JPRS ID: 8682 USSR REPORT GEOPHYSICS, ASTRONOMY AND SPACE

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~~PRS L/8682 -
25 September 1979
-
U S S~~~~~t R e o rt
p
GEOPHYSICS, ASTRONOMY AND SPACE
. . CFOUO 5/79)
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� JPRS L/8682
25 September 1979
~ USSR REPORT
GEOPHYSICS, ASTRONOMY AND SPACE ,
(FOUO 5/79)
This serial publication ~ontaino articles, abstracts of articles and news
items from USSR s~ientific and technical journals on the specific subjects
reflected in the table of contents.
Photoduplications of foreign-language sources may be obtained from the G
Photoduplication Service, Library of Congress, Washington, D. C. 20540.
Re~quests should provide adequate identification both as to the source and
the individual article(s) desired.
CONTENTS PAGE
I. OCEANOGRAPHY 1
, Translations..~ 1
Synoptic Eddies in the Open Ocean A New Discovery
in Oceanology 1
' Study of Deep Fautts 12
~ Geomagnetic Field Disturbances Created by Sea
Currents........ 23
' Electromagnetic Field of Sea Waves in an Electrically
Stratified S2a 32
Systemic Principles for Analysis of Ocean Observations.... 41
! - a- [III - USSR - 21J S&T FOUO]
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I. OCEANOGRAPHY
;
i Translations ,
~ UDC 551.46
SYNOPTIC EDDIES IN THE OPEN OCEAN A NEW DISCOVERY IN OCEANOLOGY
~ Moscow VESTNIK AKADEMII NAUK SSSR in Russian No 6, 1979 pp 43-51
~ [Article by Doctor of Physical and Mathematical Sciences M. N. ICoshlyakov]
! [Text] By the late 1950's-early 1960's oceanologi.sts had a fair gener~.l
! idea~concerning so-called macroscale circulation of ocean waters, that is,
about the system of inear~ (in time) ocean currents, from which disturbances
with periods less than a year are excluded. This idea was based primarily
on indirect data obtained by means of an analysis of the distributions of
, te~perature, salinity and dissolved oxygen in the world ocean and by means
of computations of macroscale currents on the basis of the densii.y distrib-
ution of ocean water. The links in such a macroscale circulation in the
upper layer (with a thickness of about one kilometer) in the North Atlantic
are, for example, the Gulf Stream, the North Atlant~c Current and the North
Trades Current (Fig. 1).
~dith respect to disturbances of inean circulation, by the late 1950's there
had been�a fairly good study of one extremely specific type of such dis-
turbances the so-called frontal eddies of the Gulf Stream and Kuroshio,
forming as a result of the development and subsequent cutoff of ineanders
(wavelike curvatures) of strong and narrow ocean currents (Fig. 2). [In this
article we do not examine relatively short-period (not more than several days)
disturbances of ocean circulation (tidal, inertial currents, internal gravi-
tational waves.] The Gulf Stream and Kuroshio, like other links in macroscale
ocean circulation, are primarily gecstrophic currents, that is, those in
whose field the horizontal pressure gradient is evened out by Coriolis force,
, as a result of which the current is directed along the isobars at any depth.
~ Moreover, the dependence of pressure on density, and density on temperature
leads to a rough coincidence, at individual horizons, of the current stream-
lines and isotherms. In the northern hemisphE~e to the right of the current
' there :ts usually warmer water, and to the left colder water (see Fig. 2).
The great velocities of the Gulf Stream and Kuroshio and their relatively
small width (several tens of kilometers) are responsible for the exceptional
sharpness of the temperature drop across the current, which gives a frontal
character to these currents.
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~ Fig. 1. Map of macroscale currents in the upper layer of the North Atlantic.
Particularly strong currents are denoted by thick arrows. The characteristic
velocity of the Gulf Stream and other particularly strong curz�ents is 1 cm�
sec-1, in the open ocean 1.10 cm�sec-1, special symbols denote the sites
wherE several oceanographic expeditions mentioned in the article wer.e carried
out.
It is evident that the properties of geostrophicity and frontality are also
retained for the eddies of the Gulf Stream and Kuroshio because they simply
represent the cut-off and closing parts of the frontal currents. Within the
cyclones of the Gulf. Stream and Kuroshio, penetrating into the region of the
warm ocean to the south of the currents, the water is cold, whereas within
the anticyclones, penetrating into the cold region to the north of the cur-
rents, the water is warm. Observations of recent years have indicated, for �
example, that about five pairs of cyclones and anticyclones are formed an-
nually in the Gulf Stream field. The especially well-developed cyclones of
the Gulf Stream have a diameter of about 200 km and penetrate several kilo-
meters into the depth of the ocean. The difference in depths of isothermal
surfaces between the centers of these eddies and their periphery can attain
700 m and the velocity of rotation of water in their upper part is 2 m/sec
or even more.
Gulf Stream cyclones drift for the most part to the southwest (with a velo-
city of 3-5 km/day) as some individual formations surrounded by the quiet
ocean. Observa_tions show that in any case in the upper layer of the ocean
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(to a depth of 700-1,OOQ m) this drift has a transfer, not a wave character:
- the eddy "drags along" the water mass constituting its inner part. Individ-
ua1 Gulf Stream cx~lones have a lifetime as much as. two years or more, grad-
ually losing their energy as, a result of mixing with the surrounding water, -
and can deviate a distance of more than 1,000 km from the Gulf Stream.
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64� 63� 62' 6I� 80` 59' 58� 57~ 62� 61` d0� 59~
Fig. 2. Formation of cold cyclonic (rotation of water counterclockwise) eddy
of the Gulf Stream (according to F. Fuglister and L. Worthington, 1951).
a) data for 17 January 1950, b) da.ta for 21 January 1950; the curves repre-
sent the isotherms at a depth of 200 m; water temperature in degrees F; the
arrows indicate the direction of the current in the surface layer of the
ocean.
The frontal eddies of the Gulf Stream and Kuroshio are observed iti two rela-
tively limited regions of the world ocean. What is the situation in its re-
maining parts? Are there disturbances of macroscale circulation there which
with respect to spatial scales, periods and amplitudes are comparable with
frontal eddies? By the 1950's the most popular point of view among ocean-
ologists was that the system of macroscale currents in the main part of the
wor.ld ocean, especially in jts depths, is more or less stable, and the mPan
current velocity and direction at a stipulated point in the ocean (averaged
for several days) must not, usually, differ very significantly from the
. mean seasonal or even mean climatic values.
However, in the late 1950's-early 1960's, when oceanologists began to obtain
data from long-term measurements of the temperature, salinity and density ~
of ocean water. at some fixed points in the world ocean (for the most part
' these were data from so-called weather ships), it became clear that or.ean
depths are characterized by well-expressed variations of these oceano'Z;raphic
parameters with periods of about several months. Oceanologists also gave
much attention to the results of ineasurements of deep ocean currents of
; freely drifting deep buoys made by the British oceanologist J. Swallow dur-
' ing the period 1959-1960 from the ship "Eris" (see Fig. 1) to the southwest
; of the Bermudas, where the velocity of the mean climatic current does not
exceed 1-2 cm�sec-1. These measurements indicated that at depths of 2 and 4
km there are r.ionstationary currents with a period of about three months and
velocities up to 40 cm�sec~'1.
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Thus, by the 19(~0's data had been accumulated on the presence of extreme-
ly significant nonstationary long-period water movements in di.fferent re-
gions of the world ocean. However, fundamental problems remained unclarif-
- ied: hoG typical are these movements for the ocean as a whole? In what way
are they similar to the eddies of the ~~ulf Stream and Kuroshio and how do
they differ from them? Do they constitute large-scale ocean turbulence or -
are they movements of a wave type? ~o they fill the ocean completely or
do they constitute quasi-isolated disturbances? What is their spatial scale
and how is it related to the time scale? What is their energy and where
does it come from? It became obvious that there was a need for a special
expedition for obtaining at least partial answers to these questions. The
"Polygon-70" experiment became such a measure.
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Fig. 3. Evolution of current pattern at depth of 300 m determined using data
from "Polygon-70" experiment (1970). It is clear that the system of synoptic
eddies is displaced to the west. Cer?ter of region 16�30'N, 33�30'W; side
� of square 280 km; small circles locations of buoy stations; arrows
current velocity vectors; dashed arrows velocity vectors obtained by in- ,
terpolation in depth or time; curves streamlines computed from velocity
vectors using special interpolation program; the figures on the curves rep-
resent disturbances of the stream function in 10~ cm2�sec'1; B-- high-pres-
sure centers; H-- low-pressure centers; velocity scale at the bottom.
