORAL VARIATIONS OF
GEOMAGNETIC FIELD IN SEA MAGNETIC SURVEYS
[Abstract of article by Machinin, V. A., Tsvetkov, Yu. P., Pushkov, A. N. and
Kharitonov, A. L.]
[Text] Tests of a buoy proton station intended for determining the temporal
variations of the geomagnetic field when carrying out sea magnetic surveys
_ are described. The results of an "observatory" investigation of the station
and its practir_al use in a local magnetic survey in the Caspian are given. It
is shown that the mean square survey error, without allowance for time varia-
tions, is +6.5 nT and it can be redu~+ed to �3.3 nT, introducing corrections in
the buoy station magnetograms. Allowance for variations at shore stations makes
it possible to reduce the error only to f5 nT. Figures 6, tables 1, references
5.
55
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UDC 550.380
~XPERIENCE IN CARRYING OUT GRADIENT MAGNETIC MEASUREMENTS IN THE ARCTIC OCEAN
[Abstract of article by Abramov, Yu. M. and Abramova, L. M.]
[Text] Technical specifications are given for a quantum variometer-gradient
meter developed at the Institute of Terrestrial Magnetism, Ionosphere and
Radio Wave Propagation. Also described is an experiment for measuring the gra-
dients of variations of the earth's magnetic field from a drifting floe. The
possibility for using a quantum variometer-gradient meter in the high lati-
tudes and at low temperatures is demonstrated. Figures 1, references 3.
UDC 550.370
ELECTRIC FIELD HYDROMODULATION TRANSDUCER
[Abstract of article by Klekovkin, V. A:, Selyatitskiy, V. G., Sypko, A. P.
_ and Fedyunin, S. G.]
[Text] The article describes a primary measurement transduc er for the strength
of the electric field for measuring weak constant and infralow-frequency sig-
nals in a sea medium. The equivalent circuit of the transducer is analyzed. A
conversion factor equation is derived and a structural diagram of the instrument
is given. Figures 4, references 5.
UDC 550.380.3
DYNAMIC BAROSENSITIVITY AND TRIBOPOLARIZATION EFFECTS OF MEASUREMENT ELECTRODES
[Abstract of article by Bogorodskiy, M. M.]
[Text] The errors in the measurement electrodes of the IELAN-IZMIRAN system
caused in a shallow-water zone by the dynamic effect of the waves (pressure,
velocity of flow around the electrodes, wave collapse effect) are experiment-
ally evaluated. With a salinity of 13% there is a dynamic barosensitivity of
about 15-30'1~-V/(m H20)�sec'1 and the tribopolarization for the pair of elec-
trodes is about 50-500 ~.t,V/m�sec-1. In the case of collapsing crests the ef-
fective value of the dynamic barosensitivity, ~udging from the form of the
wave, increases by a factor of 4-5. The presence of different kinds of noise,
including with a"long-period" component, of the wave group envelope type, is
demonstrated. The effectiveness of protective measures, including treatment
of the electrodes, is demonstrated. Figures 7, tables 1, ref erences 8.
. 56
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UDC 550.380.8
_ STATIC BAROSENSITIVITY OF MEASUREMENT ELECTRODES AND EVALUATION OF ERRORS IN
MEASUREMENT OF ELECTRIC FIELDS OF WAVES
[Abstract of article by Bogorodskiy, M. M.j
[Text] An experimental study was made of the response of silver chloride elec-
trodes to pressure. A special electrolytic pressure chamber outfit was also cre-
ated for this purpose. The author obtained the absolute values of static baro-
sensitivity of the measurement electrodes. It is noted that barosensitivity
anomalies correspond to internal defects of the electrodes. It is shown that it
is possible to evaluate the error in measuring the elements of electric fields
corresponding to the barosensitivity of the electrodes and channel noise. An
evaluation of the errors was made applicable to the potential, vertical dif-
f erence and divergent methods for observing the electric fields of well-devel-
oped wind waves on a deep sea. The optimum dimensions of the measurement probes
were computed. A decrease in the error can be ohtained by treating the elec-
trodes by the cited method in combination with a decrease in the noise of the
- measurement channel. Figures 10, references 22.
