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~t?~ u~~r~tf~i,~~. E~ntt.~
JPRS L/ 10061
21 October 1981
Translation
MARINE E~ECTROMAGNETIC RESEARCH.
COLLECTION OF ~'HE INSTITUTE OF TERRESTRIAL MAGNETISM,
THE IONOSPHERE AND RAQIl7 W~?VE PROPAGATION
OF THE USSR ACADEMY OF SCIENCES
Ed. by
G.A. Fonarev
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~R (1F~1('1~[, lr.S~ t~N1,Y
JPRS L/10061
21 October 1981
MARI P~E ELECTROMAGPlET I C~ESEARCH , .
COLLECTION OF THE INSTITUTE OF TERRESTP,IAL MAGNETIS~1,
THE IONOSPHERE AND RADIO WAVE PROPAGATION
OF TNE USSR ACAIIEMY OF SC I EP~CES
MQSCOw MORSKIYE ELEKTROMAGNITNYYE ISSLEDOVANIYA: SBORNIK IZMIRAN in
Rus~ian 1975 (signed to press 25 Mar 1976)~ 200 copies, pp 2-80
- [Edited by Gennadiy Aleksandrovich Fonarev, Candidate of Physico-
Mathematical Sciences]
CONTENTS
Annotation 1
I Vertical Component of the Electric Field Intensity Induced by the Irbtion
o~ Sea Water
- (L. M. Abramova, et al.) 2
Determination of the Conductivity of Sediments by Measuring the Electric
and Magnetic Fields and W~ve Velocity Gomponents at the Bottom of the
Sea
(L. M. Abramova) 8
' Statistical Characteristics of the Re3~atian of the Wave Parameters to the
_ Induced Electromagnetic FYeld ~
~ (Yu. M. Abramov, L. M. Abramova)...u 11
Complex Measurements of Electromagnetic Fields of Waves in the Coastal
Zone. (Researci? Procedure and Some Results)
(Y u. M. Abramov, et al.) 16
Comparison ~f ltao Types of Devices for Marine Electromagnetic Sounding
(L. B. Volkomirskaya, G. A. Fonarev) 28
- Measuring the Sea Wave-Induc~d Electric Field
(G. A. Fonsrev, V. Yu. Semenov) 32
~ _ a- ~ II ~ iJSSR - E FOUO]
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Estimating Electric Fields Create3 by a Ttao-Dimensional Wave Spectrum
- (M. M. Bogorodskiy) .................................e.................. 36
General Properties of the Anomalous Magnetic Field in the World O~cean
(V. G. Larkin, et al.) 44
- b -
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ANNOTATION
Articles in this collection are devoted to studies of the electromagnetic fields
� of sea waves, certain aspects of. magnetotelluric sounding and analysis of anomal-
ous magnetic fields. The collection is design2d for specialists working in the
field of studying electromagnetic phenomena in the seas and oceans.
~
1
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I't?k ~)1'~'Ic ~1 ~ ~~VI ~
VF.RTICAL COMPONENT OF THE ELECTRI~ FIELD I"r1TENSITY INDUCED BY THE MOTION OF SEA
WATER
[L. M. Abramova, V. N. Mitrofanov, S. A. Skryabin, pp 3-10]
- The vertical component of tre electric field E induced by the motion of sea water
- in the geomagnetic field B occupies a special position in the studies of the elec-
tric f ield of a hydrodynamic source and the dynamics of the source itself. This
arisesfrom theexistence in the sea of a sharp conductivity boundary: the"seawater-
air" boundary. The component E, in the general case,in the center of large-scale
movements does not depend on the conductivity distribution or the configuration of
the motion, being a function only of the local velocity and horizontal component of
the earth's magnetic field [1].
E~ = VX By - Uy ~l~
- VXy are the velocity components of the sea water.
Young, Pt al. considered this fact for the first time, as ~indicated
in ref erence [2]. Later this component was used to study the speed of mo~,~Pment of
sea water [3, 4]. For sea waves E was presented in [5], where the solution for the
electric field potential of a two-~dimensional progressive wave obtained in reference
[1J was used. For the analysis and estimates of E the above-indicated authors
either investigated the two-dimensional model of motion or it was asaumed that the
meter was placed at the middle of the flow.
The more general solution by comparison with the preceding one for E was obtained
by D. Sanford [6] for the class of movements, the horizontal dimensions of which are
much greater than the verti.cal nonuniformities. In particular, he studied the
model in which there is only a horizontal velocity component V (the vertical
velocity component is assumed to be negligibly amall by compar~on with the hori-
zontal one), which is entirely acceptable for a large class of large scale move-
ments of the aea and waves in shoal water.
- The vertical component of the electric field is expressed as follaws:
. p 0 .
- =V B-V BX-a B~(V -V )d `~JB~ Vx V d cz>
E~ x y Y xl Y y ~ Y ~
~ , ~o z 2
where Vxy'D_ Vxy d~ is the speed averaged with respect to depth considering the
H
2
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conductivity of the sediments the effective speed. D~ H+(c72/61)(HS - H) is
the average depth of the sea considering the conductivity of the sediments - the
effective depth of the sea. H is the depth of the sea, H~ is the thickness of the
layer of sediments, 61 is the conductivity of sea water, ~2 is the conductivity of
the sediments.
For potential velocity distribution (or at the ~enter of symmetri.c distribution)
expression (2i becomes (1), that is, it is the sum of two terms, the ratio of whici~
depends only on the direction of motion of the sea water. This expression, as was
pointed oi~t above, is validly used in practice when studying large-scale movements
when the velocity distribution is sufficiently stable and known.
.
In the case of wind waves the velocity distribution is of a random nar~.~re, and the
~ dimensions of the source are small by comparison with the measur ement bases;
it is also necessary to coneider the last two terms in expression (2) which depend
on the vertical component of the main magnetic f ield of the earth, BZ.
For a more detailed study o~ the distribution of E in the waves in the coastal
zone of the sea, let us consider the specific prob~em with the following velocity
distribution: ~(kX -~rt)
Vx-~VoXcosQye fX(~) ,
~ ~y =`Voy 5 in eY~e`~kx -~c~ fy l/ c3,
= Vx =Vy for: Iyl>2 .
This distribution is charactexized by the f act that the velocity components along
the cre,st (the y-coordinate) and along the wave propagation (the x-coordinate)
have different damping laws with respect to depth. The existence of such distri-
bution obviously is realistic [7]. For this model of a wave expression (2) is
represented in the following form:
-L(kz-cJf) ~
_ VZe ~~VX~By{x(~.)cosey-eB~ f,.Y(~)~siney~ ~4~
�Voysiney[~fY(~)}~kf~y~~>>> ~
- o .
where .fixy=D~~.fxy~~~di FJf~~~d~'.
From formula (4) it is obvious tha.t as a result the characteristic features of the
electrodynamic solution, the functions f(z) and fl(z) have signif icantl,y different
dependence on depth: namely,
on the surface, z= 0 .
~ }(~~~o, f,(~)=0
on the bottom z = -H
- ~
# ~ ~ f` ~ F
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1~OR (11~1~1('111 l~~l~ c1N1.1
From this condition it fullows that in the general case on the surface oi tk:e s~:a
the vertical component of the electric field E is defined only by the horizontal
component of the field B, and on the bottom,Zby the sum of two terms, one of which
arises from the vertical~omponent of the ma~netic field of the earth BZ, and the
other, the horizontal component B. Inasmuch as for one term of the expresson (41
there is no imaginary factor, theX~hase E will depend on the relation of the ve-
locity components, depth and position of Zthe point of m~,asurement with respect to
the crest. In the middle of the crest (y ~ 0) the phase E is constant with respect
to the entire depth; for other values of y the phase varies with respect to cross
section.
Depending on these factors, the magnitude of the measured signal, that is, the con-
tribution from each term of expression (4), will vary. The ratio of the contribu-
tions of the horizontal and vertical components of the earth`s magnetic field in EZ
is defined by the ratio of these components of the geomagnetic field, and it also
depends on the charact~ristic dimensions along the crest ~t/2R,, the coordinate z
(the observation horizon) and the contribution of the conducting sediments.
_ For the velocity V directed along t?:z meridian the contribution to E will occur
only as a result o~ the vertical component af the earth's magnetic fie~d, BZ,
where it will be the most significant, of course, at high latitudes, on the magne~ic
equator with this direction of the wave motion EZ 0.
In the case of latitudinal direction of the velocity and large valu~s (high geomag-
netic latitudes), the contribution as a result of the two components can be commen-
surate in a wave of equivalent dimensions with respect to wave length and crest
length, especially on the horizons ~H/2. In the middle and low latitudes the pri-
mary contribution is made by the part Ez1 caused by the horizontal component of the
primary magnetic field of the earth.
In the case of a pure "wave current" where the velocity is uniform to the bottom,
chat is, f(z) const = f, and Vy = 0,
E~-~f Vox[Bycvsey~(i- D)B~sinCy], c5>
that is, the vertical component of the electric field E of the "wave current" is
equal to zero on the surface, is maximal at the bottom and has constant phase.
Let us consider this phenomenon in the example of the electric field of sea waves.
In 1973 in the vicinity of the port of Mirnyy (the Crimea) experimental studies were
made of an electromagnetic field of a hydrodynamic source.
The vertical component of the electric field of sea waves was measured by two static
meters with silver chloride elrctrodea by the IZMIRAN~IELAN system. One vertical
measuring base was located at the botto~, and the other near the surface (Figure 1).
The length of eacb base was 1 meter; the distance between centers of the bases was
~2 meters. Both bases were located on the same vertical. Along with the electric
field sensors was a wire wave meter for recording the wave height. The depth of the
sea at the measurement point was ~5 meters. The recording of the electric field
measured on the upper and lower bases and the wave height was made on one tape of
the K-12-22 oscillographic automatic recorder. The mean amplitude E recorded by
the upper meter was 40 to 60 microvolts per meter; the amplitude recorded by the
4
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1~(1R (11~1~1c'141 1~~l: t1N1 \
lower meter was 30 microvolts per meter, and the average oscillatioi~ periocl 5
seconds. The vertical component was measured during stormy weather,
~M
SM
'I M
Figure 1.
A characteristic feature of the recorded vertical fields is the presence of a sig-
nificant phase shift between the upper and lower f ield meters. The phase fluc-
tuates fr.om 60� to 120�.
For interpretation of the results of ineasuring the electric field E of the wave
action, as an example let us consider the model of a wave with cres~ of finite length
and with a specific velocity damping law with respect to depth. We shall consider
only one velocity component VX of the type:
t(kx=wt) ~ ~ (~,H) ~
VX T Va e. cos ly k' H' c6~
where k' _?k2 + k2 . This model approximates the wave motion in ahallaw ~ater when
g < a/2.
In this case
E~=E~~+E~2, E~{=FyVX ~
' E~Z�--F~Vo ~sin eye`~kx-wt~~t~.k'H-
.
~ ? tf~ k' H} .
_ - k, + D c7)
The pair of electrodes located near the surface recorded the field amplitude E
- caused actually by the first term E. For estimation of the ratio of the signals
measured on the bottom and on the surface, let us give the actual values of:
Vn~ 2 m/sec, Fy a 0.2�10-4, T= 5 sec, k~ 0.2, !C ~ 0.06, D 3 30 meters~. Then on
t6e surface, z = 0
i.(k x-wt)
EZ = E~~ � Fy Vx 0 cos e y e (microvolts/meter) .
The second pair of electrodes located near the bottom, z= H meseured the folloV*ing:
~(kx-wt) ~ ~(kz-~,~)
E~ i=Vo Fy cos ey e Z~1 CO,S ~y~ . C~crovolts/meter) ;
5
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~ ~ ~~~A-wi) , H l=
Ez2�-VoFZ k~ sineye {tilk H- D t~t,k'H~
~(kx-c~t)
~3,~ SL11 ~(~e microvolte/meter) .
The sum of the r.omponent E on the bottom wi11 give an oscillation with an amplitude of
~27 microvolts shifted in space along the crest with. respect to E on the surface by
= an argle 60�. The amplitude ratio of the field on the surface and on the bottom
Ez surf ~ 1.5.
- Ez bottom
- According to the experimentsl data, the average value of this ratio will be ~2.0.
The scattering can be explained, on the one hand, by the arbitrary choice of the
parameters k and R and the field F(since the direction of wave propagation was
determined approximately); and on ~'he other hand, by the fact that in real three
dimensional waves the damping coefficient obtained by the experimental data pre-
supposes f aster damping of the orbita:~ velocity with depth [8].
The magnitude of the phase shift and the amplitude ratio E near the bottom and near
the surface are defined obviously by all the terms of expression (4); for mure exact
estimation of these values it is necessary to know the real velocity distribution in
the wave and the location of the meter w~th respect to the wave.
By the surface measurements of E, the order of magnitude of the peak value of the
velocity component in the east--west direction IV~ was estimated:
east-west
E~ _ (40-60)~~06= m/sec.
~~IB-3Max Fy ~.2',~
(a)
Key: a. east ~est max
This is an entirely realistic value for the speed in shallow water during a severe
storm.