4
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I
i "Polygon-70" was the next in a series of Soviet oceanographic experiments
organized and carried out beginning in the mid-1950's in different parts
I of the world ocean on the tnitiative of the outstanding Soviet oceanologist
_i Profes.sor V. B. Shtokman. The purpose of all these experiments was a study
I of the variability of ocean currents. The measurement base was polygons with
anchored buoy stations outfitted with current meters. The buoy station is
an anchor-cable-buoy station with several automatic current meters, attached
; to the cable at different horizons. Having the results of prolonged current
; measurements at several buoy stations, arranged in a definite way relative
i to one another, oceanologists are obtaining information on the spatial struc-
! ture and temporal variability of the field of currents in the inv~stigated
j region of the ocean.
: The "Polygon-70" experiment was carried out by the Institute of Oceanology
; imeni P. P. Shirshov IISSR Academy of Sciences and other Soviet oceanographic
; institutes under the scientific direction of Academician L. M. Brekhovskikh
in the spring and summer of 1970, in the tropical part of the North Atlantic,
~ in the region of the North Trades Current (see Fig. 1). Fundamental measure-
ments of currents were made at 17 buoy stations arranged in a cross, operat-
ing in the ocean from late February to early September 1970; at each station -
the measurements were n~ade at 10 horizons in the layer from the ocean sur-
face to a dep~th of 1, 500 m.
The principal result of the "Polygon-70" experiment was the discovery and
' surveying of several powerful eddylike disturbances in the current velocity
field moving through the observation region (Fig. 3). These disturbances
were so clearly expressed that they complete~.y masked the large-scale North
Trades Current. Like the frontal eddies of the Gulf Stream, they had a dia-
meter of about 200 km, had a geostrophic character and penetrated a consid-
ez~able depth into the ocean. The velocity of their movement to the west was
about 5 lan/day and the velocity of the orbital (rotational) movement of the
water in their field attained 30-40 cm�sec-Z at depths of 100-800 m. In con-
trast, however, from the frontal eddies the "Polygon-70" eddies in their
totality constituted a continuous field of cyclones and anticyclones ar-
ranged in an approximately checkerboard fashion. Ttao adjacent eddies had a
common region of maximum current velocity with which another fundamental
property of the "Polygon-70" eddies was associated, this fundamentally dis-
tinguishing them from the frontal eddies: their movement (to the west) had
; a primarily wavelike, not advective (transfer) character.
In other words, the "Polygon-70" eddies, in a11 probability are unusual quasi-
horizontal waves, in whose field the particles move in orbits close to closed.
The translational movement of the eddy (in the considered case - to the
~ west) occurs due to the phase shifts of Quasihorizontal orbital motion of
adjacent water particles. An analysis of the relationship of the horizontal
dj.mensions of "Polygon-70" eddies and the velocity of their movement to the
west indicated that this relationship is precisely that which should be
characteristic for s~-called baroclinic Rossby waves wave movements in a
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dens,it,y-stratified ocean, whose kinematics and local dynamics are determined
by the joint effect o~ the earth's sphericity and rotation. A simple hydro-
dynamic analysis. of movement in the field of Rossby wdves shows that without
fail they must move in a u~es.ter.ly direction.
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Fig. 4. Diagram of distribution of ocean level, water density and current ~
velocity in vertical section through system of macroscale geostrophic cur- '
rents in the northern izemisphere. The circles with the crosses are for cur-
rents moving in the plane of the figure; the circles with the dots are for ;
currents moving from the plane of the figure;~ a larger circle represents a ;
_ greater current velocity; the ~ curves represent individual isopycnir_ lines ~
(water density increases with depth); the shaded regions and the arrows rep-
resent the setting free of APELSC with the straightening of isopycnic lines ~
(the heavier water in this. case su}istdes, the lighter water rises); the real ;
drop in ocean level across the current is about a meter; the drop in the !
heights of isopycnic surfaces is several hundreds of ineters; the typical ~
current velocity at the ocean surface is 5-10 cm�sec-1, in.depth 0.5-1 ~
cm�sec'1. '
I
i
The eddy movements discovered during the time of the "Polygon-70" experi- ~
ment have been given the name synoptic eddies of the open ocean." Such a
name is attributable to the physical analogy between these eddies and moy-
ing atmospheric cyclones and anticyclories, manifested in an identical ~
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predominant mechanism of their generation (barocl:Lnic instability of macro-
scale circulation, a subject which will be discussed below), a similar phys-
iral nature (baroc].iaic Rossby ~aves) and quasigeostrophicity of movement.
The region of the "Polygon-70" expedition is typical for the open ocean in
its remoteness from the shores and frontal regions and the relatively low
velocities of the large-scale current. Therefore, immediately after obtain-
ing the results from the experiment it was postulated that the pattern of
synoptic eddies discovered in the polygon should also be typical for the
open ocean. This assumption was completely confirmed by both new oceanic
experiments, especially directed to an investigation of synoptic eddies in
the open ocean and an analysis, from a new point of view, of data from some
old oceanographic observations. Among the new experiments the most important
was MODE-1 (Mid-Ocean Dynamical Experiment-1), carried out by American ocean-
olcgists in the spring of 1973 in the southwestern part of the Sargasso Sea
and giving results which in essence are close to the "Polygon-70" results.
In sub sequent years, on expeditions and in an analysis of old data, synoptic
eddies or their obvious traces were discovered in the equatorial zone of the
Pacific Ocean, to the east and west of Australia, in the region of the Hawaii-
an Islands, in Drake Strait and in some other parts of the Antarctic Ocean,
in the Arctic Basins to the west of California, in the zone of the North At-
~ lantic Current, to the southwest of the southern extremity of Africa and in
, a number of other regions in the world ocean.
' An analysis of all the available data suggests that synoptic eddies are
a typical (if not universal) property of the world ocean. The specific kin-
etic energy of eddies, varying in a very wide range, is usually greater in
those regions of the ocean where there is a higher specific kinetic energy
of large-scale currents and as a rule substantially (on the average by ar~
~ order of magnitude) exceeds it. This latter circumstance directly leads us
~ to the problem of the origin of synoptic eddies, or to the question of from
whence they acquire their energy.
;
~ It can now be evidently considered clear that.'~the principal mechanism of gen-
' eration of eddies is the baroclinic instabil:.ty of large-scale currents. In
order to understand this mechanism from the point of view of energy ex-
change we recall, first of all, that the ocean is stably stratified, that
' is, the water density in it increases with depth, and second, the ocean is
stratified stably, that is, the water density in it increases with depth,
and second, as a result of the geostrophicity of macroscale ocean currents
' surfaces of equal density (temperature) in their field slop e in the direc-
tion perpendicular to the direction of the current (Fig. 4). It follows from
this that any large-scale current in the ocean has some "excess" of poten-
tial energy in comparison ~:ith such a state in the ocean wh en all the iso-
pycnic surfaces (surfaces of equal density) are horizontal.
I
, Simple estimates show that this excess of potential energy, called the avail-
! able potential energy of large-scale currents (APELSC), as an average for
; the ocean exceeds their kinetic energy hy at least two orders of magnitude.
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The APELSC also is the energy reserve from which oceanic synoptic eddies
draw their energy. In other words, the eddies seemin~ly tend to annihilate
. the slope of the isopycnic surfaces, whereas the vertical component of
large-scale oceanic circulation maintains this slope. A hydrodynamic anal-
ysis of the movements of ocean water confirms this idea in the sense that
it shows the actual instability of large-scale ocean currents arbitrary
disturbances,imposed on the main current, grow and develop into synoptic
eddies, which accomplish horizontal transport of mass (density) in the
ocean. Incidentally, it follows from this that even with a relatively low
energy of the eddies the transport form of movement in their displacement,
although to a small degree, must nevertheless be present.
Sq the mid-1970's it became entirely obvious that a further fundamental
advance in the investigation of synoptic eddies in the open ocean can be
attained only by carrying out expeditionary work in the ocean, in ir.a scale
considerably exceeding "Polymode-70" or MODE-1. The very large So~iet-Amer-
ican experiment (to be more exact, the entire complex of ocP:inic experi-
ments) POLYMODE, became a consequen.ce of a clear understanaing of this cir-
cumstancE. The principal Soviet studies under the POI~YMODE program were
carried out in the central part of the Sargasso Sea during the period July
1977 through September 1978. This work was done with the participation of
several Soviet oceanographic institutes, headed by the Institute of Ocean-
ology imeni P. P. Shirshov USSR Academy of Sciences and nine scientific
research ships. The scientific leader of the work was the director of the
Institute of Oceanology Corresponding Member USSR Academy of Sciences A. S.