UDC 550.383
PROBLEMS IN INVESTIGATING THE GEOMAGNETIC FIELD OF THE WORLD OCEAN ON THE
BASIS OF A SPECIALIZED SYSTEM FOR THE ACCUMULATION, STORAGE AND PROCESSING
OF DATA
[Abstract of article by Kolesova, V. I., Petrova, A. A. and Pushkov, A. N.]
[Text] The article sets forth the principal requirements on an automated sys-
tem and its data support taking into account the tasks involved in using the
system for: a) obtaining a unified bank of magnetometric data for the world
ocean; b) studying the structure and formulating models of the main and anom-
alous parts of the geomagnetic field and its secular variations; c) solv-
ing geological-geophysical problems. References 12.
UDC 550.383
FEATURES IN CREATING A BANK OF MAGNETOTELLURIC DATA
[Abstract of article by Tsipis, Ya. L. and Gubenko, N. D.)
[Text] A study was made of the problem of forming a data base for magnetic sur-
_ veys and an operational system for work with this base, making it possible to
solve a broad range of problems ranging from informational to the representa-
tion of the spatial-temporal structure of the geomagnetic field. The rapid in~
crease in the volume of experimental data dictates the necessity for the
speediest possible creation of such a system.
5~
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UDC 550.383
ANALYSIS AND REPRESENTATION OF THE EARTH'S MAGNETIC FIELD BY THE OPTIMUM
INTERPOLATION METHOD
[Abstract of article by Zolotov, I. G. and Roze, Ye. N.]
[Textj A method for the optimum interpolation of magnetometric data has now
been developed. Algorithms are proposed for evaluating the statistical char-
acteristics of the anomalous geomagnetic field and their errors. Figures 6,
references 8.
- UDC 550.382
INVESTIGATION OF METHODOLOGICAL ERRORS IN GRADIENTOMETRIC MEASUREMENT METHOD
[Abstract of article by Roze, Ye. N.]
[Text] An evaluation was made of the errors in gradientometric measurements
of the earth's magnetic field over the areas of the seas and oceans. Measures
are proposed for increasing the accura;;y of the gradientometric method. FiE-
ures 4, tables l, references 3.
UDC 550.382:550.383
MAGNETIC ANOMALIES IN THE OCEAN ON THE WORLD SCHEMATIC MAP OF THE ANOMALOUS
MAG~IETIC FIELD
[Abstract of article by Karasik, A. M., Desimon, A. I. (deceased), Pozdnyak-
ova, R. A. and Sochevanova, N. A.J
~ (TextJ This is a validation and discussion of the principles, procedures and
results of representation of magnetic anomalies of the oceans on the world
map of the anomalous magnetic f ield at a scale of 1:15 000 000, compiled at
the SEVMORGEO Scientific-Production Combine and~the Leningrad Division, In-
- stitute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation,
USSR Academy of Sciences,for the higher schools. In contrast to the contin-
ental part (in T)a or za isolines), the field of the ocean floor is shown
in the form of numbered axes of paleomagnetic anomalies; and only in the
places where the axes are not traced is the field given in the form of zero
isolines (L~T)a or quiet field zones. The world magnetic map is the first ex-
perience in global representation of the anomalous magnetic f ield and in the
oceanic part it differs considerably from the map of the axes of linear mag-
netic anomalies constructed by W. Pitman, et al. (1974) due to the use of
Soviet sources and new materials. Figures 1, references 9.