In conclusion, it must be noted that inasmuch as the solution (2) which we took from
[6] was obtained for the steady state problem with one restriction the character-
istic horizontal dimensions of the source are much greater than the effective depth
of the ocean the study made in thia article is valid for an entire class of sea
movements satisfying this condition: currents, tidea, long rolling seas and
tsu~iami on the shelf and wind waves in the coastal zone.
In the case of ineasuring the electromagnetic field which csn be considered as a ran-
dom process, it is necessary to consider that not only the magnitude, but also the
phase of the recorded ~omponents depends upon the position of the meter with re-
spect to the investigated wave.
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BIBLIOGRAP1iY
1. M. Longuett
Higgins, M. Stern and H. Stommel, WOODS SOLE OCEANL~GRAPiiIC INSTITUTE
- CONTRIB., 1964, p 690.
2. F. B. Young, V. Gerrard and N. Jerous, PSIL. MAG., tlo 4, 1920.
3. G. A. Fonarev, V. S. Shneyera PROBLEMY ARKTIK~ I A.~vTARKITIKI (Problems of the
Arctic and Antarctic), Leningrad, Gidrometeoizdat, No 31, 1969, p 48.
4. H. Harvey, NOAA-JTRE-72, HAWAII INST. OF GEOPH, Honolulu, 1972.
5. G. A. Fonarev, GEOMAGNITNYYE ISSLEDOVANIYA (Geomagnetic Research), I1o 13, Moscow,
Nauka, 1971.
6. T. Sanford, J. OF GEOPHYS. RES., No 15, 1971, p 70.
7. R. N. Ivanov, IZV. AN SSSR, SERIYA GEOFIZ. (News of the USSR Academy of Sciences,
Geophysics Series), No 7, 1962.
8. A. I. Duvanin, VOINOVYYE DVIZHENIYA V MORE (Wave Motions in the Sea), Leningrad,
Gidrometeoizdat, 1968.
~
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I
DETERMINATION OF T~11; CONDUCTIVITY OF SEDIMENTS BY MEASURING THE ELECTRIC AND MAGNETIC
FIELDS AND WAVE VELOCITY COMPONENTS AT THE BOTTOM OF THE SEA
[L. M. Abramova, pp 11-14]
Electromagnetic fields induced by the movement of sea water in the geomagnetic field
are used in oceanography to obtain detailed information about the velocity structure
of thP ocean movements which sometimes is very diff icult if not in general impossible
to obtain by other methods.
Another aspect of using a hydrodyn3mic source is the study of the deep struc-
ture of the earth, for the f ields induced by it depend on the conductivity, the
thickness of the sediments and the distance to the cenducting mantle. The effort to
use this source to determine the depth to tt~e conducting mantle was made by Larsen
[1] by the method of magnetotelluric sounding. Teramoto proposzd a method of de-
termining the effective conductivity of the bottom of the channel by measuring the
potential difference across the channel, the electric current density and the speed
_ of the water [2]. By using this method a zone of anomal~us conductivity was isolated
under the Sangarskiy Strait;- which is a continuation of t.he conductivitp anomaly
observed in Japan.
In the indicated papers a study was made of a uniformly layered model made up of the con-
ductivities of the ocean csl, the sediments cT2, the nonconducting crust and highly con-
ducting mantle ~m ~1, L].
The influence of the mantle on the induction mechanism depends on the ratio of the
linear dimensions of the hydrodynamic source L and the skin depth of the mantle 8~
at the frequency c.~. The ei~2tromagnetic frequency wave penetrates the mantle to
a depth 8m =(2/ (N , u~ ~ Ctm)
When d/L � 1 it is possible to neglect the mantle; for 8m/L � 1 it is necessary
- to consider the effect of the mantle when estimating the conductivity.
In this paper a method is proposed for determining the effective conductivity of the
sediments by measurements of the electric and magnetic fields and the velocity
components at the bottom. Here the class of movements for which S/L � 1 can be
used as the sounding source. This includes the,wind-driven waves and s~zell in
shallow water, the stationary and certain other movements for which the contribu-
tion of the mantle to the mutual induction process between the ocean and the mantle
- is negligible,
1Tsugaru Strait.
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Let us consider a model of the ocean movement with three-dimensional velocity distri-
bution with respect to the x, y ar.d Z�~oordinates.
In general form the compor.ents of the electric and magnetic ffeld induced by the
movement of the sea water in the model with three-dimensional velocity distribution~
according to the solution of Sanford [3] are expressed as follows:
Ex =Fi Vy* + ~x/G~ , ~l~
- Ey=-Fi VX'~+~y/~1 , (2)
eX_~,GSF~VX~~~_H~+~~~_ZH~ {y. ~3)
a
gy_~6 F V~ /~_N~ Jx
- 1 .y l _ ~ , (4)
where j~, E~ and BXy are the components of the electric current, the field and
magnetic f ield, respectively; F is the vertical component of the.geamagnetic field,
u is t oe magnetic permeability, Z61 is the specific conductivity of sea water V~ _
(1/Dj J'H V~d~ is the average velocity with respect to depth consider ing the conduc-
tivity of the sediments the effective velocity D= S(I + Y) the "effective"
depth to which the induced current penetrates (considering the conductivity of the
sediments), Y= S2/S1 is the ratio of the longitudinal conductivities of the sedi-
- ments S2 and the sea water S1, and H is the depth of the sea.
Expressing j and j from (1) and (2) and substituting in (a) and (4) , we obtain the
value of theXparame~er y-- the ratio of the integral conductivities of the layer
of sediments and sea water:
. +F~ ~X ZBX F~V _ z8y
- Ey ~ ~.~HEy Ex ~ ~,~HEx � ~5~
' Fiaving data available from ~bottom measurements on V~, EXy and BXy, it is possible
to estimate the total longitudinal conductivity of the sediments S2 = ySl,
In the case of a model with one velocity component, for example, VX, the parameter
y will be determined from the expression:
~=i+ F~V - 26X
Ey k ' (6>
The parameter S, as applied to the induction problems of wind-driven waves is quite
provisional in ~he geophysical sense, for the linear dimensions of the source can be
less than the layer of sediments; in this case S defines the effective conductivity
of the part of the sediments to which the curren~ is closed. For long rolling
seas, meteorological fluctuationa, and so on, the linear dimensions of which are
commensurate with the thickness of the layer of sediments, this parame ter determines
the effect of the entire layer.
The contribution of the conducting sediments to the process of el ectromagnetic
field induction as a result of the waves was estimated by the synchronous recordings
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F(1R (1FP(C'L41, II~F. ONl.Y
obtained during bottom measureuaenta of the magnatic field electric field E and
_ velocity components VX of the wind-~driven wa.ves � Thehvertical component of the ~~e
of the measurements was 1.2 to 1.5 meters ~4~� was 0.52'10l4 tesla.
earth's magnet~.c field in the measurement zone
By formula (6) an estimate was made of the parameter y= S2/S1. The mean valuES of
the amplitudes obtained in the time interval of ~100 seconds were taken for the
calculations: V= 2.3 m/sec, Ey = 8.4�10-6 volts/meter, B~ 1.2 ntesla. The
corresponding va~ue turned out tti be equal to 18. If we ta~e the total longitudi-
nal conductivity of sea water S= 61H = 4.8 to 6(moh), it is possible approximately
to estimate the ef~ective longi~udinal conductivity of the part of the sediment
layer through which the currents are closed
~Sy= ~Sl =I8� (4,8~6) =86-I06 (~h)
The correctness of the estimate was confirmed by the results of the spectra:L analy-
sis of these materials when for the given a priori hydrodynamic model, the spectra
of the electric f ield components were calculated by the measured velocity spectra.
The spectra calculated considering the value of S demonstrated good agreement with
the experimentally obtained estimates of the spec~ral densities of the electric
~ field. What has been stated here again confirms that the wave movements of the
field can be an additional source for studying the deep structure of the earth.
BIBLIOGRAPHY
� 1. J. C. Larsen, G~OPHYS. J. ROY. ASTRON. SOC., Vol 16, No 1, 1968, p 47.
2. T. Teramoto, J. OCEANOGR. SOC. JAP, Vol 27, No 1, 1971.
3. T. Sanford, J. GEOPHYS. RES., Vol 76, No 15, 1971.
4. Yu. M. Abramov, L. M. Abramova, S. M. Minasyan, V. N. Mitrofanov, A. S. Shcherba-
kova, "Complex Measurements of Electromagnetic Fields of Waves in the Coastal
Zone. Investigation Procedure and Some Results (see this collection)."
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STATISTICAL CHARACT~RISTICS OF THE RELATION OF THE WAVE PARAMETERS TO TiiE INDUCED
ELECTROMAGNETIC FIELD
[Yu. M. Abramov, L. M. Abramova, pp 15-21]
Up to the present time, judging by the published papers only a small number of stu-
dies were made including simultaneous recording of the parameters of the velocity
field of sea waves and electric and magnetic fields induced by the wave movements.
The small number of such studies is explained by difficulty in stating the complex
measurements at sea, including the absence of special electromagnetic marine equip-
ment.
Complex stud ies of the electromagnetic fields of the waves in the coastal zone have
been performed at the IZMIRAN SSSR [Instite~te of Terrestrial Magnetism, the Iono--
~ sphere and Radio Wave PropagaCion of the USSI~ Academy of Sciences] sin.ce 1971. In
the given paper the results are presented from full-scale studies of electromagnetic
f ields of waves, the purpose of which was establishment of the statistical relations
between the characteristics of the electromagnetic and hydrodynamic fields of the
waves.
The components of the electric and magnetic f ields of the wave action and the hydro-
logic parameters the wave velocity and height were recorded in the coastal
zone of the White Sea (the vicinity of Cape Abramovskiy).
_ The measurement procedure is described in [1]. As a result of this study, synchro-
nous recordings were obtained for three components of the magnetic f ield of the
waves BX, By, BZ, two horizontal components of the electric f ield EX and Ey and also
the hydr~ ~ic parameters the shift of the free surface ZA (A is the wave
amplitude) and the velocity component normal to the shore, Vx.
When processing on a computer, the recording was usually made at increments of 0.5 to
0.6 second.
The statistical characteristics of the distribution, the mutual correlation and
mutual spectral functions and also the coherence functions were calculated.
The statistical parameters obtained during the processing (the excess and asymmetry
coefficients of the distribution functions of the y-axes of the Wave height
recordings, velocity and parameters of the electromagnetic wave) demonstrated
that in the f irst approximation usually the hypo~hesis of normal distribution is
applied.
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An example of one of the mutual cor.relograms chazacterizing the relation of the
parameters EX and hW is illustrated in F~.gure 1.
~ All of the mutual correlograms have the form of functions tha.t damp to the 0.1
level from the maximum value in 10-20 seconds.
The form of the correlograms indicates that in both processes there is a quasiperio-
dic component present with a period of 5~6 seconds which is typical for wind-driven
- waves. The processes are close to the so-called narrow-band processes w~th charac-
teristic periods related to the frequency w0, near which the maximum energy of the
process is concentrated.
For all of the mutual correlograms characterizing the relation of the components of
the electric field (E , E) and the hydrodynamic parameters (V , 2A) the presence of
a shift of a maximum of ti~e mutual correlation function is typ~cal, indicating the
existence of a phase diff erence of the oscillations of these components. The
degree of the relation of the electric field component E and the velocity parameters
(the wave height) is low, and the mutual correlation f ac~or r = 0.5. The small
magnitude of the mutual correlation coefficient of these param~ters obviously is
expiained by the fact that the measurements were taken not at one point, but they
lay on a straight line not coinciding with the general direction of motion of the
- wave front. As for the degree of the correlation of the components E- V, it
appears to be cloaer, r~ ~ 0.7, and this is explained by the fact that the meters
for measuring these parameters were located in practice at one "point," which re-
vealed better interrelation of the processes.
ry=f~1 r~y(z) ' .
as BK4~ ~EX hw) H=~.5n
~ ati
~ nz
.
- 4 -1
v - 6 0 2 ( !0 u T(rsK,l
t . . (a)
- oZ .
-O.ti
Figure 1.
Key: a. T, sec
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Mutua~ correlation analysisof thehydrodynamic and electromagnetic parameters did
not de~.onstrate a sufficiently canvincing relation between the processes in the time
region, which is explained by imperfectibn of the measurement procedure, The re-
sults oi� spectral analysis, however, indicate the preaence of a clear relation be-
tween the investigated processes and the frequency region. A comparison of the ve-
locity spectrum (just as the wave height) with the spectra of the components
of ths electric and magnetic fields demonstrated that in accordance with linear
theory, tYtere is good similarity of these characteristics in the spectral sense,
. Figure 2 a, b.
a z ~ 2,~ Ey, E:
6.0 la/ �
H=6M -2A ~ .
---~y a
4.U ~ ~ -x- Ex .
~
i
20
A
~ Tcex.
o z.o ~~a.o , 6.o a.o io ~2 ~4 ~1~
H=15N
Z 6 ~
1a~ , x
_ 6y .
y.p ZA
. z~ ---dy .