Monin.
The basis for the Soviet work in the POLYMODE polygon was the annual meas-
urements of currents and water temperatures carried out by the Institute
of Oceanology in a system of buoy stations situated at the points of grid
intersection of equilateral triangles with its center at 29�N, 70�W (Fig.
5). The distance between stations was 72 km and the diameter of the entire
m~asurement region was about 300 km; cur?-ant meters were situated at seven
horizons in the layer from 100 to 1,400 m depth.
The results of the measurements were unusually interesting and important.
The POLYMODE eddies with respect to som~ parameters are rather close to
the "Polygon-70" eddies, occupied a considerahl.e part of the ocean la~er,
had a diameter of 150-200 km and moved westward with a velacity of 2-6 km/
day. At the same time, the high energy level of water movement in the field
af POLYMODE eddies, exceeding the mean kinetic energy of "Polygon-70" ed-
dies by a factor of approximately 3, led to the obtaining of fundamentally
new information on a process of primary interest, nonlinear dynamic inter-
action between individual eddies. This process, very well expressed in the
region where the experiment was carried out, led to such highly interesting
effects, repeatedly registered during the POLYMODE period, as a marked re-
distribution of kinetic ener~ry between individual parts of the eddy fieid,
the formation of a quasi-isolated eddy o.r a quasi-isolated pair of eddies
of different sign, the direct exchange of energies between adjacent eddies,
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the disappearance of individual eddy centers and the appearance of new
centers (see Fig. 5). As indicated by the measurements carried out during
the POLYMODE period, the temperatures and salinities of ocean waters, the
' westward movement of the strongest POLYMODE eddies had (in any case, in
! the upper layer of the ocean) a partially advective (transfer) character.
~ This means that with respect to some physical properties POLYMODE eddies
~ can be regarded as intermediate formations between "Polygon-70" eddies
I and frontal eddies althou h the
~ g y "gravitate" toward "Polygon-70" eddies.
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I l ~
a 3 -24- 6
30 ~
Ll~ ~ 0
_ -9
_15 _3 ~o
p ul -9~ ~
--3 ~
. -6
3 3 ~ -6
~ 9 i i ~ ~ 700 a ~ i
~ i
0 25 50 Hr
20 ~w/~ cm/. sec
2s~ ' ' 2a.o2 ~oo w ~ 03 ~
3~A~ d -l2 ~t'
/9 12 p Q
04 8 6 Up ~ ~
13
' ~ 5 ~5 ~ A~ -1811
`5 ~ u2 ~ U .
~ 1 ~ 5 ~
. ~7' '6 ~ '
~ ~ s
. e
700 r+ ~ ~ ~ _s
~ ~ ~ ~ i i i ~ � ~
Fig. 5. Evolution of pattern of currents at a depth of 700 m according to
~ POLYMODE data. Circles sites of buoy stations; arrows current veloc-
ity vectors; curves streamlines constructed on basis of velocity vectors
using special interpolation program; the figures on the curves are the val-
ues of the stream function in 10~ cm2�sec'1; A, j~ centers of individual
anticyclones and cyclones; together with the general movement of eddies to
the west it is easy to see a marked redistribution of energy between in-
dividual sectors of the eddy field, its concentration in individual quasi-
isolated eddies, the disappearance of some eddies and the appearance of
others.
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From everything which has been said it should be clear that an extremely ;
significant role is played by synoptic eddies in the processes of trans- ;
fer and transformation of matter and energy in the ocean. Without a care-
ful study of eddies it is impossible to have a thorough understanding of '
the ph,ysics of ocean circulation, and this means, the �~rmulation of a ;
physical model of macroscale interaction between the ocean and atmosphere ;
sufficien~ly close to nature. Such a model, in turn, is completely neces-
~ary for creating reliable methods for the long-range forecasting of weather
_ and climatic anomalies. As a result of the predominance of the kinetic energy
of eddies over the kinetic energy of macroscale oceanic circulation the
field of synoptic eddies is the real field of currents which acts on ~
vessel present in the ocean. Hence it is clear how important it is to in- i
vestigate eddies for navLgation in the ocean. The propagati~n of sound ~
in the ocean is essentially dependent on the distribution of water density
in it, which, as follows from what has been stated above, is determined ;
to a great extent by the distribution of cyclonic and anticyclonic oceanic ~
eddies. i
We note, finally, that in the centra~. parts of cyclonic eddies there is an ~
- upwelling of cold, deep ocean waters, whereas in the central parts of anti- ;
cyclones, on the other hand, the subsidence of warm surface waters is ob-
served. As is well known, the regions of upwelling of waters are charac- ,
terized, in comparison with regions of subsidence, by a considerably great-
er biological productivity, and accordingly an investigation of eddies '
is also important for commercial biology.
Thus, an experimental and theoretical investigation of synoptic ocean eddies ~
is becoming one of the most important directions in the development of phys-
ical oceanology in the upcoming years.
j
- At a session of the Presidium USSR Academy of Sciences at which the scien-
tific communication of M. N. Koshlyakov was presented, commentaries were
made by Academicians G. I. Marchuk and L. M. Brekhovskikh.
G. I. Marchuk. In order to visualize more clearly the phenomenon discover- -
ed in the ocean, we will turn to atmospheric phenomEna. In the atmosphere
it is customary to observe fronts of cold and warm air. The air movements
in these fronts are variable and nonuniform. It has been demonstrated by
N. Ye. Kochin (and later by other researchers) that such movements are un-
stable. As a result of realization of instability rather stable formations
arise eddies (cyclones and anticyclones). An atmospheric eddy lives
approximately a week, gradually dissipating.
These same eddies have now been ~iscovered in the ocean. Oceanic eddies
live considerably longer (water aensity is far greater than air density)
and play an extremely important role in its life. This discovery is of
very great importance for explaining many macroscale phenomena in the
ocean.
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_ Now scientists are trying to answer the question as to why the earth's cli-
mate is changing, why it is that each year there is no repetition of the
events which should be repeated in a we11-determined, stable system. One
of the explanations is evidently as follows. Somewhere, probably in the
zone of the temperate latitudes, under the influence of some definite con-
ditions, large temperature anomalies develop. These anomalies, which cannot
be recognized from the surface, begin to migrate. They can migrate a month,
a half-year, one-two years and unexpectedly emit great quantities of heat
into the atmosphere. '
A further study of the ocean (the first step has already been taken by thF:
discovery of eddies) will make it possible to find the triggering mechan-
ism which is responsible for interaction between the ocean and the atmo-..
sghzre.
L. M. Brekhovskikh. Earlier the ocean was regarded as a stationary system.
The currents in it were regarded as mor e or less constant; these currents
were also plotted on maps. After the discovery of eddies we must now speak
of "weather" in the ocean. We must study it as carefully as weather in
the atmosphere because weather in the ocean also influences the weather
of our planet in the most decisive way. It also exerts a great influence `
on processes transpiring in the ocean: on the life and distributian of
nutrients, on the distribution of all kinds of wave disturbanc~es. In short,
_ a new page in ocean science, interesting and important, has been opened.
In conclusion, the Vice President of the USSR Academy of Sciences, Academ-
ician V. A. Kotel'nikav, thanked M. N. Koshlyakov for an interesting sci-
entific communication.
COPYRIGHT: Izdatel'stvo "Nauka," "Vestnik Akademii nauk SSSR," 1979
[496-5303]
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i~DC 553.26
~
STUDY OF DEEY FAULTS ;
Moscow VESTNIK AKADEMII NAUK SSSR in Russian No 6, 1979 pp 77-85 ~ '
;
[Article by Doctor of Physical and Ma.thematical Sciences Yu. P. Neprochnov]
[TextJ Zones of deep, transformed faults are interesting because deep rocks '
of the earth's crust emerge here at the surface of the ocean floor and are ~
accessible for direct geological investigations. Detailed geological stud-
ies in zones of transformed faults can substantially supplement ocean
~ drilling, which makes it possible to penetrate into solid crustal rocks
to only a small depth tens, in the best case, hundreds of ineters. A
comparison of geological and geophysical data will make it pussible to
obtain answers to important questions relating to the nature of magnetic ~
and gravitational anomalies, on the composition of the main layers of the
~ earth's crust detected in seismic investigations in the ocean.