58
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UDC 550.382
INVESTIGATION OF STRUCTURE OF GEOMAGNETIC FIELD ELEMENiTS ALONG A GEOTRAVERSE
IN THE NORTH PACIFIC OCEAN
[Abstract of article by Kolesova, V. I., Petrova, A. A. and Efendiyeva, M. A.~
[TextJ The article gives the results of a spectral-profile analysis of the geo-
magnetic field along a sublatitudinal profile in the North Pacific Ocean. A
joint analysis of component and modular measurements made possible the u~ost
complete study of the~spectral structure of the geomagnetic field, clarifica-
tion of the principal classes of anoma.Iies and determination of their spatial
and dispersion properties and also made it possible to ascertain th~ charac-
teristic features of the spectral structure of the field i,n different geo-
morphological provinces and to refine the position of the boundaries of indi-
vidual anomalous regions. In the spectral structure of the components and the
modulus of strength of the geomagnetic field there are individual spectral
minima which are bf interest for determining the base levels for anomalous
fields of different frequency composition. The fe~tures of the spectral struc-
ture of the geomagnetic and gravity fields are compared. Figures 1, references
6.
UDC 550.382
PALEOMAGNETIC APPLICATION OF DATA FROM COMPONENT MAGNETIC INVESTIGATIONS
IN OCEAN
[Abstract of article by Shreyder, A. A. and Trukhin, V. I.]
[Text] A method for determining the parameters of the vector of magnetization
of a two-dimensional disturbing body on the basis of anomalies of the vertical
and horizontal components of the vector of the earth's magnetic field is de-
scribed. The results of an analysis of the errors of the method and the re-
sults of computations on the basis of real mag~netic anomalies observed in the
Indian Ocean during the 58th voyage of the scientific research ship "Vityaz
are given. References 6.
~ UDC 550.382:550.838
MAGNETIC CHARACTERISTICS OF TWO MAJOR TRANSFORMAL DISLOCATIONS IN THE
SOUTHEASTERN PACIFIC OCEAN ,
[Abstract of article by Gorodnitskiy, A. M., Litvinov, E. M. and Luk'yanov,
S. V.]
[Text] The materials of a hydromagnetic survey in two polygons in the south-
eastern part of the Pacific O~ean, carried out on the 24th voyage of the sci-
entific research ship "Akademik Kurchatov" in~1977, are analyzed. The south-
- ern polygon (polygon IV) was selected in the zone of development of the
59
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Eltanin fault zone; the northern (polygon V) polygon was selected in the re-
cently discovered Kurchatov fault. Magnetometric observations made it pos-
sible to clarify the specifics of the structural-tectonic plan of both zones
of dislocations, define the principal stages in their formation and evolu-
tion and compare this with the nature of the geological development of the
entire southeastern part of the Pacific Ocean. The results of the analysis
emphasize the role of magnetometry in the general geological-geophysical
complex of regional study of the ocean floor. Figures 3, references 2.
UDC 550.383
SOLUTION OF THE INVERSE PROBLEM OF DETERMINING THE SOURCE OF A PHYSICAL FIELD
IN A DIPOLE MODEL
[Abstract of article by Semenov, V. G.]
[Text] New unambiguous and invariant express methods have been developed for
determining the localization of a physical field in a dipole model. An equa-
tion for the interrelationship of gradient parameters of a physical field
was derived for an arbitrary model of a source. Figures 2, references 4.
UDC 550.382
ONE ALGORITHt4 FOR FI~TITE-DIFFERENCE MODELING OF ELECTROMAGNETIC FIELDS
[Abstract of article by Varentsov, I. M. and Golubev, N. G.]
[Text] The article examines the possibilities of formulation of an effective
algorithm for the modeling of two-dimensional electromagnetic anomalies (in
the case of an E-transform) suitable both for the mass solution of direct
problems and for the solution of inverse problems by the method of automated
trial-and-error. The modeling problem is reduced to a system of linear dif-
- ference equations solved by the upper relaxation iteration method. The opti-
mum value of the relaaation parameter, ensuring rapid convergence of the upper
relaxation iteration method, is determined by means of the prediction and cor-
rection procedures. Provision was made for additional means for accelerat-
ing the process of solution of the problem and checking the accuracy of mod-
eling results. The algorithm is applied using a YeS electronic computer and
- makes it possible to solve a broad range of problems in geoelectrics. Figures
3, tables S, references 31.