~.o ~ . - x- 6~ 6
.r
, ;
I~ ~~f~~
z.~ ~ ;
~
~
~ .
~ ~
~ T
~ � ~ ~
y ~
~ � ` ~ i~ / ~ ~
i~, ~/i/+ -
- z 4 6 8 10 12 !6 Tcex.(1)
Figure 2
Key: l, second
The curves for the estimates of the spectral density functions of the wave height 2A,
the velocity VX and the electric field components EX and Ey have basic peaks at the
periods of the wind-driven waves. The peaks are well expressed and coincide with
each other. In the estimates of the spectral densities there are additional peaks
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i,G,4,8,pa4 (g~
. ecn E~ 1~
~
~o ~ .
,s
' -e
,
,
' ; A
~
~ ~ ~ 4- s
2 J~ ~ - - c
< !
~
,
i ~
~ ~ ' r .
/ ~
0 0 ' d0 � p T,ceK.
z ~ (b)
r .
~ -4
.
-i
-a ~
Figure 3.
ICey: a. radians b. second
at rhe periods close to the basic period which are lok'er with respect to amplitude,
_ but coincide with each other for all components.
The presence of a relation between the electromagnetic f ield and the velocity field
- parameters in the frequency region also confirm the calculated mutual spectra for
these parameters. Figure 3 illustrates the mutual spectrum of the components EX -
VX, SXy(w).
The wave frequency is plotted on the x-axis, and the mutual spectrum characteristics
are plotted on the y-axis:
G is the mutual spectral density function,
- C is the cospectrum,
Q is the quadrature spectrum,
0 is the phase shift between components.
- The graphs of the components of the mutual spectra indicate that the energy exchange
between the investigated components takes place primarily in the range of periods of
4-8 seconds corresponding to tlie wind-driven waves. On the remaining periods, the
energy exchange is insignificant. The nature of the phase curves i.s different for
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different components, urhich is explained by the separation of the observation
points in space.
The coherence of the investigated parameters is high; its peak~ come on the same
frequencies as the spectral den~ ity and mutualZspectral density p~aks. Figure 4
shows the coherence functions F(w) _ ~SXy(w)~ /SX(w)Sy(w), 0< F(w) < 1 as a func-
tion of the wave period calculat ed for the electric field components, velocity and
_ wave height.
F?(~)
f.0 ~ " .
/ 1
1 ` / 1
~ ~ ` `+1 . .
- Ql ~ � 1 '1 . ~
_ / ~ . ~
i ~
' A
Q6 ~ ~ Ex -z
~ ~i'' ~ ----fx-Vx
~ ~ t~ 1~ i -�-E,~-Ey
a4 1'~~ -x- Ey-2~
\
_ ~ , ~i
0.2 ~ � ~
~ � .
r
~+~t~.,._ rfCK. ~a~
2.0 6.o c.o ao
Figure 4.
Key: a. T, seconds
The investigated results of th e spectral analysis of the parameters of the hydro-
dynamic and electromagnetic wave fields under various meteorological conditions in-
dicate that there is a clear and stable apectral relation between th~.se parameters.
- This again confirms that the el ectromagnetic fielde are a sufficiently exact representa-
tionof wave hydrodynamic processes in the sea. ~
BIBLIOGRAPHY
1. Yu. M. Abramov, L. M. Abramova, S. M. Minasyan, V. I1. Mitrofanov, A. S. 5hcherba-
kova, The Complex Measurements of Electromagnetic Fields of Waves in the Coastal
Zone. (Researct? Procedure andSome Resulte)," See this collection.
~ 15
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COMPLEX MEASUREMENTS OF ELECTROMAGNETIC FIELDS OF WAVES IN THE COASTAL ZOidF,. (RE-
SEARCH PROCEDURE t1ND SOME RESULTS)
[Yu. M. Abramov, L. M. Abramova, S. M. Minasyan, V. N. Mitrofanov, A. S. Shcherbakova
pp 22-40]
At the present time marine electromagnetic measurementa are acquiring great aig-
nificance ~a the overall complex of marine geophysical research.
In spite of their obvious urgency, the measurements of the variable electromagnetic ~
field widespread .for dryland research has still not received suff icient development ~
under marine conditi.one, The reason for this lies primarily in the fact that during
~ experimental studies in the sea difficulties arise connected with the sealing of the
measuring equipment, its stabilizati_on on a moving platform (buoy and floating sta-
tion) and chemical agressiveness of sea water. In addition, the studies of the
electromagnetic variations in the sea are complicated by the appearance of an addi-
- tional source of a variable electromagnetic f ield a hydrodynamic field caused by
movement of the conducting sea water in the magnetic field of the earth.
~lhe most powerful interference when studying the morphology of the variations in the
sea in the short-period part of the spectrum are the electromagnetic fields of
wind-driven waves and swells.
The data from theoretical calculations and experimental measuT~ements indicate
that the maximum amplitudes of the electromagnetic f ields of sea waves have values
from tenths to units of gammas in the magnetic field and from tenthe to hundreds of
millivolts per kilometer in the electric field in the range of periods of 1-40
= seconds, which is entirely commensurate with the electromagnetic fields caused by
an ionospheric source in the same frequency range ($hort-period oscillations) and
even exceeds them. The structure of the distribution of these f ields in the water
_ and in the air has a complex nature connected with the conditions of the movement
of waves in the world ocean, the conductivity diatribution in the ocean and sedi-
ments, the depth of the ocean, and so on.
The electromagnetic fields induced by a hydrodvnamic source can have a significant effect
on the operation of marine electronic reconnaissa~c~ g~r of the electroma.gnetic current
meter (EMIT), lowering the reliability of the measured values. On the other hand,
the induced fields as a function of conductivity, thickness of the sediments and
distance to the conducting mantle, offer the hope for future use of electromagnetic
fields of the hydrodynamic source to study the geoelectric section jl].
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It is no less import.ic~t W~tuay Chr ~lacCr~iuagnetic iialay ~t t?v.lt'~~~ly~?au?.l.: ~rlytu
in the interests of oceanography. At the present time the EMIT [electromagnetic
current meter] is widely known and is finding practical application in oceanography.
The ~lectromagnetic fieZds of wind-driven waves and swells can also be used to study
the nature and the characteristic features of their source.
The enumerated factors indicate the urgency of setting up theoretical and experi-
mental studies of electromagnetic fields of wind-driven waves and swell.
The small number of experimental stu3ies of these phenomena is connected with the
difficulty of setting up this type of ineasurement at sea. The wind-driven wave and
swell fields attenuate rapidly with depth; tYiere is an alternative either to sta-
bilize the measuring elements in the hydrodynamic field wtien performing measurements
at the source or remove the sensors from the source, increasing the sensitivity of
the measuring device. Both alternatives still run intQ technical and procedural
difficulties. On the existing leve~ of ineasurement equipment and means of setting
it up in the sea, reliable measurements of the electromagn~tic fields of sea waves
can be taken most successfully under shoal water conditions. Technically it i~
~ easier to measure the magnetic and electric fields of waves in shoal water; both
scalar and component sensitive elements can be used with the same degree of success.
here, for they are installed on the bottom. The advantage of ineasurements under these
conditions is the possibili*yo uf using differential devices permitting isolation of
the wave f ields in "pure" form. For this purpose one measuring sensor is placed in
the range of the electromagnetic fields of the waves, and the other at a considerable
distance from the source, on land. In the absence of noticeable geomagnetic variation
field gradients of external sources, the difference of the signals of these sensors
is proportional to the electromagnetic field of hydrodynamic origin. In addition,
for cextain wavelengths in the short-period ~:1rt of the spectrum, even a shallow
sea (H 5-7 meters) can be considered as "deep" (H >~1/2), which permits use of
short wind-driven waves as a micromodel of long rolling seas in deep water.
In the USSR and abroad there are a quite large number of magnetometric and electro-
metric devices for recording variable electromagnetic fields on the dry land under
stationary conditions. The specific nature of the operation of the meters under
marine conditions as part of buoy, bottom and floating stations limits the possi-
bili~ies of the application of this equipment, especially when measuring components
~2)�
The basic requirements on the equipment for measuring the electromagnetic fields of
_ sea waves with respect to resolution (0.01 to 1 N in a magnetic field and 0.1 to 10
microns/m in an electric field) and frequency range (1-0.03 hertz) demonstrate that
such observatiora ~an be made using the dev3ce for measuring electromagnetic field
variations in the sea.
In this paper primarily the results of ineasuring the elec*_romagnetic fields of sea
waves are considered which were obtained on an expedition for complex investigation
of variable magnetic fields in the vicinity of Cape Abramovskiy in the White Sea in
1973.
Taking measurements of the electromagnetic fields of sea waves in this region
was complicated by the fact that it is in a zcne of increased magnetic activity.
On the other hand, the advantage of ineasurements at high latitudes is that
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basically only thz verti.cal component o~ the earth's primary magnetic field
� is present, whi,ch simplifies :Lnterpretation of the data ebtain~d and the choice of
models.
~ The region in which the measurements are taken is characterized by a flat coastline
with a slope of 1-2� directed from west to east. At this location the syzygial
tides have a height on the order of 7 meters, and the quadrature tides 6 meters, and
they have a strict semidiurnal nature.
'The diaoram for deploying a set of ineasuring equipment is presented in Figure 1.
Atmaximum low tide the depth of the sea at the point of installation of the sensors
is 1 meter, and the c?istance to sh~re at low tide is 300 meters. .
The electric potential differences were measured by static meters on two mutually
perpendicular bases by 5 silver chloride electrodes of the IZMIRAN-I~LAN system.
Different combinati.ons of these electrodes made it possible to select the length of
the measuring bases equal to 10 or 20 meters. The signal from the electrodes tra-
veled along a P-268 type cable to the recording equipment located on the shore.
All of the measured values :.n this experiment were recorded on the 12-channel K-12-�
22 automatic recorder; the sensitivity of recording the potentiaZ diff erences was
0.03 mv/mm. The diagram of the install:ation of the electrodes in the sea is pre-
sented in Figure 2. In addition to measurements of the potential difference of the
wave electric f ield, the potential method was used, the essence of which consists
in the fact that one of the electrodes (the measuring electrode) is placed directly
in the measured field, and the other ("zero") outside the range of this field. The
signal picked up from the electrodes is in this case proportional to the potential
of the measured electric field at the point of installation of the measuring elec-
trode.
Inasmuch as the investigated signal varies synchronously in time with the speed of
t;~e wave relative to the measuring electrode, the component of the measured electric
field parallel to the direction of this velocity is defined as follows:
a V~ a
Ex ` V
at ' cl>
where EX is the elpctric field intensity component,
~ is the signal measured by the potential method,
- V� is the phase wave velo~ity with respect to the measuring electrode.
Lead plates 50 x 700 x 3 mm served as the zero electrode in the potential measure-
ment wethod. They were dug into the ground a distance of 2Q0-300 meters from the
edge of the water on the land.
The m a g n e t i c f:. e 1 d c o m p o n e n t s of seawaves were measured by a f erro sonde three- ~
compoaent magnetometer installed on the bottom. The "y" component sensor was set up
perpendicular to the meridian and parallel to the shore; the "x" sensor was set up
_ in the direction of the meridian and perpendicular to the shore, and the "z" sensor,
vertically.
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~
?+~tu~ri,6 ~h~ _ _ N
rnfr6~~N
0 ~ A
o ~ .
~
~o ~
(g) _ ~ o ~ n~5
~ .
0
D a N ~z S
r o
z
Ki ~4 N3
f ~ g s-e
nNxNA ~nax�
oTnue~
' o ~
~ � . ~ A'
~ . '
(e)
06Pb18 ~
H=1~0 = !5M ~
~
~ .
\ AA60PA~~aoE ~
IIONEIC~EHNE ~
- Q
QATyNK CKOpOCTH N QAB/1~HNF (a)
Figure 1. 3A~KTPOJ~b/ ('b)
Q-MAI'NNTONErP
_ Key: a. laboratory facility e. scarp H= 10-15 mete~rs
� b. speed and pressure gage f. ~ximum low tide line
c. electrodes g. depth pro~file with
d. magnetometer respect to the A'A line
h. depth scale
The general complex for measuring the magnetic field components was made up of the
follow:.~ig: ~
1. SG-56 magnetometer with sensor,
'l. comp~ensator for the constant component of the earth's msgnetic field,
3. connecting cable,
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3 _
�
_ ' S ~
. .y 4
- 2
J i- ~eKr~? poa '
2~rca6u�
3-,~on.~a6oK
4 - a Kop~
5- ~a.~c
Figure 2.
Key: 1. electrode 4~ anchor
'L. cable 5. halyard
3. float
4. recorder,
5. power pack,
6. nonmagnetic container made of fiberglass.
The sensors of the magnetometer fastened orthogonally in a common fzame and the
magnetometer were placed in a sealed container. In turn, the container was fastened
to a massive nonmagnetic slab and was put on the bottom from a boat at maximum low tide.