Transformed faults were the principal feature studied by a multisided geo- ;
logical-geophysical expediti~n of the USSR Academy of Sciences aboard the i
scientific research vessel "Akademik Kurchatov" (24th voyage, December ~
1976-April 1977). The scientific program of the expedition provided for ~
a comparative study of zones of major faults intersecting the Mid-Atlantic j
Ridge, the East Pacific Ocean Rise and ad~acent basins, i
The expedition was organized by the Institute of Oceanology imeni P. P. ~
Shirshov USSR Academy of Sciences. Participating in the voyage were spec- ~
ialists of the Institute of Geography, Institute of Geology of Ore Depos- '
its, Petrography, Mineralogy and Geochemistry, Institute of Terrestrial !
Magnetism, Ionosphere and Radio Wave Propagation, Geology Institute and
Institute of Physics of the Earth imeni 0. Yu. Shmidt USSR Academy of Sci- ~
ences and also the USSR Geology Ministry and Moscow University. i
The total extent of.the expedition rou*_e, including studies in the polygon,
was about 29,000 miles. In contrast to the preceding expeditions, on this
voyage transformed faults were studied not only within the limits of the
rift zones of the ridges, but also at a distance from them, in regions ;
with a more ancient crust. Most of the work was done in five polygons i
each with an area of approxima.tely 100 km2, situated in the fault zones '
;
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~
Atlantis, Kane, Galapagos, Eltanin and an earlier unknown fault on the
western slope of the East Pacific Ocean Rise (Fig. 1). In the polygons
; specialists first carried out a geophysical survey, including depth sound-
; ing, magnetometry, gravimetry and continuous seismic profiling (CSP) along
a grid of Y:ins with c~istances between them of 1-15 km. The results of the
i survey were processed on an electronic computer on shipboard ar~d repre-
sented in the form of composite geophysical sections. This was follawed by
~ compilation of maps of bottom relief ma netic and
, g gi:avitational anomalies,
~ thicknesses of the sedimentary cover and relief of th~e acoustic basement.
' Tlsing data from a geophysical survey it was possible to determine the most
i
favorable sectors for the dredging of bedrock, sampling of bottom sedi-
ments, heat flow measurements, and for placement of self-contained bottom
, seismographs, by means of which deep seismic sounding (DSS) was carried
out and seismicity was studied.
A great volume of geological and geophysical research was also carried out
' along the ship's track. It should be noted that for the first time in world
~ practice CSP was carried out at a speed as great as 15 knots; a good quality
i~ of the seismic records was maintained. In work by the DSS method use was
; made of pneumatic sound sources with a great power, this ensuring an ade-
i quate depth and detail of investigations of the earth's crust. This made
; it possible to automate the process of observations and primary processing
~ of records from bottom seismographs.
The extensive geophysical and geological materials collected on the voyage
were partially processed aboard the ship. Their laboratory analysis is now
continuing. This article gives the most interesting preliminary results ob-
tained by the geomorphology and tectonics, magnetometry and geothermal stud-
ies, CSP, DSS and seismology, gravimetry, lithology and stratigraphy, radio-
isotopic methods and petrography detachments.
The polygon work was begun in the zone of the Atlantis fault. This fault
is one of the largest transformed faults in the Atlantic Ocean. It extends
in a sublatitudinal direction for almost 2,000 km, approximately between
29� and 30�N. Detailed geological-geophysical investigations of the region
of intersection of the fault and crest zone of the Mid-Atlantic Ridge were
carried out in 1969 on the sixth voyage of the ".Akademik Kurchatov." In
this sector the displacement of the axial rift valley of the ridge along
the Atlantis fault is about 30 miles; an anomalous structure of the earth's
crust was discovered under the fault canyon.
The first geological-geophysical polygon on the 24th voyage of the "Akad-
emik Kurchatov" was situated on the eastern extension of the Atlantis
fault at a distance of appro.ximately 700 km from the crest of the Mid-At- -
- lantic Ridge. Here the fault is well expre~sed in the relief and is repre-
sented by two sublatit~;dinal depressions with depths of 5,500 and 5,800 m.
The crests of the rises adjacent to them were situated at depths of 4,000-
4,500 m. The steepness of the depression slopes averaged 5-8�, locally
, attaining 20�.
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,
~
,~o vo ac ~o o I
. - - 1'tn6qt ,
Q'� , ~ ' ~
� � 1 �.H+~~u~rjd !
� '
_ ~
W - ~ ~a ~ ,o ~
_ - ~ Our~=Aea-r~da ~
/ / ~ ( ' ~ � ~ ~ ~ A~rQuw I..,' . . ~
:Q ~ / _ L.~ _ ~ p
~ ~ ~~7 i! Bu~ewcr~d _ ~
~ ~ ~ ~.n~.rt;io, ~
~ u ~c. c.c i
0 i - p i
" i
� \ ,A � nL1N ~ 1 . ~ ` i
~ tl'
30 - x ~
~ ? ~ ' i
I
v ~
W ' p i
\ ,p
a~ ~s ~H ~
~ ~ .
~ � ' !
~ ~ i
izo vo eo ~o 0
i
~
Fig. 1. Track of the 24th voyage of the scientific research ship "Akad- (
I
emik Kurchatov." 1) part of track with depth sounding, magnetometry and ~
gravimetry; 2) part of track with CSP; 3) part of track without magnetometry; ;
4) polygons; 5) stations; 6) ports of cal.l; 7) isobaths; 8) faults; 9) axes j
of ridges; 10) regions of inetalliferous sediments, I-V) polygons in the ~
fault zones Atlantis, Kane, Galapagos, Eltanin, on ~~~estern slope of East ~
, '
Pacific Ocean Rise. ;
In the region of polygon I there was a relatively weak anomalous masnetic I
field. Here there is a linear positive anomaly, displaced along the fault ~
for approximately 30 miles, as in the rift zone of the mid-nceanic ~
ridge. It is identified as anomaly 24 (age about 60 million years). A pos- i
itive anomaly corresponds to the central depression of the fault. This de- j
pression is characterized by an increased heat flow value. !
I
The depressions of the Atlantis fault correspond to small negative free-air ~
anomalies and positive Bouguer anomalies up to 380 mgal (in the text and in i
the figures the gravity anomaly values are given in the system of American ~
control points). .
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According to CSP data, the sublatitudinal depressions are filled with sedi- '
ments w~.t}i a ttiicknee~A up to 400-80Q m. On the slopes of depressions the
~ sedimentary cover is insignificant and in places is absent.
In the depression under the layer of unconsolidated sediments there are
rocks in which seismic waves are propagated with a velocity of 5.3 and 7
~ km/sec. Thus, the deep structure of the Atlantis fault in the investigated
j sector was as anomalous as in the rift zone of the Mid-Atlantic Ridge.
I
' Rock material in the form of small rock fragmPnts was obt~ined by three
~ dredges, a heavy corer and a scraper. Hydrothermally modified basalts were
raised from the slopes of the southern depression. On the northern slope ~
; of the main depression there were basalts, gabbros and serpentinites. It
~ is interesting that in addition to alpinelike hyperbasites and tholeiitic
basalts, typical for the rift zones, an alkaline complex of ultrabasites,
gabbros and basalts was discovered in the fault.
~ Thus, the Atlantis fault in the polygon region is a complex echelonlike tec-
tonic zone. The maturity of relief forms, considerable concentrations of
~ sediments, a relatiuely weak magnetic field, and absence of present-day
' seismicity is evidence of its antiquity. At the same time, a number of
' criteria (good expression of the fault in the bottom relief, numerous out-
! crops of basaltic la~~:as, increased heat flow values, presence of mudflows,
" anomalous crustal st'ructure, adaptation of magnetic and gravitational anom-
alies to the central~depression of the fault) indicate its tectonic activity,
which, evidently, is intensified periodically as stresses accumulate along
the fault.
In polygon II, in the zone.of Kane fault, detailed seismic and magnetomet-
; ric studies were made in the region of borehole 396 by the American ship
, "Glomar Challenger." The purpose of the work was a comparison of geophys-
, ical data on~the fine structure of the crust with the results of borehole -
~ logging and magnetic measurements in cores. The analysis of the collected
materials is still not finished.