UDC 550.382
SOLUTION OF INVERSE PROBLEMS IN GEOELECTRICS BY ITERATIVE TRIAL-AND-ERROR
MF.THOD
[Abstract of article by Zhdanov, M. S., Varentsov, I. M. and Golubev, N. G.]
[Text] A method for solving two-dimensional inverse problems is examined. It
makes it possible to use the results of both synchronous observations of
fields and point soundings. The trial-and-error principle is used in the
60
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solution. The parameterization method ia employed for increasing stabi]ity
of the problem, that is, a solution is.sought in a definite class of func-
tions. The minimizing of the functional of deviation of the selected field .
- from the observed field is accomplished by methods not using derivatives and
allowing limitation of the sear~h region. A solutfon of the direct problem is
faund by the finire differences method. Figures 2, t;fbles 1, references 9.
UDC 550.37:550.380
USE OF MODULAR MAGNETOMETERS IN SEA MAGNETIC VARIATION RESEARCH
[Abstract of article by Berdichevskiy, M. ~1., Zhdanov, M. S., Trofimov, I. L.
and Fonarev, G. A.]
[TextJ The practical feasibility and suitability of sea electromagnetic sound-
ings by means of modular magnetometers is emphasized. Formulas for computing
impedance are given in a_new form. References 3.
UDC 550.380
PROMISING METHODS FOR ELECTROMAGNETIC INVESTIGATIONS OF STRUCTURE OF THE
EARTH'S CRUST IN THE OCEANS
[Abstract of article by Kalashnikov, N. I. and Korepanov, V. Ye.]
[Text] The article discusses different variants of apparatus for shelf and
deep-water placement, especially a sea varian[ of the long cable method and
a station for sea magnetotelluric sounding. The authors give the principal
results of in situ tests~of both types of apparatus carried out in 1974-1978.
Figures 3, references 7.
UDC 550.37:550.380
ELECTROMAGNETIC SOUNDINGS WITH MEASUREMENT OF THE ELEMENTS OF THE
POLARIZATION ELLIPSE IN THE AREAS OF NORTHERN SEAS
[Abstract of article~by Molochnov, G. V., Radionov, M. V. and Rybakin, V. N.]
[Text] This is an analysis of the dynamics of behavior of effective resistance
curves for geological sections characteristic for the areas of northern seas,
on the basis of which a method is proposed for carrying out electromagnetic
soundings. The results of field work are given. Figures 1.
61
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UDC 550.37:550.380
EXPERIENCE IN MEASURING VARTATIONS OF THE MAGNETIC AND ELECTRIC FIELDS AT
GREAT DEPTHS IN THE PACIFIC OCEAN
[Abstract of article by Belyayev, I. I., Polonskiy, Yu. M., Svetov, B. S, and
Khalizov, A. L.]
' [Text] This paper gives the results of experiments for registry of variations
of the earth's electric and magnetic fields on the floor of the abyssal
Pacific Ocean carried out in 1978. During the 21st voyage of the scientific
research ship "Dmitriy Mendeleyev" specialists registered variations of the
latitudinal component of the electric field by means of a conducting.line 1
km in length and a magnetic field module using a proton magnetometer. Basic
data are given on the bottom magnetometric station used, as well as informa- .
tion on formulation of the experiments. The recorded variations are described.
References 1.
' UDC 550.380
EXPERIENCE IN THE REGISTRY OF V9RIATIONS IN THE MODULUS OF THE VECTOR OF THE
EARTH'S MAGNETIC FIELD BY THE KMS SEA QUANTUM MAGNETIC VARIATION STATION
ON THE SEA FLOOR
[Abstract of article by Finger, D. L., Filatov, 0. V. and Ignatov, I. I.]
[Text] A method is described for the placement of a quantum sea magnetic vari-
ation station (KM5) on the sea floor. Three such placements were carried out
~ in the Caspian Sea at depths of 80-110 m. Experimental investigations indi-
~ cated the suitability of the KM5 for the registry of variations on the sea
floor. Figures 2, references 2.