The slab was held on the bottom by weighta for greater sta.bility. The signal from
the magnetometer was transmitted over a KNSh-18 type cabl~ to shore to the recording
system. A composition current was fed over the same cable to the sensors.
The components x, y and z of the magnetic field were recorded with speeds of 6 mm/
sec or 1.5 mm/sec. The magnetometer had the following scale divisions of the analog
recording by comgonents: x= 0.52 'y/mm, y~ 1.0 Y/mm, z= 0.48 y/m~.
The measurements of the hydrologic paramE=ers of the waves (velooity component normal
_ to shore, V and wave . height 2A) were taken by electrochemical converters convert-
ing the mec~ianical inputs to an electric signal.
~n addition to the enumerated measurementa when performing the operations, the
metec~rological and hydrological conditions in the vicinity of Cape Abramovskiy were
observed and recorded by the hydrographic service of the meteorological station.
Every three hours the following characteristics were recorded: the wind speed and
direction, the average wave height, the nature and predominant direction of the waves~
the water level at the measurement point. These data ~rere taken into account when
~rocessing and analyzing the observation results.
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~ crystal variation meter .of the V. N. ~bzQV system ~as set up on shore. The
magnetic activity when measuring the electromagnetic fields of the waves was esti-
mated by the readings of this meter.
As a result of the studies, synchronous recordings were obtained for the electrotttag--
netic f ield components and the hydrodynamic parameters at different depth~ resultin~
from the tides. A sample recording is presented in Figure 3.
The procedure for processing the experimental data depends to a signi~icant degree
on the purposes and goals of the study. The following set of parameters was
processed:
1. The electric potential differences on bases perpendicular and parallel to the
shore (the electric field components EX and Ey, respectively).
2. The wave potential at the point
3. The magnetic field components ~X, By, BZ�
4. The velocity components of the water perpendicular to the shore, VX.
5. The displacements of the free surface at a point, 2A.
In order to establish the amplitude-phase relations between d~fferent f ield components
from synchronous recordings, the ordinates E, B, V, A were picked up, and the ampli-�
- tude and phase relations were studied for pairs of these parameters~
When using the statistical method of interpretation of the results obtained, the
recordings were deciphered by special standard curves. The volume of one realization
included less than 80 to 1Q0 wave periods [3J. The digitalization step size was
selected as 0.5-0.6 second. The ordinates were reckoned from the base line.
The primary processing was done on the "Mir-1" computer by the programs of [4].
For each parameter of the electric, magnetic and hydrodynamic f ieldsthe statistical
ch~;:acteristics of the investigated processes were calculated: dispersion, mean
square deviation, asymmetry coefficient, excess coefficient and their errors. These
- ~~alculations demonstrated that both the hydrodynamic parameters and the characteris-
tics of ~the electromagnetic field of the sea waves (periods and ampliturlP~l are
subject to a normal distribution law on the wholp.
Histograms and distribution curves of the wave heights, velocity and electromagnetic
_ field which had been constructed by empirical data w~re used to study the statisticafi
properties of the amplitude and period distribution of the investigated processes.
Let us f irst consider the amplitude distribution.
Figures 4-5 show the amplitude histograms of the components E, E of the electric
field, the velocity VX and wave height 2A for different depths ofy the sea H= 1.5
meter and 7 meters.
Ranges of values of the investigated element are plotted on the x-axis on
the graphs, and the number of cases is plotted on the y-axis in percentages of the
total number of terms of the series n(n = 30~). The upper scale of the x-axis is
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~ ./~.1 w ~
~ ~ .
. ~..-�`-`K-, (a)
_ ~ x
~+~1
~~`r^~1./ ln. A'
V
E,~ n 0, 5z , r/NN �
f 9 � 1' ~ y~NN .
Fr = o,4d r/NN ~
�A - 0,3"~�N
Figure 3.
Key: a. sec
the transformed distribution series, and the lower scale is expressed in units of the
investigated element. The relations constructed on the basis of the histograms are
the distribution or recurrence curves of the element.
Using the recurrence curve data, by successive summation of the number
of cases, the x-axes of the integral distribution curve called the element guaran~
tee curve in oceanography, were calculated and constructed.
The characteristic values of the investigated element are as follows: y is the mean
value or center of distribution, y50~ is the value of the element with 50% guarantee,
y is the value of the element of greatest recurrence (mode); they permit deter-
n=max
mination of what type of distribution is characteristic of the given parameter..
Thus, for y= y50% - yn=max' there is a symmetric distribution curve. Examples of
the recurrence and guarantee curves of the electric field and velocity amplitudes
for sea depths of 1.5 meters and 7 meters are presented in Figures 6 and 7.
Analogous calculations and constructions were performed ~or the periods of the
electromagnetic fteld and hydrodynamic parameters, Figures 8-11. As is obvious from
the histograms, waves are most frequently observed with periods of 2-4 sec. Such
periods have the highest recurrence rate in the electric and magnetic field of the
waves. The analysis of these curves must give answers to the following questions:
1. Does a relation exist between the amplitudes and periods of an electromagnetic
_ and hydrodynamic f ield and in which components is it the closest.
2. How does the variation of the sea depth at the measurement point influence the
properties of the distribution curves.
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(a) N =15?+ CKdpOCmb ~
- Bb~cem.a -
20 6onHet, Yx
zR 30
t0 I
~ ~ 20
~ ' ?~4 , .
o ~ ~
~ , ,
01 o.s r o (N) ~0
~ o ,
3ajy i i . '
I ~-~4 0 4 ~x
20 Q2 ~6 29 (�k�/ce,r )
-
t0 -
E
-4 ~ , ~ z y i
0.5 co ~75 2s 3.3 X 10 -
Figure 4. '
hey: a. wave height o. m/sec
b. speed d. EP = electric field
An analysis of the histograms, the recurrence and guarantee curves for the amplitudes
and periods indicates that the statistical relation exists and is quite re-
liable.
The peaks of the distribution curves with respect to amplitudes clearly coincide with
each other, Figures 6-7. The amplitude distribution curves of the electric field
- and velocity are closest to each other. The peaks of the electric field and velocity
distribution curves by periods do not coincide with each other. The peaka of the
electric field distribution curves Ey, as a rule, are shifted somewhat in the long-
- period direction.
The estimates of the similarity of the distribution curves made by the ~olmog o~rov-
Smirnov number ~ demonstrated that with a probability a= 0.01 all pairs of
velocity and electric field distribution curves give values of the coeff icient ~ less
than ~~r, which indicates the presence of re?iable similarity of these curves.
- The distribution of the magnetic field components both by periods and by amplitudes
is less clearly exprc:ssed by comparison with the other elements. This is explained
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- JO (a) .
' CKOpocm a ~
~ Vx
zo ~
. .
~o ~ ~
~ _d ' _4 . ~ 4 , Vx
0.2 R7 , l.2 (.~/c~K) ~b)
zo 3n E~
c~~
~o ~ ~
-a ~ o -4 ~ EX
~ ~
0 f.0 3�D 5.0 ~~6~.u~�!0-z
(d) '
z4 3/1 E y
_ ~o .
-a -ti o ~ Fy
0 3 z.7 51 (ru~~,~,.~.,o-:
- Figure 5.
Key: a. velocity c.electric field E
h. m/sec d. (millivolts/meter~ ~10-2
by the fact that the magnetic field as an integral characteristic ia the sum
" of the interaction of the electric currents in scme part of space.
Let us consider the distribution characteristics of the elements of the inveatigated
fields for different sea depths. It is known that in deep water (g >~/2) and
shallow water (H a/2) for all spectral components.
The statistical wave height distribution in shallow water ~ri = 1.5 meters), as Figure
6 shows, is characterized by a decrease in the variety of t-~ie- wave heights
as well as the amplitudesof the induced electric field. This is explained by the
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~a N=~.SM . y H- ~ '
30 Vx..
6 y zo
30 ,
f0
20 .
.
!0 0 3.0 iU jceK.
~-~-T, ce~r. 'j~ (a,
r, i.5 ?.5 3�5 ~ ~a) Ey
30 6x . 20
zo ~o
T,ceK.
o so 70
% l.s z.~ 7.5 rte~. . ~a~ .
zA ~ Ex
30 ' 30
_ ZO 2~
r0 . , ~o ,
(a) (a)
ZS ~,5 ~.g T,ceK. p 3.0 7.0 TceK.
Figure 8. Figure 9.
Key: a. T, sec Key: a. T, sec
- TceK ~a~
. ~ ' . .
~o H=2M ~
. ~
. .
so ~
.
~ -
~------''T-v-==-~= R
a.o ~ ~y,so~
, ~
. i y~.~+az
to ~ ~ yzso%
~ ~ yz max
1 . �
I �
I �
p 30 100
Figure 10.
Key; a. sec
breaking of high ~raves when traveling through shallow water. The amplitude distri-
bution and guarant~e curves become symmetric, approaching normal gaussian distribu-
tion. Analogous distribution characteristics are manifested by camponents EX and Ey
of the electric f~eld.
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T�
(a)
~ N=7?, ~
s.o - i\\ ` r
. _ - - y,,~~
- ' - _ = y ax
S.0- . i"~-~,_~ zn`
~ , ~ Yx
i ~ ~ .
lo. ~ . - Ey
~
9.0 ~ ~
I
0 s0 /Oo
Figure 11.
Key: a. T, sec
Thus, the investigated distribution characteristics make it possible to consider that
there is a defined statistical-probability relation with respect to amplitude and
period between the parameters of the hydrodynamic source and the components of the
induced electromagnetic field. The recurrence and guarantee curves of the electric
field and velocity are closest to each other.
This result indicates expediency of the search for a functional relation .in the
electric fields and velocities during further.studies of the magnetohydrodynamic
processes in the sea.
BIBLIOGRAPHY
1. J. Larsen, GEOPHYS. J. ROY. ASTRON. SOC, Vol 16, No 1, 1968, p 47.
2. V. V. Novysh, I. I. Belyayev, D. L. Finger, L. M. Abramova, MORSKAYA MAGNITO-
METRICHESKAYA APPARATURA (Marine Magnetometric Equipment), MG SSSR VIEMS,
Moscow, 1974.
3. I. F. Shadrin, PROTSESSY RAZVITIYA I MET~DY ISSLEDOVANIYA PRIBREKHNOY 20NY MORYA
(llevelopment Processes and Methods of Investigation of the Coastal Zone of the
Sea), Moscow, Nauka, 1972.
4. ALGURITMY I PROGRAMMY STATISTICHES~:OY OBRABOTKI I NABLYUDENIY NA ETSVM MIR I
MINSk-22 VASKHNIL (Algorithms and Programs for Statistical Processing and Obser-
vations on the Mir and Minsk-22 Digital Computers of the All-Union Academy of
_ Agricultural Sciences), izd. Pochvennogo inst-ta im V. V. Dokuchayeva, Moscow,
1973.
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COMPARISON OF TWO TYPES OF DEVICES FOR MARINE ELECTROMAGNETIC SOUNDING
[L. B. Volkomirsk~aya, G. A. Fonarev, pp 41-45]
The most urgent problem for interpretation of electromagnetic soundings using natural
fields is the problem of the influence of the horizontal geoelectric nonuniformities.
When performing magnetotelluric soundings in the sea, the eff ect of the nonuniformi-
ties can be especially perceptible, for the measuring devices can be in direct
proximity to these nonuniformities. In the theory of marine magnetotelluric sound-
ings, the Tikhonov-Kan'yar bottom unit and separate magnetic device are considered
prospective [1].
In this paper a comparison is made between these two types of magnetotelluric de-
vices.