The site of polygon II was selected in the neighborhood of Hess depression,
~ situated not far from the crest of the East Pacific Ocean Rise in the zone
, of the Galapagos fault. Here the preceding expeditions of the Institute of
~ Oceanology discovered sharp bottom relief forms favorable for the dredging
of deep crustal rocks. Detailed geomorphological studies in the polygon
considerably refined the map of bottom relief in this region. The depth
of the Hess depression attains 5,400 m; the northern slope is very steep
up to 20�. The bottom sectors surrounding the depression are situated
, at depths of 3-3.5 km. .
; The magnetic field within the limits of the polygon is characterized by
complex positive and negative anomalies with an amplitude up to 750
, The maximum negative anomaly is associated with the Hess depression. It
. , is also traced farther on the western slope of the East Pacific Ocean
Rise, where its intensity gradually decreases. Along both sides of it ~
there is a system of sublatitudinal sign-variable anomalies, complicated
by meridional displacements. These anomalies, evidently, are associated
; �
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i
with the development of the Galapagos rift zone. All three measurements '
of the earth's heat flow (two of them were carried out to the west of the
Hess depress.ion in the region of the crest of the East Pacific Ocean Rise, '
and one to the south of the depression) gave increased values from '
2 to 8 heat flow units. y
400 ,
200
0 Ta ~
0 i
-200 ~
Mran mgal ~ -
300 ~
` -400 ;
I
250 i 1 ~ G 6 ~
~ ~ r 1 ~~-'"1..-_~.~_- i
200 rf an
- 1 ~ 5o i
~ Gfa i
i5o 0 Gce.e. o i
S -5oN ~
. i
ro ~ c ;
;
� so ao eo so ioo ~so ~ao
M
I = = I
~2 ~ DSS ~ ~ DSS ~
~ ~ s tation ~ ,
~ ;
. ~
3 � `r cv ~ i
c~ m ~
3,5HM~~~! ~o~~�~~ ~ 3,5""'~c i
4 ~ ~r v�~v ~ / . I
vvv NU �wvr ~ ~
~ FJCJMM/C V r w ~J,~JKM/C , I
5 cT.2153 ~r~ ~r 4 i-
n n
I
B W~v 3 f
8,8 HM/C g 8 IlM/ y y~ 4 I
C
~ iCIII~ S eC
~ 5
8 '
" ~ ~ 8
8~2 HM/C r~ 7
9 B
2
KM/~
IO HM
Fig. 2. Geological-geophysical section along meridional profile across Hess
depression. 1) lenses and intercalations of plagioclastic olivinites; 2)
gabbro complex (troctolites, olivine gabbro-norites, olivine gabbros); 3)
dolerites; 4) basalts of the upper complex; 5) basalts of the lower complex;
6) upper surfaces of magnetic bodies; 7) refracting boundaries and velocit-
ies according to DSS data, 4 Ta~-- curve of magnetic anomalies, Q Gb
curve of gravity anomalies in Bouguer reduction, Q Gfa curve of free-air
gravity anomalies.
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~ CSP data indicate the absence or very small thickness of unconsolidated
sediments Uoth in the depression and in the remaining sectors of the
polygon. An analysis of samples of sediments covering small sectors of
I the Hess depression indicated that they were formed for the most part
i due to the destruction of bedrock. The deposits bear traces of the effect
~ of thermal springs with which the enrichment of sediments by iron and
I manganese hydroxyls.is associated.
' DSS on six profiles situated around the depression yielded quite detailed
~ information on crustal structure. All three investigated sectors are char-
i acterized by similar seismic sections, including layers in which the waves
j are propagated with velocities 3.5, 5.5 and 6.8 km/sec. The Mohorovicic
i discontinuity is situated at ~ depth of about 5 km below the bottom sur-
! face. In two days bottom seismographs registered about 30 earthquakes, f~r
j the most part associated with the Hess depression. Four successive deep
; dredgings were carried out on the steep northern slope of the depression. ~
' The rocks collected on this voyage, and also on the 8th and 14th voyages
, of the scientific research ship "Dmitriy Mendeleyev;' make it possible to
; construct a full section of the oceanic crust (Fig. 2). -
The geological section correlates well with respect to the depths and thick-
nesses of the main layers with a seismic section of the earth's crust: a '
' layer in which waves are propagated with a velocity 3.5 km/sec corresponds
~ to basaltic lavas; a layer in which the velocity of wave pr.opagation is
5.5 km/sec, which corresponds to a basalt-dolerite dike complex; a layer
in which the velocity of wave propag~.tion is 6.8 km/sec, corresponding
to a complex of gabbroids.
~ A study of the magnetic properties of the samples indicated that both
basalts and gabbro-diabases have a high magnetic susceptability and remanent
magnetization. These two types of rocks eviclently also serve as sources of
; the observed magnetic field anomalies.
The entire complex of investigations carried out in polygon III confirmed
the hypothesis of a young rift nature of the Hess depression and made pos-
sible a detailed validation of this hypothesis. The rift nature of the de-
pression is indicated by the sharp forms of bottom relief, the absence of
a sedimentary cover, hydrothermal phenomena, tholeiitic low-potassium ma.g-
matism, high seismic activity, presence of sublatitudinal anomalies and
high gradients of the magnetic and gravitational fields. At the same time,
it is not precluded that the Hess depression and the entire Galapagos rift
, zone were formed on a more ancient transformed fault, which, judging from
geomorphological, magnetic and gravitatianal data, continues to the west.
The system of Eltanin faults, on whose northern fault (Heezen fault) poly-
gon IV was selected, is unique with respect to both the scales of hori-
zontal displacements of the ridge crest (about 900 km) and with respect
to the sharpness of relief forms - the depth difference along the southern
slope of the fault canyon attains 5 km, The idea of studying the Eltanin
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fault on the 24th voyage of the "Akademik Kurchatov" was proposed by Cor- ~
responding Members USSR Academy of Sciences A. S. Monin and A. P. Lisitsyn. ~
i, (A canyon with very steep aud high slopes~ which attracted the attention ~
oF geologists and geophysicists, was discovered in this region during tt~e
14th voyage of the "Dmitriy Mende~eyev".) ~ ~
The system of Eltanin faults was earlier studied using only infrequent
reconnaissance profiles. Therefore, the first detailed geological-geophys- -
ical studies in polygon IV are interesting in themselves. The investigated ~
sector of the fault is a linear canyon with a northwesterly strike with a '
depth to 6 km. The steepness of the slopes attains 20-25� (Fig. 3). ~
i
In the magnetic field of this region there are linear anomalies parallel
to the axis of the LasL racific ~cean Rise, one of which, in the northern ~
block, is tentatively identi~i~;i,as anomaly 4(age 7 million years). An I
analysis of the anomalies is evi:%?,~nce of absence of considerable horizontal
displacements along Heezen fau~~. Eviuently, the principal displacement j
occurs along Tarp fault, situat~3 to the south, as is confirmed by seismo- i
logical data. '
The strikes of gravlty anomalies coincide with the direction of the fault. ~
Large horizontal fisl~ ~radients corres~ond to the canyon slopes. However, ;
the maximum value of the Bouguer anomaly over the fault (+320 mgal) cannot
be considered very great, taking into account the depth of the canyon. ;
~
According to CSP data, the thickness of the unconsolidated sediments in the
polygon is very insignificant, and in many sectors, especially on the steep
slopes, there are no sediments.
The results of geological investigations, for the first time carried out
in the zone: of Eltanin faults, are of exceptional interest. The bedrock
material was obtained using four dredges, two scrapers and two concussion
corers. On the southern slope, where the depth differential attains 5,100
m, it was possible to obtain a compJ.ete section of the earth's crust, in-
cluding the principal rock complexes (from top to bottom)~ basaltic, basalt-
dolerite, gabbroid and ultrabasic.
The expedition's geologists made two ui~ique finds: on the peak of the south-
ern crest they discovered limestones with Cretaceous coccoliths (determina-
tions by V. V. Mukhina and M. S. Ushakova), and from depths 5,200-5,600 m
it was possible to raise enormous blocks of puckered amphibolitic schists.
The Cretaceous coccoliths were probably redoposited, since the age of the
foraminifera found here is not more ancient than the Upper Miocene (deter-
minations by M. S. Barash). However, the presence of a great amount of
Cretaceous and Paleogene coccoliths in the limestones, with an almo5t com-
plete absence of Neogene-Quaternary coccoliths, can be evidence of the
close positioning of shows of Cretaceous and Paleogene rocks, from whic`~
material was transported in the Pliocene or in the Miocene. Relatively an-
cient rocks fiave already been repeatedly encountered in the axial zone
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of the mid-oceanic ridge in the Atlantic. This possibly explains the crus-
tal blocks persisting at the center of the ocean which have not been drawn
I into the spreading process.