UDC 550.37:550.380
PRELIMINARY RESULTS OF MAGNETIC VARIATION MEASUREMENTS IN THE SOUTHERN
CASPIAN AREA
[Abstract of article by Shneyer, V. S., Finger, D. L., Dubrovskiy, V. G.,
Pyatibrat, 0. M., Pukhomelin, A. F., Bobrov, V. N., Gaydash, S. P. and Ig-
natov, I. I.]
~TextJ The authors give the results of a preliminary analysis of magnetic var-
iations on sublatitudinal and meridional magnetic variation profiles in the
Southern Caspian. On the basis of ineasurements with bottom stations it was
possible to determine the distribution of the normalized amplitudes of vari-
ations of the z-, H- and D-components. A strong variability of z and D on
the submeridional prof ile and a weak variability on the sublatitudinal pro-
file were discov~~ ed. The preliminary interpretation reveals a marked nonuni-
- formity of the sedimentary cover in the submeridional direction, in the zone
of contact between the megadepresSion and the platrorm, and its slight varia-
bility in a sublatttudinal direction. No asthenospheric inhomogeneities were
discovered. Figures 1, references 3.
62
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UDC 550.380.8
SOMG RESULTS OF MEASUREMENTS OF THE ELECTRIC FIELD IN THE COASTAL ZONE OF
THE CASPIAN SEA
[Abstract of article by Novysh, V. V. and Bogorodskiy, M. M.]
[Text) The investigations were made near Krasnovodsk in the coastal zone by
means of an electric field meter with two orthogonal measurement bases, each
of 3.8 m. During a storm there are slowly changing fields up to 120-150
- � V/m with a decrease in their values as the storm attenuates. Figures la ref-
erences 1.
UDC 550.37:550.380
INVESTIGATION OF THE ELECTRIC FIELD OF SUBMARINE SOURCES IN THE CASPIAN SEA
[Abstract of article by Korotayev, S. M.]
. [1'ext] The article presents the results of profiling of the natural electric
f ield along the eastern shore of the Caspian for the purpose of seeking sub--
marine sources and their quantitative evaluation. It was found that there is
a group of ~ubmarine sources on the Krasnovodskiy Peninsula traverse. The
characteristic velocity at the sources, computed on the basis of field anom-
alies, was about 0.01 mm/sec. Figures 2, references 6.
UDC 550.37
COMPUTATION OF DISTURBANCES OF THE EARTH'S MAGNETIC FIELD BY LONG-PERIOD
VARIATIONS OF OCF.t~N
[Abstract of article by Belokon', V. I., Rodkin,. A. F. and Smal', N. A.J
[Text] A system of equations and boundary conditions was formulated for com-
puting variations of the earth's magnetic field induced by long-period varia-
tions of the ocean. The use of the approximation h/AC � 1, where h is ocean
- depth, aG is the characteristic horizbnta] scale,made it possible to exam-
ine the problem of flow of currents into the bottom. References 3.
UDC 550.37
GEOMAGNETIC FIELD VARIATIONS FROM SEA WAVES ALONG SHORE WITH SLOPING BOTTOM
[Abstract of article by Smagin, V. P. and Savchenko, V. N.]
[Text] A method is proposed for computing geomagnetic field variations caused
by potential wave motion of a fluid along a shore with a constant bottom
slope. An algorithm is given for determining the horizontal and vertical
63
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c:u~n~~onen[s of the induced magnetic field along the shore,~ whose bottom slope
is considered equal to (QCn =~'1/2, n= 1, 2, 3,... The case of a vertical
precipice l~c~ _~/2) is examined in detail. References 3.
UDC 551.463.7
EXPERIMENTAL INVESTIGATIONS OF VERTICAL STRUCTURE OF THE NATURAL
ELECTROMAGNETIC FIELD IN THE OCEAN IN THE FREQUENCY RANGE ABOVE SEVERAL Hz
[Abstract of article by Karnaushenko, N. N. and Kukushkin, A. S.]