Let us consider the two-dimensional model of nonuniformity. Let a plate of finite
thickness d consist of two halfplates in contact along the interface for x= 0 and
having conductivities 61 # 62� At the top and bottom of the plate is an insulating
medium. The external inducing f ield is uniform and equal to BQl Let us propose
- that ar_ a deptY. oi ul ~ d there i~ a u.nirorm iield source ~3 = ~(B0, ~1~ . Ir~ Lhib
case in [2] a method was proposed f or gradual approximation to construct the approxi-
- mate solution. According to this method for the m+ 1 approximation the field com-
ponents are expressed as follows:
a ~k ~'t, ,
g~ 1~y,~)-_ 16y~yo,~)-~ ~y� -
_-��gm d a~k(~ yo,0 dyo ; cl~
y~yo, ) ~y
m.~
( , C~ g ( p~+ ~ ~ B~ ~ (~o, 0) ~yo ~ c2~
~ y ~ oy ~ 1 _
_ ~ ~o y .
g,,,.i d_Z . d_~�� B~'~ (yo,d) d o, c3~
y~y, ) Boy~y~ J yo y . y
where r(~/'~o) is the Green function. Then for the f irst approximation consid-
_ ering the expressions for the Green functions given in [3], from (1, 2, 3) it is
possible to obtain:
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~ ~ ~
BZI~~ ~(LB~+~~IJp.d~~~\ 1)n~~~n~dnio(nz~e ~~.5~n7L~~~~ ~4)
~ ~
EX(~c)==~~~Bo
f (Bo,d~)~~( I)n)~~R c~s~n~ � ~S~
=dnz ~dnx ~�LR: -ol.nz~ eXP~ dn~ y~-~{~;
~ ~
By(y,0)=zBa+ dCBa+~( ~)~}(Ba.d)J~~R x c6>
d y ~
~(dni_~n2~{E~~d~ y~ e~~ y_El/ dn~ y) e n~
< <
~ By (y,d)=1.}~Bo,d~)- ~~Bo+~C i)" (BO,d,)]~ �n ~
~,o t n_o cn
! �~n: f dnt y
~~dn~"dnz) Ei~dnzl~~e -~j,~dnty)e ~ �
Here
~n _K~ ' ~n - L ~ ?t 1U k1 W~l,c.0 G
~n = nr/CI.; ' -
- a=l.~.. � ,
Let us consider the case where ~,,y(~,d)=~oy(~,(~~ ~ and let us write the relations of
the components EX/By~Z_d and ByIZ_O~Bylz-d'
EX _`i~[~+~~ ~~n,L~n\ i~n dR! edn~ _ 11 z ,
~ ~ y urtz
~ _ n+0 ,
By 7=d ~ 9~L1~~ * \ ~/nJ ~~n \dn! dnz ` ~8~
- n�0 n=0
where: A-=E~~dnzy)e nzy_Ei,~-dnty)e n,y;
g Z.Q ~'~L~~~1 ~/nJ~ERL1d 1 ~ ~1 n1---
yl ~ ~~.1~
n ir ,
Qyli~d 2- ~ ~ d~z (9
n,o ~.o
The most general method of interpreting the magnetotelluric soundings in all cases
consists in direct calculation and subsequent interpretation of the curve pT, the
apparent resistance.
In the case of ineasuring by theTikhonoV~Kan`yar bottom. device the curve pT is cal-
culated by the formula:
.AT =1~,12zT , - cio)
where I~!nl - I ~y IZ d
, The methods of calculating the curve p for a gradient magnetic sounding are inves-
tigated in [4]. We shall use the fornlula;
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_ ~ .[Rc ~ a~d-t]~Im(~ ~i aedJz ~ ~11~
' t~T~d ~
where ae = ~ c,~i~~.o 6" .
For our case a thiak plate this formula has a small error. Let us convert for-
mula (11) . For this purpose we mak.e the assumptioa tha.t ;d~ i,/Re ae:
Then: ~.~0~
PT =P, ( I g---y~-I)~ ( thZX ~
,
where x = ~L ~w~ , ~
~
It is theoretically possible also to perform more exact calculations by formula (11),
but in this case it is necessary to perform the calculations on high speed computers.
In the figure there is a graph of the functions p~ for different relations be-
tween the conductivities of two halfplates, where we denote the apparent resistance
of a unif orm plate as p0.
For the calculations of Ex~Hyl and -~~~-=d , by formulas (8, 9) we assumed that
a =d v a = 0~
the measurements are performed in the sea at d~stances of O.ld from the nonunifor-
mity. With approach of the observation point to the nonuniformity the relations
must be maintained qualitatively. The solid lines ~oin the points calculated by
3T~Po . .
~ g ~ ~ .
. !
7 ' ~
5
3
. ~
~ .
~ / 2
1 - "
o ! z q 6 8 i 0 ~~2/6r
(8, 9) with limitation to the f irst term in the series considering smallness of
a02y, a01y; the dotted curves were obtained from the asymptotes of the formulas (8,
9) for Q1 = Q2. Curve 1 is constructed for measurements by the Tikhonov-Kan'yar
method. Curve 2 is constructed for the methnd of magnetic gradient sounding.
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~ A comparison of the two devices permi.ts tfie conclusi.on to be drawn that the Tikhono~-
Kan'yar bottom device is significantly more strongly subjected to the influence of
the nonuniformity. This indicates that th,e distortions ia the electric field are
greater than in the magnetic f ield.
BIBLIOGRAPHY
1. M. N. Berdichevskiy, L. L. Van'yan, IZV. AN SSSR. FIZIKA ZEMLI (News of the
USSR Academy of Sciences. Earth Physics), No 11, 1969, p 51.
2. R. Treyman, GEOMAGNETIZM I AERONOMIYA (Geomagnetism and Aeronomy), Vol 10, Vo 4,
1970, p 588.
3. P.. Treywan, GEqMAGNETIZM I AERONOMIYA, Vol 10, No 3, 1970, p 478.
4. I. L. Trofimov, G. A. Fonarev, GEOMAGN~TIZM I AERONOMIYA, Vol 12, No 2, 1972,
p 301.
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MEASURIIIG THE SEA LJAVE-INDUCED ELECTRIC FIELD
[G. A. Fonarev, V. Yu. Semenov, pp 46-51]
It is known that during propagation of sea waves in the earth`s magnetic field not
only magnetic, but also electric f ields are induced. The calculation of the magni-
tude of the induced electric field based on the potential hydrodynamic theory of
motion of a fluid in a two-dimensional progressive wave, was performed by the authors
of [1, 5]. Analogous calculations for waves chara~terized by the eddy nature of
motion of the fluid in them were performed by the authors of reference [2]. Inas-~.
much as the process of induction of the electric field by sea waves is described
most simply by a mathematical ~.odel presented in the first papers, the analysis of
the measurement procedure and interpretation of the electric f ield of the waves is
performed on the basis of this model.
The electric field in~duced by sea waves is measured usually by the method of ineasur-
ing the potential difference between two different points in space inside the fluid.
The magnitude of the electric field potential ~ at any point of a two-dimensional
wave is described in the form [1]:
~(xo; zo)~a(~o)cos(kxo-~t).
Here a is the amplitude of the induced potential ~hich depends on the speed of the
fluid particles in the wave and on the intensity of the constant magnetic field of
_ the earth; k= 2~r/a, W= 2~r/T, where ~ is the wavelength, and T is its period. The
waves are considered to be steady, propagated in the direction of the X-axis.
Let us consider the case of ineasuring the horizontal field induced by the wave. Let
us propose that the potential difference is measured between two points in the sea
lagging behind each other a distance L in the direction of propagation of the wave.
The magnitude of the recorded potential difference is then written in the form:
`~~-~-~2, ~o)-`P~~~2' ~o)--za(~o)5rn( i~
~S1nwt -
The expression for the potential difference, if it is measured in the vertical direc-
tion can be written in the form:
~P(Xo; 7o)-~(Xo; ~{~)=[al~o~-a(~oa~)Jcos(kxo-~,f).
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Thus, from the expressions abtained ~t i:s ohv~ou~ tb.at the measurements of the
horizontal and vertical electric f~eld of tf~e w~ves d~.�fer noticeably; tile poten-
tial difference in the vertical direction does not depend on the relation between
the wavelength and the distance between the electrodes at the same time as the
horizontal field is essentially determined by this ratio.
The measured potential difference of the horizontal electric field as a function of
the sea wave length expressed in magnitudes of the length of the measuring base is
presented i_n Figure 1. As the unit in the figure, the maximum possible signal
picked up from the electrodes equal to 2a is uaed. Thus, the measured potential
difference can be highly insignif icant, or absent in general in the case where the
distance between the electrodes is a multiple of an integral number of sea wave
lengths.
It is necessary to note that the indicated procedural characteristic of ineasuring
the potential difference can in individual cases lead to the appearance of a hDri-
zontal electric field of groups of waves on the recordings. This situation can be
realized when the spacing between the electrodes is equal to or a multiple of the
basic wavelength in the sea wave spectrum. For example, when measuring a horizontal
_ electric field in the sea with a depth of three meters waves with periods of 3.~ and
4.8 seconds will be recorded with maximum possible amplitudes if the spacing between
the electrodes is 60 meters inasmuch as the lengths of these waves are equal to 17
_ and 24 meters respectively [3]. The periods of these waves are close and, conse-
quently, the formation of beats on the electric field recording is possible. Thus,
the groups of waves isolated by the recording of the horizontal electric field can
be unrelated to the group structure of the wind-driven wave field in the sea [4].
It is possible to identify the groups of oscillations in the recording of the elec-
tric field with the groups of the wi.nd-driven sea waves directly only when observ-
ing the vertical component of this f ield.
Let us now consider the procedure for interpreting the data carr:ied out most fre-
quently with the application of spectral analysis. From the above-investigated
proeedure for measuring the electric field induced by sea waves it follows tha.t in
the spectrum of the potential difference in the horizontal direction sharp decreases
in magnitude of the spectral density are observed on frequencies which correspond to
wave lengths which are multiples of the length of the measuring base. Therefore when
interpreting the estimates of the spectral density of the process which is a record-
ing of the potential difference of the horizontal electric field of the sea, it is
necessary to consider that the usually applied smoothing of the spectral density
can lead to significant reduction of the signal in the frequency range, the wave
lengths of which are less than the length of the measuring base.
Now let us consider the experimental data. In Figure 2 spectra are presented for
the synchronously recorded amplitudes of the sea wave and variations of the hori-
zontal electric field. As is obvious from the figure, the spectra of the investi-
gated processes differ noticeably: on the spectrum of the electric field recorded
in the direction perpendicular to the direction of wave propagation with a distance
between the electrodes of 300 meters, sharp, statistically significant "troughs" in
the spectral density are obvious at the same time as analogous phenomena are not
observed i.n the wave spectrum. Thus, it is possible to propose that waves with
periods of about 10 and 20 seconds have a crest length equal to or a multiple of
300 meters.
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_ ~ � _
~ .
' ~
.
I -
I
~
N
I
I
I ~
d
� ~
M
� O
. J
N
~
p o0 ~ ~T
- d CO Oi ~
Figure 1.
Thus, using the peculiarities of the procedure for observing the horizontal electric
field induced by the sea waves, it is possible to determine the relation bet~reen the
wavelength and the length of its crest and also directly to check the I~ydrodynamic
disperse relation using a spectral analysis of the recordings of this field.
The conclusions drawn are valid both for stationary measuring bases and in the case
of moving electrodes. However, in the last case it is necessary to consider that .
the recorded period of Che electric field oscillations can fail to compare with the
sea wave period.
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~C?~ttRJ ' ~�~~[~J .
. (B)
~ ~
a ~ .
.z ~ .
s .
to' ,
:
s '
, .
~ ~ 1 a9 ~ a
_ ~o: ~ a ~ 1
2
3
10~'
Z s
2 �
i0 20 ~0 5 3 ceK. ~Ca .
Figure' 2.
Key: A. cm2-sec
mv2-sec
G. sec
BIBLIOGRAPHY ,
1. G. A. Fonarev, GEOMAGiQITNYYE ISSLEDOVANIYA (Geomagnetic Research), No 13, Moscow,
Nauka, 1971.
2. A. B. Leybo, V. Yu. Semenov, GEOMAGNETIZM I AERONOMIYA (Geomagnetism and Aero-
~ nomy), Vol 15, i1o 2, 1975, p 231.
3. ~3. Meote, WEDENIYE V GIDRODINAMIi~U I TEORIYU VOLN NA VODE (Introduction to Hy-
- drodynamics and Wave Theory in the Water), Leningrad, Gid.rometeoizdat, 1974.
4. V. S. Bychkov, S. S. Strekalov, MORSKIYE NEREGULYARNYYE VODNY (Irregular Sea
Waves), Moscow, Nauka, 1971.
5. M. S. Longuet-Higgins, M. E. Stern, H. Stommel, PAPERS PHYS. OCEANOG. METEOROL.
MASSACHUSETTS IiJST. TEHCN. AND WOODS HOLE OCEANOG. INST. Vol 13, No 1, 1954,
p 1.
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ESTIMATING ELECTRIC FIELDS CREATED BY A TWO-DIMENSIONAL WAVE SPECTRUM
- [M. M. Bogorodski~, pp 52-61]
~ Hydrophysical electrical electrode stuclies are p~rformed for the soluti~n o~ a
= number of scientific and practical problems. In this paper a study is made of the
possibilities of interpreting the data from the point of view of the theory of small-
- amplitude potential waves, beginning with the concepts of sea waves as the probable
process having the property of ergodicity. In the linear approximation the surface
can be represented in the form of the sum of a large number of simple waves having
different anplitudes, lengths, propagation directions and random phases [1, 3, 4].
The results are found in the form of integral spectra.
_ Let us introduce the cartesian coordinate system xoy, placing the origin of the co-
ordinates on the level of the undisturbed sea surface. The elementary wave, the
beam of which makes an angle 6 with the x-axie can be written in the form
' ~ y. 2, f) = a ~5---~~ cos~r~t � E -k (x ~osB ~~si.o 9)~ (1.)
~ ,
' where S(x, y, z, t) is the vertical deviation,
k= 2n/~ is the wave number (J~ is the wave letrgth),
w~ 2tr/T is the angular frequency (T is the wave period),
- h is the 3epth of Che sea,
E is an arbitrary phase shift.