, Y
9b0
500 �
I 250
~ ATa I
~ ~
i wran m~al -2so
, aoo ~1
j 25d^~"`~~1 ~ I ~G6 150n
i 200 1 ~
fr vn_.^~..
100
~ 150 ~ ~ Gta 50
' ~ ~GC6.b
~
' S -50
~ u~ ~
~
ro NN'7
~ F n
0 r~o 4OD UN 80 BO ~QO I~IO MM
~ ~
2 n
TTT 2
~station
3 n �0 3
n '
i
4 000 0~ 4
N' m
~ . 5 c~i ~1 ~ `r 5
N~
v v g
i 8 Nr
. ~7
I Fig. 3. Geological-geophysical section along meridional profile across the
Heezen fault in the system of Eltanin faults. 1) amphibolitic schists; 2)
peridotites (Harzburgites, lherzolites); 3)'granulites (olivine-, pyroxene-,
j amphibole-, plagioclase-); 4) gabbro; 5) dolerites; 6) basalts; 7) lime-
stones, Q Ta curve of magnetic anomalies; Q Gb curve of gravity anom-
alies in Bouguer reduction; QGfa curve of free-air gravity anomalie~.
Amphibolitic schists under such conditi~ns as in polygon IV were found in
~ the ocean for the first time. ~ao types can be discriminated among them
on the basis of mineral composition. One type, the predominant one, is
i schists enriched with amphibole. Their chemical composition gives basis
for assuming that they were for.med from tholeiitic basalts, and some from
tuffs of this same composition. Schists of another type were found in in-
' . dividual fragments. Their leucocratic composition, with considerable
~
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quantities of quartz and a small thickness of the intercalations make it
~oreihle to povtulnte thr~t they were formed durj.ng the metamorphiem of.
sedimentary rocks of siliceous composition. The degree of inetamorphism of
the schists corresponds to the facies of epidotic amphibolites. Analyses
of amphiboZitic schists have not yet been finished. In particular, at- ~
remn~~ are being made to determine their absolute age, which in many re-
spects can help in reconstructing tectonic conditions.
Y aoo ~
200
o ~Te
- 2f1O
. wr~� mgal !
350 ~
~ ~r.,~,.% ~ 300
OG
w~an mgal i ~ 6250 ~
100 1 ^ ,r I
~ J ~ 200
50 ~v '
150
0
o Gce.s, Gfa
-50
- 100
FO C
~ 7O 4O 6O 8O 1OO ' 12O NM
~ II
I ~ ~ i
m m M i-
2 V U
j nss ` ~ ~ ~
3 ~ ~ ~ ~
rn u i
VyV
N
"4 �M/ Fig. 4. Geological-geophysical section
5 3~6 ` ~ N "~~v along meridional profile across the ~
5,s HM/c N��~ation ~ Akademik Kurchatov fault. 1) basalts ~
s � and tuffs of basaltic composition, 2) ,
- , y20HM~~? refrac.ting boundaries and velocities ~
~ y' determined using DSS data, ~ Ta i
e g$ MM~~ 5,5 NM~c km/sec curve of magnetic anomalies, ~ Gb '
- curve of gravity anomalies in Bouguer ~
� 72�M~~ reduction, L1Gfa curve of free-air
lO NM 8~0 KM/ � , gravity anomalies.
2~
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i A geophysical survey in polygon V d~.scovered and over an extent of 200 1cm
I investigated a ne~o, very large transverse fault intersecting the western
slope of the East Pacific Ocean Rise, approximately along 37�S. The maximum
depth of the fault canyon was 6,600 m and the depth drop along the highest
i northern slope in one of the sectors exceeds 5.5 lan. Such deep faults were
' earlier unkno~on in the East Pacific Ocean Rise. It is proposed that this
newly discovered fault be called the "Alcademik Kurchatov" fault.
~
The magnetic field of this investigated region is characterized by consider-
i able anomalies and sharp gradients; the strongest of these are associated
~ with the northern block of the fault (Fig. 4). The fault canyon corresponds
~ to a band of magnetic f ield negative anomalies.
' On the CSP records unconsolidated sediments with a thickness of less than
i
j 100 ia are noted only in the deepest axial part of the f ault; in the
I remaininb reg:ions in the polygon the sedimentary cover is absent or very
; thin.
; DSS r evealed an anomalous structure of the earth's crust under a canyon sim-
; ilar in structure to that in the Atlantis fault. The southern block of the
; crust has a sequence of layers customary for the East Pacific Ocean Rise
i with a total thickness of about 5 km. In the course of two and a half days
~ of observations the bottom seismographs did not register a single earth-
; quake.
- Geological work on the canyon slopes indicated that the fault cuts through
, a great thickness of basalts and hyaloclastites. The rocks which were rais-
~ ed constitute semirounded, oxidized and weathered fra~nents with a ferro-
' manganese crust. The presence of tectonic breccias gives basis for postulat-
ing that the volcanic stratum is underlain by a metamorphic complex. Phos-
phatized organogenic limestones are encountered on the northern crest.
Geological and geophysical materials indicate a relative antiquity of the
Akademik Kurchatov fault.
The investigations carried out during the 24th voyage of the "Kurchatov"
- confirmed the great possibilities of detailed geological-geophysical stud-
ies in zones of transformed f aults for study of deep layers of the earth's
; crust which for the time being are inaccessible for oceanic drillin~. For
example, in the Hess depression and in the Hezeen fault it was possible to
; obtain complete sections of the earth's crust. A comparison of these sec-
tions with seismic and geomagnetic data made it possible to refine the na-
ture of the seismic layers and detect the principal sources of magnetic
field anomalies.
~ It has been established that transformed faults, even at a considerable
~ distance from the rift zones of the mid-oceanic ridges, retain the anom-
~ alous structure of the earth's crust, specific magmatism and anomalies of
~ geophysical f ields associated with them. As indicated by geological and
i geophysical data, the studied faults evidently are inher ited structures
~ 21
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which penetra.te to a great depth. Their tectonic activity does not cease I'
beyond the limits of the rift zones. ,
Lithological studies along two sections across the eastern slope of the
East Pacific Ocean Rise and in the Bauer depression made it possib le to ~
refine the boundaries of regions of propagarion of inetalliferous sediments
and study the facies types of these sediments. Investigations of the field
of inetalliferous sediments indicated that manifestations of the presence
of inetals. both along the axial zone of the rise and in the zones of trans- ~
formed faults vary and anomalously high conte~.lts of iron, manganese and '
other accompanying elements have a strictly local character. A new region '
of high metal contact of deposits was discovered in the zone of contact '
between the East Pacif ic Ocean and West Chilean Rises. The Pleistocene ~
noncalcareous pelagic oozes here contain up to 25% iron and up to 7% man-
ganese. The materials from this and preceding expeditions (8th and 14th I
voyages of the scientific research ship "Dmitr iy Piendeleyev") indicate
that genetically the metalliferous sediments are associated with hydrother- ~
mal activity and its activity plays a decisive role in the formation of
these deposits. In turn, hydrothermal springs are associated with active ;
faults in the ear th's crust. ~
i
As indicated by the expedition results, detailed geological and geophysical ,
investigations of zones of deep faults on the ocean floor give very valu- ~
able materials necessary for understanding the processes involved in the ;
formation of the earth's crust, refinement of the nature of the principal ~
crustal layers and anomalies of geophysical fields, determination of the
scales of ore shows and their prospects. Therefore, further systematic
mu~tisided study of these zones is of great importance. ,
COPYRIGHT: Izdatel'stvo "Nauka," "Vestnik Akademii nauk SSSR," 1979 '
i
[49b-5303] . ;
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UDC 550.373
GEOMAGNETIC FIELD DISTURBANCES CREATED BY SEA CURRENTS
I Moscow GEOMAGNETIZM I AERONOMIYA in Russian Val 19, No 4, 1979 pp 708-714
i
[Article by S. S. Perepelkin, B. I. Verkin, I. 0. Kulik and R. I. Shekhter,
Physical-Technical Institute of Low Temperatures Ukrainian Academy of Sci-
ences, submitted for publication 19 April 1978]
I Abstract: The authors computed the spatial dis-
I tributior.,,of the magnetic field generated by
! the movement of a jet of conducting fluid in
j a layer of finite thickness in a constant ex-
~ ternal field H~. The article gives numerical ~
estimates of the geomagnetic disturbances
created by sea currents of different scales.
i
! [Text] At the present time, in connection with active interest in study of
i the world ocean, attention is being given to the possibility of studying
; sea currents and other sea movements [1] on the basis of the second~ry
; magnetic fields created by them. Reference is to fields generated by the
' movement of a conducting fluid in the earth's permanent magnetic field.