[Text] The authors give the results of in situ investigations of the ver-
tical structure of the natural electromagnetic field in the tropical zone
of the Atlantic Ocean and deep regions of the Black Sea in the frequency
range above several Hz. The collected data make it possible to evaluate the
change in the spectral makeup and dropoff in the intensity of field varia-
- tions as a function of frequency in the case of a constant depth. Figures 3,
_ references 19.
UDC 550.37:550.380
MEASUREMENT OF THE ELECTRIC FIELD OF WAVES BY TOWED ELECTRODES
[Abstract of article by Novysh, V. V., Smagin, V. P, and Fonarev, G. A.]
[Text] It is demonstrated on the basis of experimental data that a towed elec-
trode line the EMIT (electromagnetic current recorder) at the time of
waves registers the electric f ield of sea waves. By using records on courses
perpendicular to and parallel to the wave crests it is possible to determine
the elements of the waves: period, height and length of a wave. Figures 1, ref-
erences l. ,
UDC 550.37:550.380
INVESTIGATION OF STATISTICAL CHARACTERISTICS IN MAGP~fETIC FIELDS OF WIND WAVES
[Abstract of article by Kazakov, A. V., Medzhitov, R. D., Rutenko, A. N. and
Shekhovtseva, Ye. L.)
[Text] The article gives the results of investigations of the magnetic fields
of surface waves carried out in the summer of 1977-1978 in the coastal zone of
the Sea of Japan. The measurements were made at depths of 8 and 30 m over a
long period of time under different hydrometeoro'ogical conditions. A quanti-
tative relationship was established between the parameters of the waves and
the magnetic field generated by them. Figures 2, references 7.
COPYRIGHT: Institut zemnogo magnetizma, ionosfery i rasprostraneniya radiovoln
(I7.MIRAN) , 1979
5303
CSO: 1865/162-A ~
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~ UDC~551.466.3:535.31
THEORY OF OBSERVATION OF UNDERWATER OBJECTS THROUGH WAVE-COVERED SEA SURFACE
Moscow IZVESTIYA AKADEMII NAUK SSSR: FIZII:A ATMOSFERY I OKEANA in Russian
Vol 18, Pdo 4;, Apr 82 (manuscript received 9 Dec 80, after revision 6 Apr 81)
pp 408-415
[Artj.cle by S. V. n~^*;enko, Marine Geophysical Institute, Ukrainian Academy of
SciencesJ
[Text] Abstract; The article gives a theoretical
analysis of the distortions introduced
by the wave-covered sea surface in the image
of underwater features observed fr.om the at-
mosphere. It is postulated rhat the spatial
structure of both ob~erved features and
waves has a random character. The quality of
observation is evaluated using the magnitude
of the error in measuring the spatial lumin-
osity of the feature. It is shown that there
is an optimum relationship between the stat-
istical characteristics of the distribution
of luminosity and waves and the parameters
of the measuring instrument.ensurin~ a mini-
mum of this error.
The possibility of observing underwater features from the atmosphere is depend-
ent on their contrast, degree of turbidity of the water and atmosphere, super-
posing of the brightness of air haze, light scattered in the sea and brightness
of the water-air discontinuity on the image [1].
We will investigate the joint influence exerted on tx�ansmission of the image of
underwater features by the wave-covered sea surface and the averaging effect of
the measuring instrument, neglecting other interfering factorsr allowance for
which is possible independently.
A problem similar in its formulation was so?-~d in (1], where the influence of
- the sea surface on image transmission was studi.ed by an analysis of the scat-
tering function, the energy distributian in the edge image and the frequency
contrast of the transfer function. In saurce [2] a study was made of the image
_ transfer of a point through a one-dimensional sinusoidal wave and formulas were
given for computing the displacement of a point and the blurring of an object
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wi~h an increase in the exposure. An approximate model of image transfer
through the wave-covered discontinuity of two media with different refractive
indices was described in [3], where the author determines the multipoint stat-
istical characteristics of the brightness image of a self-luminescent ob~ject
_ or feature observed through the wave-covered discontinuity.