I.et us first define the electric potential caused in the water by the effect of the
earth's magnetic �ield HX, H, H with monochrome (1). The results of studying the
Y
electric field of a monochromatic vave [6] permits recording the electric potential
for such a wave in the form:
~rx.~,~.t~=c~~ycasB-N~s?~6~~ ~(x,y.~,t~,
- c2>
where HX and HY ar2 the components of the earth~s magiietic f ield,
- ~ ~ _ ,l~~k~ ~ is [he phase velocity.
Y
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The wave elevati,ons will be represented in the �ot~a of the sum of the large number
of monochromes of the type of (1) , describing each of the.~t in the form;
~~a (x,~.~,f)= a~~ e~~ a~ee . 5~~ ~
~
t.~~~ -k~~x~se~ +~~S~e~].r.. c3~
In this case the total wave elevation can be represented in the form:
X~~.~.~.t~= ~ ~a~~e.~ awee . S~k. ~.h~ x
a
~ _ s.
(4)
- ~~osj~t.~~~-k~(x~ases +~S~es)].
Here, in accordance with the papers by Yu. M, Krylov [1] and V. Pier.~on I4J we shall
- consider that the phase eij of each term of (3) is a random variable uniformly dis-
cributed in the interval from 0 to 2~r, on the basia of which the value of X(x, y,
z, t) is also random. We shall also consider that the pha.ee ei~ is an aligned
- ergodic function of the horizontal coordinates and time so that for the point A(x1,
yl' ~1~ '
j - �t~ ~ x~ ~s ~ > > (5)
and also
a = o. '
_ (6)
The total electric potenti.al of the point A with respect to the bottom where it is
f.ound to be equal to zero will be found by summing the elementary terms of (2):
~~~~y~~~t~-~ ~ ~J~~,B-~)~~~ (x,y,e,t), c,~
~=:m ~=-a
where for multiplfcity of the recording the following f unction is lntroduced:
~~~~,6,~~=~~~Nyeos6~-HxsuzB~~'SSk' (8)
~
or, what amounts to the same thing:
~ J(k,6,~) _-~-fi~ k~f~~Ny co,sB~ -Hz sin 6~J ~ sk~ ~+h z c9)
z
The electric potential dispersion of the point (x, y, z, t) ean now be written as
= the sum of the individual contributions of the type:
0~~~2 - ; ~.2(~ e~~ow ee~ . ~ ~lo~
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On transition to continuity, the integral spectrum of the electric pot:ntial of the
point acquires the form:
~
_ ~z~~~=z ~~~z~~',e,~~a2~~,s~~e~~~. c~~~
O
- The intensity of the electric field E(x, y, z, t) can also be considered as the
sum of the intensities created by the individual monochromes. From (7) we have:
E~~~ y ~ t~= a ~l~y,~.t) _
m rt
~k~~~~+h)Y~~(~)al~e) o~aeX c12>
~=-,n ~=-z
x ~,~~~`t -k~ ~a,~es ~~s~e~)~~
E~.~y~t)= a~rx~~,t~_ c~3~.
x ~x
~ ~
_ ~ ~.k~~~c~~~~~~ es) oWae ~$es x
~_-m s__~.
xs�~~t~~`~ -kG(x~os8. ~ys~ed~,
s ,
_ . Ey lx-~~ ~~ax- t~ _ ~
~
m ri,
= ~ ~k ~ e.~,r--'
~~s ~ ~ d a~ee S~ed x c~4~
s=-z
xs~j~t+~~~=k~~x ~~ed ;ys~e~~].
When making the transition to the continuity the integral apectrum of the camponents
of the electric field intensity at the point acquires the form:
~ _ -
~ E~ ~~~-z f~kz~`~~~z~~`h~~JZ(~e,~~~~~~e~~e~~ c15~
,
o
- .
Ex(~)=z k2r~~~,~Ze~z~~;e,~)~z~~e~ded~; ~16,
, ,
o -T
~
Ey z .~fk~w~s~ze ~z(~; e,~~~z~~e~~e.~~ c~>>
~
o
where 2
~(w, 6, z) can be represented by expression (9) considering that k(w) is the
solution of the equation:
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~ ~ ~ = k ~ kh . ~is>
It is essential to note that for z>~h even a narrow region of angles 9 for which
a2(w, @) # 0 makes a defined contribution to the spectra of all three components of
the electric field vector. From formulas (12), (14) and (15) it is obvious that
E does not have correlation with E or E. Simultaneously it is obvious that the
z x y
the two-dimensional terms Ei~X and Ei~Y are distinguished only by the proportion-
aiity factor which permits confirmation of the presence of the correlation between
any mutually perpendicular components of the horizontal intensity of the electric
field at the point with the exception of the isolated directions in which the cor-
relation changes si;n.
In the following calculations we sha~l conaider that the two-dimensional energy
spectrum of the elECtric potential b(u, v, z) is given as a function cf the wave
numbers u and v directed along the ~ and y axes, respectively. The variables u and
v will be introduced in terms of the variables w and 6 as follows:
u = k (c~r) co,~ B
7I~ = k (w) sin6 (19)
where k(w) is the solution of equation (18).
In the new vari~,.bles the expression for the integral spectrum of the electric poten-
tial will be written in the form:
~ ~
~z~~~ - z ~z~", ~r,,~) dc~~drr. ~ZO>
In particular, the spectrum b2(u, v, z) can be given in the form:
z ~ ~z(~, 4) ~JZ(c~; 8,,~
B (u, --k~~j w~ , ~21~
~
where the inverse transition from the wave numhers (u, v) to the variables (w, A) is
easily realizable considering (18):
_ a2(w,e~~z~~~,e,~~=az~u~~a~; ~~~;e~,~]X
~ ~ Xk~~,). ak
~ ~ZR - .x'~
yz - ys '
emerging from the origin of the coordinates of the initial spectrum b2(u, v, z)
has the form:
. �
VB 2(jL~~.~) _ ~ ~~2~(L, U~ G~ll'~a
_o, . (24)
where
u' = u coS 6~? rrsi.z 6
_ S~ e � ~ ~se ~ ~25~
- Inasmuch as the spectrum (24) and the autocorrelation function for the potential
.~e( R~~ > with respect to the same direction are uniqu~ly related [5], we have:
~
- ,~'B (R,~)=~'Jz GB (u,'~)~sRu'd~c'. c26>
0
Now we can write the dispersion of the potential difference at the points A and B
in terms of the known values of
-
U z(R, e, _ (~A_~e )z= z~~ ~~~)._,Y~'B (R ~ c2,~
where
~ R = ~(xz -x~z.(yz-y~)z
. (2s)
2
~(z) is the dispersion of the aligned function ~(z), for example, (11), (20).
The magnitude of the autocorrelation function of the electric potential with respect
to direction enterinb into expression (27) can be represented in the form of the
integral frequenc}r spectrum if we consider tt~a.t from (26) ,(25) ,(24) ,(20) and (19)
it follows that: ~
~ (R~~)_ / z ~
a,~--- z B ~k ~se; kS~e,~~~,~~Rk~s~(6-e)]d6
- , ' c29)
from which considering (18) we have:
~R~~~ _ ~~e ~R~'~~ k(w)] dar, , cso>
B D � .
where z ~ k~t
~grR'~~k~~'~=~ t~kh + X
~
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~
_ x Jz ez[k~,~e;ks;,9,~~~(Rk~S~e-~~de;
.
cs- ~rk kh � ~ ~
d~~ ~ (~k~.+ )
- z k ~ kh ' -
In the case where the spacing between the electrodes is large, that is, for
.
R� ~ , L .~e (R,~)~--~0, . (3i)
where L is the average crest length expression (27) degenerates, acquiring the form:
~ = z Uz(~~, (32)
In the special case where the wave spectrum is limited to a comparatively narrow
frequency band ~w and the directions A6 (swell), applying the theorem of the mean
to the expressions (11), (16) and (17) and assuming, without limiting the generality
~
6= 0, considering (32) we have:
Ex = k z(~r) ~ z~~~ k z~~) U 2(~) ~ ~ (33)
_ E y = ~ c34>
.
The course of the horizontal electric field intenaity E in the vicinity of the
point (x, y, z, t) can now be approximated in the foraa:X
Fx ~x, y, t)= ' k UZ(~) S~~~t -k~w~ ~ ~13~
~
,
Sometimes instead of the mean square values for the speed of the estimates it is
convenient to use the mean modulus values. As a result of the proposition of
narrowness of the frequency band we have:
. U2.(~) =2~ I U~~>+ . ~
and it is possible to rewrite (13) in the form:
Ex~x, j, = ~ k~w~~t1~~~~5~~~ t _k~~,~.x . ~3
Expressing k(w) in terms of the average wavelength a, we have the working formula
for estimating the mean amplitude of the horizontal component of the electric field ~
am(L ) at a depth z for the swell propagated from the direction coinciding with the
X-ax~s:
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C
~~c~(~)~= ~,`4 zr~) - 4~ 3 I U~z~ 35
. ~ . . ' ( )
Considering (13), (13) and (31), we have:
lun~~~~l]- 4 = U~~~~
. ~ I ~ (36)
where the sign am denotes the average amplitude. Let us note that the expressions
(35) and (36) do not depend on the form (10) of the function ~2(w, d, z) or on the
proposition (6) which require [2] confirmation. Significant generality of the
expressions (35) and (36) makes it possible to use them for experimental checking of
tiie relations (6) and (10).
Conclusions:
1. Within the framework of the linear theory of small-amplitude waves propagated
_ in a sea of arbitrary fixed depth and interacting with the earth`s magnetic field,
two-dimensional integral spectra are obtained for the electric potential and three
components of the electric field at the point where the two--dimensional spectrum of
the wave elevations on the sea surface is given. It is demonstrated that for all
horizons above the bottom, even the narrow nonzero region of the two~dimensional
wave spectrum creates nonzero spectra of all three components of the electric in-
tensity field; here the correlation between the vertical and horizontal components
of the electric intensity within the framework of the linear model is absent, and
the horizontal components of the electric inrensity, in general, are correlated.
2. In the general case of a two-dimensional spectrum of the electric potential
connected with the two-dimensional wave spectrum, the expression is found for the
integral spectrum of the electric potential difference arieing at the ends of an
arbitrarily oriented horizontal base as a function of its length and orientation.
It is demonstrated that if the length of the base is much greater than the mean
wave length (or the mean crest length), and the spectrum of the electric potential
difference at its ends will be equal to twice the spectrum of the electric potential
of the point located at the same depth, and it does not depend on the length and
direction of the base. The relation found from its experimental study of the
variation with depth of the electric potential spectrum, independently of the
propositions regarding the distribution of the phase shifts and the damping with.
depth and also independently of the presence of a"zero" point for electric measure-
ments.
3. In the special case of limiting the two-dimensional wave spectrum by the narrow
frequency band and propagation angles (swell), operating relations have been ob-
tained for finding the mean amplitude values of the electric potential and hori-
zontal component of the electric intensity at the point where, for example, by the
measurement results the magnitude of the mean square (or the mean modulus) value
of the aligned potential difference on a"long" base and the mean wave length are
known. These relations also do not depend on the propositions of the course of the
, electric potential field with depth.
The author expresses his sincere appreciation to G~ A. Fonarev and V, Yu. Semenov
who looked at the paper and made a number of valuable comments.
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BIBLIOGRAPHY
1. Yu. M. Krylov, SPEKTRALrNYXE METODY ISSLEDOVANIYA I RASCHETA VETROVYKH VOLN
(Spectral Methods of Investigating and Calculating Wind-Driven Waves), Lenin-
grad, Gidrometec,izdat, 1966. ~
2. A. B. Leybo, V. Yu. Semenov, GEOMAGNETIZM I AERONOMIYA (Geomagnetism and Aero-
nomy), Vol 15, No 2, 1975.
3. M. S. Longuet-Higgins, VETROWYE VOLNY (Wind-Driven Wav.es), IL, 1962.
- 4. V. J. Pearson, VETROVYYE vuLNY, IL, 1962.
5. V. V. Solodovnikov, A. S. Uskov, STATISTICHESKIY ANALIZ OB"YEKTOV REGULIROVANIYA
(Statistical Analysis of Adjustment Targete), Moscow, Mashgiz, 1960.
6. G. A. Fonarev, GEOMAGVITIVYYE ISSLIDOVANIYA (Geomagnetic Research), No 13, Moscow,
Nauka, 1971.
/
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G~,NERAL PROPERTIES OF THE Ai10MAL0US MAGNETIC FIELD IN ~tIE WORLD OCEAN
[V. G. Larkin, V. i~. Lugovenko, A. G. Popov, pp 62~79]
In accordance with the work program of the Soviet Antarctic Expeditions from 1970 to
- 1974 on the expeditionary vessels, diesel electric ~'Ob~," diesel electric "Navarin"
and scientific research vessel "Professor Vize," measurements were made along the
way of the modulus of the total intensity of the earth's magnetic field.
The surveys were made along the longest routes,which were in the Atlantic and
Anarctic Oceans (Figure 1). The total length of the processed marine magnetic pro-
_ files is about 100,000 km.