; In this study the problem has been solved for jet movements of the sea,
I taking inCo account both the longitudinal and rotational components of vel-
I ocity in the jet. An.important consideration. is allowance for influence of
~ the sea water - air discontinuity, deforming the streamlines and screening
i the magnetic field over the conducting medium. As a result, the magnetic
~ field in the air is extremely sma11, al~hough in principle it can be reg-
i istered by modern ma.gnetometers [2, 3]. Since the magnetic fields created
j by a disturbance of the surface layers of the sea decrease exponentially
; with depth [4-7], measurements within the sea, at an adequate distance
i from its surface, can become an effective method for studying deep currents.
i Distribution of magnetic field in a fluid with an arbitrary velocity field.
~ A determination of fields in a moving conducting medium involves the joint
~ solution of the Maawell equations and the Navier-Stokes equations, deter-
; mining the dynamics of the fluid [8, 9]. A precise solution of the.problem
i requires stipulation of the sources generating the currents, but this goes
~ beyond the framework of this article.
i
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~ 23
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r~n urri~icu, u~L v~:::~
Duc: to the weakness of the earth's field it is possible to neglect its ~
influence on the nature of the current and take into account only the ~
magnetohydrodynamic effects in the permanent magnetic field H0. There-
fore, being interested in the problem of detection of magnetic fields
associated with currents, it is possible to formulate the problem of ;
electromagnetic disturbances induced by a stipulated hydrodynamic velo-
~ city field v(r), leaving to one side the problem of the formation of cur-
rents. In a stationary case, when there is sufficiently slow movement
I v~: c, determining the electric E and magnetic H fields, has the form '
~io-ii]: - . - - - . .
rot H= (4n~c) j, div R=O, rot E=0, div j=0,
j=o{E+c-'[vXH�]}, ~ ~1) '
where j is the density of the induced current, O' is conductivity of the ,
medium.
i
In the case of small values of the Reynolds magnetic number Rm the system ~
of equations (1) can be solved with the arbitrary dependence v(r). The ,
- solution has the form '
I
1 (cE+vXH�) XR 1 ~(H� rot v) ( 2)
H=~I� -I- f R~ dV, E= 4nc �f R dV,
4nvm
where = c2/4.r~cs is the magr~etic viscosity of the medium, R is the radius
vector drawn from an element of the volume dV to the observation point.
[Rm = va/ ~ m, where v is the characteristic velocity value, a is the lin-
ear dimension.]
The solution (2) is correct in an unbounded medium. In the presence of sur-
faces or discontinuities of the media, other than the ordinary conditions
of regularity imposed on the functions E(r), H(r), it is necessary to re-
quire satisfaction of the corresponding boundary conditions. In particular,
on the boundary with the nonconducting medium it is necessary to require
satisfaction of the conditions of nonpassage of an electric current through
the discontinuity:
(E-f-c-'vXH�) n=0, ~ 3)
where n is the normal to the surface. The corresponding solution can be ob-
tained from (2) by the images meth~od (for a plane discontinuity) and is an-
alyzed below f or specific ehamples of currents.
Field of linear rotating jet. We will stipulate the distribution of velo-
cities in a fluid in the for.m (in a cylindrical coordinate system) vr = 0,
v~ = u(r) e(a - r), vZ = 0, where ~(x) is a Heaviside step function,
that is, we will assume that the fluid rotates in a tube with the radius a
with a distribution of the velocity of rotation along the radius u~ u(c).
24
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The sea water - air discontinuity~ parallel to the axis of the ~et, passes
at the distance d from the axial line of the ~et. The outer magnetic field
H~ is oriented arbitrarily relative to the jet. Using expressions (1), (2)
we find the components of the H fields and current density:
h.=(Ni /2vm) {[uo(r)-uo~a)-r-~u:(?')~6(a-r)- ~4a)
-r-au2(r)A(r-a)} coscp, (4b)
h.=(H,~�/2v,�) {[tto(a)-tao(r)-r==uz(r) ]9(a-r)- r-~uZ(r)6(r-a)} sin~,
~
~ un ~r) = f u ~P) p"dP~
o ~5)
E~=- (tl,�/c) u(r) p(a-r) , jr=- (a~t (r) Hl�/c) 9(a-r) sin cp
(the omitted compcnents are equal to zero). H 1~, HZ~ are the magnetic field
components directed perpendicular to the axis of the jet and along it, h=
H- H~ are disturbed fields related to rotation.
As can be seen from the formulas (4a, 4b), the magnetic field decreases
with distance in cunformity to the law h N r-2, which corresponds to the
field of an infinitely long magnetized filament with a magnetic moment of
a unit length dependent on the radius of the jet and the second moment of
the velocity of rotation u2(a): m= H 1~u2(,a)/4~?m.
We note that the electric current arising in the medium is determined.only
by the magnetic f ield component transverse to the axis of the jet and locaZ-
ized within it. It follows from expression (5) that the total current in
the jet section is equal to zero. Therefore, the determined distribution
of the induced fields is not dependent on the presence of a discontinuity
and is correct both within the fluid and outside it. The order of magni-
tude of magnetic field strength in the air is determined by the expression
~~c~hoQZl3r~,
where h~ is expressed through the value of the Reynolds number
~0=f~1 Rm/2� . ~ 6/
Magnetic field of a linear jet with a longitudinal velocity component. The
role of the sea water - air discontinuity is more significant in the pres-
ence of longitudinal movement of the fluid in the jet. For the purpose of
studying this problem we will stipulate the velocity distribution in the
form vr = 0, v~ = 0, vZ = v ~(a - r) and again we will use expression (2).
We obtain for the case of an unbounded medium
E,=- (It1�v/2c) y(a/r) sign (r-a) cos E~=- (1I~�v/2c) x(a/r) sin
hj=- (H1�Rml2) [ (r/a) 6 (a-r) (a/r) A (r-a) ] sin q~, ~ ~ ~
j: (ovHl�/2c) x (a/r) cos
Im=- (avlf~ /2c)Y (a/r) sign (r-a) sin cp.
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;
Nere we have introduced the function x(x) = 8(1-x)+x2 e(x-1). [We noCe
that the cited expression for the magnetic field hZ at great distances
r~ a coincides with the results in [12] for a jet with exponentially blurr-
ed edges.]
As can be seen from formulas, (7), the electric field and Che current are
determined by the component of the permanent field H 1 0 and in contrast ;
to the case of rotational movement are propagated through the entire con-
ducting medium, relatively slowly dropping off with increasing distance
from the axis of the jet j N r'2. However, the distributions (7) are not ap-
plicable near the discontinuity, where the current pattern is substantially
deformed. '
, '
The solution satisfying the boundary condition (3) is reduced to a suitable
choice of systems for representations of jets situated equidistantly outside ~
the conducting layer. The center of the jet is situated at the distance
,~,/2 - d from the "core" of the plane conducting layer, the layer thickness
~,(see inset in Fig. 1). The distribution of the magnetic field has the
form of an infinite sum for all images. Transforming the corresponding ex-
pressions by means of the Poisson summation formula [13], it is possible
to represent the final distribution of the additional field in the follow-
ing form: h,=h~=0, hj=h=�6(a-r)-(~tRma/4l) (Nx�~=-I-H~ ~
(8) ~ ~
h:�=- (R,�/2) [Ns� (~r/a-a/r) cos ~+11~ (r/a-a/r) sin
where
sh nx/l sh nx/l
~ ch ~x/l-cos ny/l ch ~x/l-c~s n(y-2d)/l ' ~9~ ~
~
sin n(y-2d) /l 1 sin ~y/l i,
~y ch ~x/l-cos ~ (y-2d)/l ~ ch nx/l-cos ny/l ~
;
We note that the currents generated by a linear jet lie in a plane perpen-
dicular to its axis and limited by the thickness of the conducting layer. !