A feature of this study is that it examines the observation of random spatially
elonsated features using optical radiztion detectors which perform spatial aver-
aging of the image. Many natural formations on the bottom and in the water lay-
er can be modeled by features of the mentioned structure whose investigation
is possible by optical methods. TY~e spatial averaging of the received image
is a property of any real radiation detector. Accordingly, the combination of
such initial premises makes it possible to obtain research results suitable
for direct practical applicatiQn. The quality of observation is evaluated us-
- ing the mean square error between the initial and measured luminosity distrib-
utions [4]. It is shown that it is dependent on the choice of the degree of
averaging and is the highest when it has a finite value. Here we will examine
observations at the nadir as ensuring minimum image distortion [1).
In arder to simplify the analysis we will examine a problem in which the ob-
ject of ineasurement and waves are assumed to be one-dimensional (Fig. 1).
Z
0~~ ~'!'fe) ly~ I B~
I
B
_ al '
Ha B
0 ~ .
~f~x) ~ 4
~ G LI
I
I
- NB ~
iY N
a, -..1~
- ' 0 8 A s
st ,
_ Fig. l. Diagram explaining derivation of principal
relationships.
Retaining the physical essence of the analyzed phenomena, such an approach makes
, it relatively simple to obtain final numerical results. The x-axis of the mean
level of the wave-covered surface is stipulated in'the figure by the point 0.
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The atmosphere is situated above it and the water below. At the depth IiW below
the sea surface there is a diffuse self-luminescent ob~ect to be observed, ex-
tending in the direction of the x-axis, whose apatial distribution of luminos-
ity is described by the random function f(x). At the height fIa above the sea
surface at the point 0" there is a detector of optical radiation whose optical
axis is directed to the nadir. The difference in the level of the wave-covered
surface from the mean is described by a centered random function of the space
coordinate ~(X).
An analysis of the process of observation of an underwater feature will be
made on the basis of the premises of geometrical optics without allowance for
the absorption and scattering of light in the water. The ray emerging from
the point A of the observed feature and received by the detector at the point
0" travels the following path. It is propagated in the water medium at the
- angle ~ to the vertical BB' to the point Q at the water surface. The tangent
` CC' to the sea surface at this point is slanted to the horizontal at the angle
o~, whereas t;ze normal NN' to this surface also is deflected by the angle oC
- from the vertical BB'. At the point Q there is refraction of the ray and it
emerges fron~ the water at the angle ~ to the normal NN'. The detector at the
point 0" picks it up arriving at the angle e to the vertical.
Since the ~(x) surface is curvilinear and random, the picture picked up by
the instrument differs from the f(x) function describing the distribution of
luminosity of the observed object and this difference has a random character.
We will find the error introduced by the wave-covered sea surface and instru-
ment to the image sensed by the latter and we wi13. evaluate the limits o' ap-
plicability of such a method for observing underwater ob~ects. For this pur-
pose we will first obtain the correlation between the output signal Y of the
measuring instrument and the investigated ob~ect f(x).
_ We will find the position of the point A, situated on the observed object, which
is sensed by the instrument as visible at the angle e to the vertical. The seg-
ment LQ is the ~(x) value. Accordingly, the abscissa of the points L and B is
~ ~ x~m [H.-~ (x,) ] te e.
(1>
Since the straight line CC' is the tangent to the ~(x) curve at the point
with the abscissa xl, then
tSa~ d-
~ I ~�.~�~~~xs).