Magnetic observations were performed by the co-r~orkers of the IZMIRAN Institute us-
ing the towed marine quantum T-magnetometer providing for obtaining field values
with accuracy to +2 gamma. The mean square error of the surveys, including the
errors for f ield variation, inaccuracy in gridding the vessel, and deviation
amounted to about +35 gammas.
All the data obtained on the sparse profile grid permit the solution of the most
general problems with respect to interpretation of the anomalous magnetic field
and its relations to the geological structure of the ocean floor.
At the present time throughout the entire world interest is increasing in the
exploitation of the mineral resources of the world ocean at ~reater and greater
depths and at greater and greater distance from the shore,
The revelation of the history of the world ocean, its tectonic regionalization are
important theoretical problems, the solution of which is necessary, in particular,
also to discovery of the laws of the location of mineral deposits jl].
Magnetometry is perhaps the only geophysical method which can provide information
not only about the structure of our planet, but also about the evolution of its
development. The geophysical~analysis of the anomalous magnetie field in the oceans
is an effective means of determining the chronological, kinematic and geometric
characteristics of mo~�ement of the lithospheric plates.
Since the results of the hydromagnetic survey ate a continuous recording of the geo-
magnetic field along individual profiles of great extent, it is expedient to sub-
ject the anomalous magnetic f ield along these profiles to a statistical analysis.
The expediency of a statistical analysis ie connected with the fact that it permits
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(a) cxe~w au~pWpy*ce ~+arnNTNenc N7MEpe~xi+ ~
, ~~i i
I~~'
~ ' ~ .
i ' i ~
~ a. .
~ ~ ; ~ fi ~ra.
I ~ ~ I ~d~
i
I
I ~
1
i
~ ~ ' �r
~ ' i
- ~
~ i
~ I 0
~ ~ ~
- !e
~ ~ ry \
~ \ ~
i~
.
) f ~
NfN. ~ ~ qpr. Mtl~Mifrr.
Figure 1.
Key: a. chart of the magnetic measurement routea
b. Canary Islands
ca Bellingshausen Iles
d. Orkney Islands
e. Sandwich Islands
f. Novolazarevskaya station
g. Molodezhnaya
h. Amery
i. Mirnyy
j. Vostok
k. Leningradskaya
- 1. Kerguelen
discovery of the principal defining properties of the f ield wh3,ch can be related to
the basic peculiarities of the structure of the ocean floor. In contrast to the
usually accepted procedure when individual anomalies are interpreted, in a statis-
tical analysis preliminary separation of the field as a united process into its
individual elements takes place, each of which reflects some property of the
anomalous magnetic field which, in turn, is related to some peculiarity of the
structure of the ocean crust.
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Let us present a brief description of the investigated statiatical parametera and
their physical meaning.
The dispersion of the anomalous magnetic field R basically represents the charac-
teristic of magnetization of the magnetic sources'~(as a rule, basalts making up
the sea bed).
The correlation radius of the anomalous magnetic f ield rp 3 reflects the horizontal
dimensions of the anomalies, which is basically connected'with the depth of the
sources and their tiorizontal dimensions.
The mathematical expectation of the anomalous magnetic field (M) represents the total
effect: inaccuracy of approximation of the normal field, average depth of sources,
measure of magnetization, and so on.
For estimation of the general properties of the f ield and its relation to the geo-
logical structure of the earth's crust, a statistical analysis has be~n used more
than once. Thus, in reference [2] a correlation analysis of the anomalous magnetic
field of the Pacific Ocean was performed, and the diff erence in values of r0 and
R was noted for the mid-ocean rise and slopes. Tectonic mapping was carried'out
basically with respect to the general pattern of distribution of the anomalous
magnetic f ield (the amplitude of the anomalies, their horizontal dimensions) using
data on the statistical characteristics of the anomalous magnetic field (~he dis-
persion and correlation radius). In reference [3] a statistical analysis is pre-
sented of the circular latitudinal prof ile of the vertical component of the mag-
netic field passing near 40� south latitude, and the possibility of applying the ,
autocorrelation analysis for regionalization of the anoma.lous fields is demonstra-
ted. The statistical characteristics of the anomalous magnetic field in the cen-
tral part of the Atlantic Ocean were investigated in reference [4] in which the
results of the autocorrelation analysis are also presented. In this paper regiona-
lization of the sea bed is carried out with respect to the morphological attri-
butes, and a study is made of the behavior of the statistical parameters within the
limits of the isolated zones. In reference [5] a study is made of the properties of
the anomalous magnetic field in the vicinity of the Indian Ocean using the sliding
energy spectrum procedure. A statistical analysis of the aaomalous magnetic field
of the Inaian Ocean was also carried out in reference [6J in which ~ method was
developed for quantitative discription of the variations of the anomalous magnetic
field on long individual profiles.
However, up to now the problem of the difference or sirailarity in the statistical
properties of the anomalous magnetic f ield of the continental and ocean crust has
not been finally solved. Thus, in ref erence [7] the conclusion is drawn that the
structure of the continental crust differs theoretically from the structure of the
ocean crust, which f inds it reflection in the difference of the statistical proper-
ties of the anomalous magnetic field. On the contrary, in reference [8] the
authors arrive at the conclusion of similarity of the average characteristics of
the magnetic field of the continents and oceans. This difference in points of
view obviously is related first with the fact that when analyzing the anomalous
magnetic fie.'d various procedures were used, and secondly, the fact that in these
papers the regionalization of the territory of the dry land and the oceans as uni-
form regions was not clearly carried out in the sense of the geological structure
of the region.
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In references [2, 9] an estimate is made of the statistical properties of the
anomalous magnetic field separately for different tectonic provinces and it was
demonstrated tha.t the tectonic provinces uniform in the genesis sense have station-
ary anomalous magnetic fields. For tnis purpose in order more precisely to define
the concept of the nature of the anomalous magnetic field of the ocean crust and
its relation to the structure of the sea bed, we made estimates of the statistical
properties of the f ield along a number of profil.es of the marine magnetic survey.
The statistical analysis procedure was identical to the one used in reference [9]
- in which basically an analysis of the anonalous magnetic f ields of the continents
was performed.
The ocean floor can be divided into four large provinces differing with respect to
origin and development [4]: the midocean ridges, the slopes of the ridges, the
deep sea trenches and coastal regions. Therefore when generalizing the statistical
analysis of the anomalous magnetic field, average field characteristics were deter-
mined segarately for each province.
The procedure for estimating the statistical properties of the field was reduced to
the following. The normal field TH~ was isolated for all profiles of the surveys by
representation of itby a spherical --harmonic series with n= 9 harmonics. Then the
obtained difference OTa = T- T~ was centered, and the statistical parameters of
the anomalous magnetic field were calculated for the aligned values of the anomalous
field.
In order to obtain information on the statistical properties of the anomalous mag-
netic field along the prof iles, a special program was used to perform the calcula-
tions on a digital computer. The essence of the program consists in the follawing:
1) Information is input to the digital computer on the profile of the field T(the
coordinates of the point5 of rotation of the prof ile, obserued values of T every 5
km, the magnitude of the secular variation).
2) For each value of the field T the normal field TH and the f ield ~Ta are calcula-
ted.
3) The file of values of ~T formed is aligned for the aegment of the profile L
which must "slide" along the initial prof ile. For the aligned values of the anoma-
lous magnetic field, the autocorrelation function and other statistical character-
istics are calculated.
4) Then the sliding segment L is shifted along the file of values ~T by some amount
~L, the calculation is repeated, then a new shift by ~I, takes place,aand so on to
the end of the profile.
For all routes L was selected equal to 1~20 km, and DI, - 125 km.
The selected model of the norma.l field is not always suff iciently high quality. As
a result of analysis of the mathematical expectation of several sections in the
Antarctic Ocean it was discovered that inexact alignment of the anomalous magnetic
fields along the profiles is connected with the fact that:
1) the variable part of the field is not considered in the analysis;
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2) the model of the spherical harmonic series approximates the main geomagnetic
field in southern latitudes with some error (the mathematical expectation reaches
150 gammas).
By the results of statistical processing of the analyzed profiles of the anomalou$
magnetic field we constructed maps of the graphs of some of the statistical parame-
ters. In Figures 2 and 3 the maps of the graphs are presented for the parameter Q,
(Q = and the correlation radius r~.3 of the anomalous field.
The maps were constructed as follows. All of the analyzed sections were applied to
the base with a scale of 1:15,000,000, and the ~rofiles of the sliding segments were
numbered along the profiles.
The lines for the arrangement of the profilea corresponded to the median value of
each of the investigated statistical parameters when constructing the graphs of
these parameters along the prof iles. The values of the parameters exceeding the
median were glotted to the north (for sublatitudinal profiles) or to the east (for
submeridlanal profiles) of the profile line and they were plotted on the maps by
solid lines on the corresponding vertical scale for each of the statistical parame-
ters. The dotted lines desigr?ate the values of the parameters ~hich are lesa than
the median value.
When analyzing the maps of the graphs of the stat;stical parameters it is necessary
to consider first of all the requirement of co-dimensionality in which the relation
is laid out between the choice of the length of the analyzed section and tne size
of the tectonic structures. The selected length of the profile 1020 km, which is
optimal for statistical representativeness of the analysis can be recognized as
commensurate with the large tectonic structures such as the ocean trenches, the
slopes of the midocean rises and the seamounts themselves. Secondly, it is neces-
sary to consider the requirement of sameness of the method of obtaining the �
statistical characteristics of the anomalous magnetic f ield over all the ocean.
profiles and for the aeromagnetic profiles on the continent j9], to solve the prob-
lem of similarity and difference of the statistical characteristics of the anomalous
magnetic f ield for sections of the continent and ocean.
The parameter 6(Fi~ure 2) is distributed most regularly. On the map it is quite
clear that the increased values of this parameter are associated with the regions
of the midocean rises. Thus, for example, the southern part of the Midatlantic
Ridge, the western and eastern branchea of the Indian seamounts aave values of
Q= 17~-180 gammas. The deep sea trenches are characterized by reduced v~lues of
the parameter Q reaching about 100 gammas here. As for the very large values of
Q~ 220-250 ga~as in the vicinity of the African-Antarctic Ridge on the Pacif ic
Ocean seamount and also in the African-Antarctic and New Zealand trenches, this is
obviously connected with the fact that the profiles of the hydromagnetic survey
in these regions run along the linear anomalous zones.
From the graphs of r~.3 (Figure 3) it is obvious that the minimum values of this
parameter (5-6 km) are characteristic for the majority of midocean ridges if the
survey profiles are run across the strike of the ridges. The deep water trenches
located at significant distances from the axis of the ~idges have values of rQ.3
for the same arrangement of the profiles with respect to the strike of the
structures, three or four time~ greater than over the ridges themselves, and they
are equal to 16-25 km.
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~~I Y `a~__f_._..
1 . .
.
~ .
- ,
; ~
~ /~P~w~
,.~.:4.t ~ ~C)
: ~.Yf~Y.u ~ `
(b)
.
.
I
_ ' ~
� . r
~ ~ .
,
. ~
.
. ~ ~
~
I ' ,
r ~
~ .
� M
1 M
~ ~~.,~~y (s> ~ ~ .
d `
_ c ) (f>. 1
" rlrw 1C/h,~V /
.1. ,
~ .r.._.~ ~g)
~ ' `h, ! .
~
M
/ '
/ .
~ . ~ ~
\
'
t`
V~
~ ~ ryi~ rI~.~ROs
~ ~ `s eo~~ 4Tb
/ ~ ~
~F~*~�--
'4
~ .
Figure 2.
- Key: a. map of the graphs 6 of the f ield (~T) a
b. South America
c. Africa
d. Bellingshausen
e. Novolazarevskaya
f. Malodezhnaya
g. Mirnyy
h. Vostok
i. Antarctica
Leningradskaya
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. .
ti w...~ R~l~~ '
~..e~.,..~, ~ y
(a) . .i~' .
~ ~ .
~ � r ~ :
r ~
r �
d � +
r
~
r s/'- ~ ~
1 ~ 1
_ i ~ ~
~ j .
~ V
/ ~ i
/
� i
M
M
I~N~~ ~
~~I/~MLllyl
(d) .�,~.y..
(e ~
1 ~
� r � r w+ i
~~g~
f)
, ~
a.w. h1
~ A l1 ~
~ ~ . .
~ ` .
/
.
\ ~
a
~~Q1� f 0/iMRO~
I~M/1 (,~~a
!
vi
_ ~
Fi.gure 3.
Key: a. South America
b. Africa
c. Bellingshausen
d. Novolazarevekaya
- e. Malodezhnaya
f. Vostok
g. Antarctica
h. Leningradskaya
i. map of the graphs of r~~3 of the f ield (OT)a
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The slopes of the midocean ridges of seamounts occupy an intermediate position
with respect to the values of Q and r0.3'
Since the magnitude of the parameter r0.3 is influenced by the direction of the pro-
file with respect to the st.rike of the anomalies, when genpralizing the results, the
values of the correlation radiuE of the anomalous magnetic field were used which
charactertzed the anomalous field along the profilea cutting defined structures
acr~ss their strike.