It follows from Fig. 1 that the distance of the point A from the point B is
- equal to x3 =[HW +~(xl)] tg c~ . Accordingly, the abscissa of the point A is
x,mz,+x,~ [N,-~ ~x~~.~ tg e+ ~H,+~ (x,) ] te w, ~2~
where o~ + y, Equation (1) can be regarded as an equation for findin; the
abscissa xl. However, due to the random character of the L(xl) parameter its
precise solution cannot be obtained. 4le will take advantage of the circumstance
that in actual practice the amplitude of the wave ~ is much less than
the height Ha at which the measuring instrument is situated. From expression
(1) we find that xl = Ha tg e, and expression (2) assumes the form
x,� [H,-~ (N, tg 9) ] tg e+ [N.-I-C (N, tg 6) ] ~g W. ( 3)
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Thus, at the angle e to the normal the measuring instrument picks up the point
- of an object whoge abscissa is given by expression (3). The luminosity f(x2)
of the ob~ect at this point has the form
f { [H,-~ (H, tg 9) ] tg A+ [H�+~ (Ha tg 6 ) ] tg cp} . (4 )
The argument of this function is random since the parameters ~ and~Q are ran-
dom. Accordingly, the value (4) is random even for a specific f(x) record. We
will simplify its argument. For this we use the notation tgoC, f'?= tg e,
Remote optical instruments usually have a very high angular resolution. Accord-
ingly, it can be assumed that ~1'j~ ~ l. The angles of inclination of the waves
are usually also small, that is ~X ~1. In this case tg -~)/n,
I ~ I~X
where n is the refractive index of water and the distribution of luminosity (4)
assumes the form
n-1
_ f [Aox~ n H�~ ~x~) ] ~ ( 5 )
where ~
. ~qo..1.}- N' ~
[B = w(ater) ] . : . ~6~
and it is taken into account that = xl/Ha. Thus, with the mentioned assump-
tions the random character of parameter (5) is determined by the random form
of the function f(x) and the random character of wave slope f,(x) = d~(x)/dx.
The total signal received by the optical instrument is a superposing of the
signals (5), that is - ~ -
Y(~)~f h~x)f~Aox+nn1H.~~s)]dx, ~
- , (7 )
where h(x) is the instrument function of the sensor of this instrument, which
is the projection of the directional diagram of the optical receiver
onto the mean sea surface (Fi�. 1),and characterizes the weight with which dif-
ferent parts of the image are sensed by the instrument. The Y(~) parameter is
dependent on the random funcLion ~(x). ~
If the waves are absent and the resolution of the instrument is inf initely
high, that is, the conditions ~(x) = 0 and h(x) = b(x) are satisfied, the in-
strument output signal is precisely equal to the value of the f(x) function
at the nadir point, that is, Y~ = f(0). The difference between the Y(~ ) and
Y~ value is determined by the presence of waves and a finite resolution of the
measuring instrument. The mean square difference of the Y(~) and Y~ values
is the dispersion of the measurement error
E'~E)~~~'~~)-~'o~'"'y'(~)-2~)-I-Y'~ (g)
dependent on the random function of slopes ~(x). In expression (8) averaging
is carried out for all possible cases of the random function f(x) with a con- ~
stant record of the random function ~(x). Assuming the distribution of lumin-
osity f(x) to be stationary and ergodic and using expression (7), we obtain
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Yo'�'I"(~) -o',
w ~
~'o_~'~g)~ f h(x)14[A,x+ n-1K.~(~) ~dx,
n
-a ,
s
Y~~ f
f ~~~,)h~x:)B~Ao~xs-x~)~'~H.~~~xz)-~~xi)~}dx,dx2,
n
where U2 is the dispersion of the f(x) function; B(J~) is its correlation func-
tion. Expressing the latter through the S(k) spatial spectrum of the f(x) pro-
- cess, we find
( 9a )
YeY~~)~~Jh~~~s~k)eXP{f~tAox+n-1 H.~~s),~dxdk,
)L
~s
�
Y=(~)= f~~ h(x~)h(x,)S(k)exp{ic~[A,(~,-x,)+
~a
+ n-1H.~~~~:)-~~x~)),}~~~:dk�
~ (9b)
Since the ~(x) function is random, the dispersion of ineasurement error E 2(
is also random. We will find the mean value of the dispersion of ineasurement
error � 2=~ E 2(~ for the set of records.of the wave process; here the sym-
bol