_ In connection with the fact that the magnitude nf some of the statistical parameters
(especially the dispersion and correlation radius) is essentially influenced by the
height of the magnetic survey with respect to the magnetic sources, it is necessary
to reduce the obtained values to the identical relative level o� the survey.
For this purpose the calculated mean statistical parameters of the anomalous mag-
netic field for profiles cutting the middle ridges across their strike were recalcu-
lated upwarcl so that ttie recalculated values of the parameters gave a representation
of the properties o� the anomalous field on the same altitude with ~espect to the
magnetic sources. The parameters Q and rQ.3 for the midocean ridges were recalcula-
ted to a hei~;ht of h= 2 km, for the difference ~h between the average depth of the
ocean over the ric?ge (~2 km) and the average depth above the trenches (~4 km) is
about 2 km. The parameters of the anomalous magnetic field for the slopes were
recalculated f or ~h = 1.5 km, and ~h of the trenches was taken equal to zero. The
parameters of the anomalous magnetic field for the coastal regiona were not recalcu-
lated, for it is difficult to estimate the eff ect of the magnetically active sources
of the ocean crust in this zone as a result of the presence of magnetic sources of
the continental shelf.
If we approximate tiie correlation func~t~T~ of the anomalous magnetic field by an
exponential-cosine function: R= R~e cos ~T, in which the parameter a de-
fines the rate of decrease of the function R, and the parameter ~ reflects the basic
_ periodicity of the function, we obtain the following mean values of the parameters
~ of the anomalous magnetic field for different provinces:
Ocean provinces Statistical parameters Before re- After re-
calculation calculation
~ :~lidocean ridges R 32400 2 18225 2
q,~ 0.1 km 1 0.08 km 1
~ 0.14 rad�km'1 0.12 rad�km 1
r0.3 6 km 8 km
_ Slopes o� the ridges R~ 22500 2 1690 2_1
a 0.7 km-1_1 0.7 km -1
~ O.J9 rad�km 0.039 rad�km _
r0.3 9 km 13.8 km
In Figure 4 the relation is presented for the mean value of the parameter ~ as a
function of the distance to the center to the middle ridge with respect toisolated
zones the solid line corresponds to the initial values of the parameter, and
the dotted line, to the recalculated ones.
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In Figure 5 an analogous relation is presented for the parameter.
The upper solid line corresponds to the average values of the par~meter r0.3 with
respect to all profiles, the lower solid line, with respect to the prof iles cutting
= across th~ midocean ridges and the dotted line is the analog of the last curve
- recalculated upward.
,
200
- !50
.
~
~ ' -
~
~
~
~
100
cpeAUxHO- r l (
orreaxuvecKUe~a~ cKh~~4sr r'~r~j~doxo6oaNbr: np
~6pe~+cxare
RO,t[NpTNA noAHRruu XOTA06UHbi paKOxb~ �
Figure 4. Graph of the statistical parameter Q.
Key: a. midocean rises c. deep sea trenches
b. slopes of the rises d. coastal regions
Since the parameter es is a function of the degree of magnetization of the sources,
it is possible to arrive at the conclusion that in the last ten million years the
magnetization of the rock has decreased somewhat, and at a signif icant distance
from the rise the rock formed several tens of millions of years ago has still less
magnetization.
This conclusion finds its confirmation in referen ~e [4], the authors of which,
estimating the distribution of the natural residual magnetization of the ocean re-
sults and the dependence of the amplitudes of the ocean anomalies on the depth of
the floor and on the distance to the axis of the midatlantic ridge arrive at an
- analogous conclusion: the decrease in the intensity of the magnetic anomalies on
going away from the axis of the ridge is connected not only with an increase in
depth of the floor, but, primarily, with variation of the nature of the sources of
the anomalies.
The average values of r~~3 of the anomalous magnetic field turned out to be equal
- to 6 km, 9 km and 20 km, respectively, for the middle ridges, slopes and trenches.
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, ,r~~a)M � -
40
30
20 ~ . '
~ ~
i
/~i
!0 ~
0 f -
cpeRUxxo-(b) ~~c~ d ~ ~e~~ ca~exs:e
oxeaNuvecKUe ~xn H! rny6D~o6o,aHae 1n+
noSZNRTUA noliNATUU. KOTAO6c1Hbt p:+uuNb~
Figure 5. Graph of the correlation radius r0.3
~ey� a. r0.3, km d. deep water trenches
b. midocPan rises e. coastal regions
c. slopes of the rises
After recalculation of the survey for one altitude, new values turned out to be 8
- km and 13.8 km, respectively, for the middle ridges and their slopes. This fact
obviously indicates an increase in the horizontal dimensions of the hlocks into
which the ocean crust is broken on going away from the axis of the middle rise.
The unrecalculated values obtained for the parameters a and r0.3 coincide well with
_ the analogous parameters of the anomalous magnetic field calculated in reference I4],
in spite of the fact that the authors of this paper applied another procedure for
estimating the statistical properties of the anomalous magnetic field: another
_ model of the normal field, another (and inconstant) length of the investigated
profile and an entirely different stepsize of the sampling of the field values
Ox = 0.5 km. This indicates reliability of the results that we obtained and also
that the sample of initial values of the field used by us (Ox = 5 km) was sufficient
in the first approximation to discover the frequency properties of the field even in
the vicinity of the midocean rises, for the difference in values of the parameter
- r~.3 which we obtained in reference [4J does not exceed 1 to 1.5 km.
From what has been discussed above it follows that the statistical properties of the
ocean are different for its different geomorphological provinces. Therefore it is
expedient to compare individual uniform provinces of the oceans among each other,
and these provinces with the untform regions on the continents.
For example, if we compare the anomalous magnetic fields of the most ancient plat-
forms (of the Siberian type) with the anomalous magnetic fields of the youngest
midocean ridges, the difference in horizontal dimensions of the ma.gnetic anomalies
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is isolated clearly (the median of the distribution of the parameter r 3 of the
anomalous magnetic f ield of the Siberian platform is 22.5 km). This p~obably is
connected with different horizontal dimensions of the blocks of the continental
at~d ocean crust and, possibly, is defined by different thickness of the entire litho-
sphere within the limits of the compared regions. A comparison of analogous parame-
ters for the same platform and deep water ocean trenches does not give a noticeable ~
dif�erence which obviously is caused by approximately identical thickness of the
lithosphere of the compared regions.
In connection with the fact that the analysis of the anomalous magnetic field has
great significance for the creation of new global tectonics (plate tectonics), we
studied the anomalous magnetic field in the southern part of the Atlantic Ocean
also from the point of view of the hypothesis of expansion of the ocean floor.
'Ifao sublatitudinal profiles of rhe marine magnetic survey were subjected to analysis,
the location of wfiich is presented in Figure 6. From a compa~i~on of the observed
value of the field with the curves for the time variations of the f ield on the same
days when the observations ot the magnetic f ield were made along the profil~es in
Figure 7 it is obvious that the measurements were taken on days w~th undisturbed
magnetic field.
Profile I(Figure 7) has the picture of the anomalous magnetic f ield which is typi-
cal of the midocean rises. As for profile II, although it is appreciably south of
the South Atlantic ridge and in the bottom relief of the.ocean in this part there is
no significant rise as occurs in the vicinity of prof ile I, the picture of the
anomalous magnetic f ield along profile II is astonishingly similar to that which is
observed in profile I.
60 50 40 30 20 10 0 10
10 10
65A56 ~
' ~ ~~iT-`..~'y~6
rli�
~~ii i I
- _ Z 2 .
40 ~ - - 40
50 . ~ 50
c'nP
O
o �
- ~II
70 60 50 40 30 20 f0 0 ~0 0
- Figure 6. Location of prof iles I and II.
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.{~r (a) -
. -
. ~
M ~
~ ~ t ~
�
~ (b)
.w .
i,~ Ti,( ~
J 1 ! ~
~ iN
~ ~
Graphs of T~ and Ta along the profiles I and II.
Key: a. profile I
b. profile II
Considering this fact and also based on the data on the seismic activity in the
- vicinity of profile II [10] and the presence in this region of a slight rise of the
ocean floor, we have drawn the conclusion of a continuation of the South Atlantic
Rise from Bouvet Island southwest in the direction of the Antarctic continent.
Thus, it is possible to consider that the rif t system of the South Atlantic Ridge
has its continuation to the southwest, and in the vicinity of Bouvet Island there
is a node from which three rift systems radiate analogously to one which is ob-
served in the center of the Indian Ocean. Estimates of the separation of the ocean
floor made by profiles I and II confirm identical rate of separation of the acean
floor in the South Atlantic and in the vicinity of the southern Sandwich archipelligo..L~
Generalizing the results of the studies, it is possible to draw the following con-
clusions:
1. Regular variation of the statistical properties of the f ield in various parts of
the World Ocean is demonstrated.
2. It is shown that the magnetization of the ocean rock and horizontal dimensions
of the blocks of the ocean crust vary uniformly as a function of the distance to the
axis of the ridges.
3. When comparing the spectral composition of the anomalous magnetic field of con-
tinents and oceans, differences are discovered in the spectrum of the midoceanic
rises and ancient continental platforms, which indicates a difference in structure
of the ocean and continental crust of these regions.
- 4. In the spectral composition of the ancient platforms and deep water trenches no
- noticeable difference is detected which indicates similarity in the structure of
these regions and also that the thickness of the lithosphere under these structures
in practice is identical.
S. The difference in frequency properties of the anomalous magnetic f ield does not dis-
appear after recalculating the survey levelfor one altitude.
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6. On the basie of analysis of the constructed maps of the graphs, an effort is
ma.de at tectonic regionalization of the ocean floor.
7. A continuation of the South Atlantic Ridge to the southwest of Bouvet Island in
the direction of the Antarctic continent was discovered, and the conclusion was
drawn of the existence of a nade in the vicinity of Bouvet Island from which three
rift systems radiate.
BIBLIOGRAPHY
1. V. V. Fedynskiy, V. Ye. Khain, MINERAL'NYYE RESURSY MIROVOGO OKEANA (Mineral
Resources of the World Ocean), Moscow, Nauka, 1974.
2. M. A. Effendiyeva, ANOMAL'NOYE MAGNITNOYE POLE TIKHOGO OKEANA I EGO SVYAZ' SO
STROYEiVIYEM OKEANICHESKOGO DNA. AVTOREF. KAND. DISS. (Anomalous Magnetic Field
of the Pacif ic Ocean and Its Relation to the Structure of the Ocean Floor.
Author's Review of Candidates Dissertation), Leningrad, 1970.
3. Ye. N. Roze, M. A. Effendiyeva, GEOMAGNETIZM I AERONOMIYA (Geomagnetism and
Aeronomy), Vol 8, No 4, 1968.
4. Ye. G. Mirlin, et al., ISSLEDOVANIYE PO PROBLEME RIFTOVYKH ZOid MIROVOGO OKEAi~TA
~ (Investigation of the Problem of Rift Zones in the World Ocea.n), Moscow, Nauka,
1974.
5. V. N. Lugovenko, A. N. Pushkov, METODIKA GEOFIZICHESKIKH ISSLEDOVANIYE OKEANOV
(Procedure for Geophysical Studies of the Ocea.ns), Moscow, Nauka, 1974.
6. H. A. Roeser, "Fourier Analysis of Widely Spaced Magnetic Profiles from the
Northwest Indian Ocean," GEOL. IB. E2, Hannover, 1974, p 81.
7. V. N. Belugina, E. A. Burtseva, V. N. Lugovenko, N. N. Lugovenko, TEZISY DOi~OV
VIII I:ONFERENTSII PO POSTOYANNOMU MAGNITNOMU POLYU, PALEOMAGNETIZMU I SVOYSTVAM
GORNYKH POROD CH. I. POSTOYANNOYE GEOMAG~TITTIOYE POLE (Topics of Reports of the
8th Conference on the Constant Magnetic Field, Paleomagnetism and the Properties
of Rock. Part 1. Constant Geomagnetic Field), Moscow, 1970.
8. T. N. Simonenko, T. A. Gorshkova, A. A. Petrova, TEZISY D~KI~ADOV VIII KONFEREN-
TSII PO POSTOYANNOMU MAGNITNOMU POLYU, PALEOMAGNETIZMU I SVOYSTVAM GORNYKH POROD,
CH. I. POSTOYANNOYE GEOMAGNITNOYE POLE, Moscow, 1970.
9. V. N. Lugovenko, STATISTICHESKIY ANALIZ ANOMAL'NOGO MAGNITNOGO POLYA TERRITORII
SSSR (Statistical Analysis of the Anomalous Magnetic Field of the Territory of
the USSR), Moscow, Nauka, 1974.
10. I. S. Kulon. RAZRASTANIYE OKEANICHESKOGO DNA I DREYF MATERII:OV (Expansion of the
Ocean Floor and Drift of the Continents), Leningrad, Nedra, 1973.
COPYRIGHT: IZMIRAIJ, 1975
- 10845
CSO: 8144/1460 ~
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