The distribution of the magnetic f_ield within the layer over the jet (x = i
0) for different positionings of the jet is sh~wn in Fig. 1. The solid
curve corresponds to a jet situated in the middle (d =.Q/2), the dashed
curve represents the current depth d= 3~,/4. The y' coordinate is reckon- ~
ed from the middle of the layer. The field scale is determined by the ,
parameter hp, determined by formula (6), in which as v it is necessary to ~
take the velocity of longitudinal movement. I
According to the results, the field at the boundary of the layer (the same i
as the current component normal to the boundary) becomes equal to zero. ~
From the continuity condition and the Maxwell equations it should also !
become equal to zero at any point outside the conducting medium. The de- ~
termined field distribution resembles the result correct in the case of i
two infinitely long solenoids. Thus, the role of the discontinuity is re- ~
I
duced to the screening of the f ield of an infinite jet outside the con- ~
ducting medium. I
25 _
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I FOR OFFICIAL USE ONLY
i
~ / hT
/ 0
I
i ~ ~
i � ~
~ ~
i ~l,%2 ~ ~ ~ y - ~~Z y,
I ~ ~ d
i J I L
i Za . Z
I
~ ~
; Fig. i.
;
~ To be sure, a real jet has a limited length. Assuming this length to be
, equal to 2L and stipulating the velocity distribution
; ~ v==v6(a-r)6(L-~z~), (10)
'
j we will evaluate the arising "scattering fields" outside the fluid. .
' The velocity distribution (10) is characteristic of a current created by
~ the inflow and outflow operative at the points z= fL. In actuality, a
jet of a finite length must have a transition region where ordered trans-
: lational movement, Scattering, disappears. The model which we adopted takes
; into account the contribution to the magnetic field from currents generated
by the translational movement of the fluid in the jet and the contribution
; of the random currents arising as a result of the complex, unordered move-
; ment of the fluid near the ends of the jet is neglected.
i �
I
~ Substituting the distribution of the electric current in the Biot-Savart
; for. mula in the form j= j p 8(L ~ I 1, wher. e j ~ is determined from solu-
~ tion of the boundary problem similar to (8), (9), we obtain the distribution
~ of the additional field in outer space. We will not fully write the corres-
ponding distribution due to unwieldiness and we will cite only the asymptotic
form at great distances ~R ~ 1~:
Rmll��a( d 1 Y R,�H��a( d 1
h= 4l 1 l~ . 2) F,, hy-hx X' h= - ~4l \ l 2/ F~' ~11)
~ X X
� F~ _ _
(RZ-f-Z,2)'~' (Rz-f-'/,ZZ)'~' ' (12)
Z, Z2 .
' . ~ F" _ (Rx+7,,2) � ~Rz..}..ZYz~ y, '
i
' �
~ 2~
j
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run urri~trw uo~ u1vLi
i
whE~re X= x/ Y~ y/ , Z= z/.p, are the reduced coordinates of the ob- I
servation point; Z1,2 = L/,~,+Z;~R is the distance from the center of the ;
jet to the ohservation point in the cited coordinates. '
i
y0/~ ~
Z ~
I
I
i
~
1 I
i
, i
1
i
~
, ~
.
~ i
, h~ ~~Z � i
i
i
Fig. 2. ~
As can be seen from expressions (11), the direction of the additional field ~
is dependent on the positioning of the jet relative to half sea. depth. In a ;
case when the depth of the jet is equal to half the thickness of the fluid i
layer, the magnetic disturbance in a dipole approximation (11) becomes equal ~
to zero. The field distribution (11) is illustrated in Fig. 2, which shows
the horizontal field component directly over the jet (x = 0, z= 0) as a i
function of y~ the distance to the sea surface. The field scale in the I
air is determined by the exp~ession ~
h,-rhaalL-Z (d/l-'lx),' ~
which tends to zero when L-> i
~
Numerical estimates of geomagnetic disturbances. The results make it pos-
sible to estimate the geomagnetic disturbances of the jet. Their value and ,
the law of decrease with distance are determined both by the parameters I
of the jet and by the distance to the observation point in the sea~or in ;
the air. At the same time that the disturbance of the rotating jet con- ~
forms to a law correct for the magnetized filament, the nature of the ~
, asymptotic form of the magnetic field in a translationally moving 3et !
changes considerably with movement along its length. It is interesting to ~
compare the characteristic magnitudes of the geomagnetic disturbances ~
created by the translational and rotational movements of the fluid. i
i
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~ I .
~ ~ FOR OFFTCIAL USE ONLY
; (
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j Table 1 gives the characteristic values of the geomagnetic disturbances
of a jet for dif~erent current conditions and ohservation regions (a is
the radius of the jet, 2L ts its length, Q is sea depth), Rm�t and R~rans
, are the values of the Reynolds magnetic number for the rotational and
' translational components of jet velocity. In a case when translational and
I' rotational components of jet movement exisC simultaneously, their con-
I' tribution is summed. The values cited in Table 1 determine the maximum
field values, their dependence on distance is determined by the more de-
' tailed expressions derived above.
When R~ L, that is, at a distance from the jet small in comparison with its
' length, the fields in the air for translational and rotational movemer.ts are
~ related as
' htrans~hrot,,, volRZ/uoaL=,
where v~ is the characteristic velocity of the translational and up is the
characteristic velocity of rotational mov~ments. The magnetic field of a
; rotating jet decreases in the outer space in conformity to the law R-2, slow-
er than, the field of the magnetic dipole h^~ R-3. For a j et of f inite length
or a jet having a curvature of its movement at the characteristic distance
~ L, this law will be correct at distances from it not exceeding L. Such cur-
rents can be registered relatively easily. A similar conclusion can evidently
be drawn for local disturbances of the jet associated with rotation. When
R> L the magnetic field of a limited longitudinal jet decreases with dis-
tance in conformity to the law R-3 and at shor~ distances attains saturation
(see Fig. 2).
' Table 1
RapaKrep Aexxcex}~rt 1 I BxyrpR riopt[ 2 I 3 B eoaAyze
~ 4 Bpau~aau~axcx crpy~n H�, Rm /6 6 H1Rm /6
' S CTpys c npoAonbar~x AB~tsFCC- ji~ RnocT~2 7. Ho RaocTal 2L~
axeM m 1 m ~
~ KEY: .
l. Nature of movement 6. rotational
2. Within sea 7. translational
' 3. In air
, 4. Rotating jzt
5. Jet with longitudinal movement
Table 2
~ - Uo. KJi ]/o. HM
L, HM l L, KK
-0,5 I 0 I 5 I 10 I f00 -0,5 I 0 I 5 I 10 I f00
;
5 1 0,05 0,01 0,0(N 6�iQ-8 100 1 f0-' 10-~ 10-' 4�i~s
!0 1 I 0,01 I0,008 IO,WS I 10-5 II 1000 I 1 I10-~ I10-6 10-6 1-�
IO
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i
~
Table 3
i
~
vo, 1tL[ vo, xnt i
M i I 5 1 io I ioo M i. I 5 I io I, soo ;
i
50 0,001 2� 10-~ 4� 10-5 10-6 I ~50 0,2 0,01 0,005 6� 10-5 ~
1U0 I0,01 0,0~1 I 3~10-~ I 5�10-8 ~I 10001 1'0 I 1 I 0,3 I 4~10-' ~
I
,
~
Tables 2, 3 give numerical estimates of geomagnetic disturbances obtained ~
for a number of values of the L and R parameters of practical interest cor- i
responding to both large-scale ocean currents and to relatively small ~et ;
disturbances [14]. Table 2 gives the values of the geomagnetic disturbances ~
(in gammas) created by the translational movement of a fluid in a jet when i
a= 100 m, d=~ km, Q= 4 km, o'= 4 Gm/m, v= 102 cm/seG; y~ _-0.5 cor- i
responds to the field of~an infinitely long ~et within a fluid layer at the ;
depth 500 m, yp = 0 is the sea surface. Table 3 gives the values of the geo- ~
magnetic disturbances (in gamrnas) for a rota~ional movement of the fluid ~
in the jet k~hen d= 1 km, o~= 4 Cm/m, u= 10 cm/sec. As can be seen from ;
- the cited data, the field disturbances can vary in a wide range from frac- ;
tions of a gamma to 10-6 gamma. The existence at the present time of super- ~
conducting magnetometers [15] makes it possible to register magnetic fields ~
to 1Q-6'r and their gradients 10'6 ~'/cm. In a study of deep currents ~
it can be of interest to meas.ure the field within the sea at a relatively i
short distance from the surface (such, however, that it is possible to
neglect the exponentially decreasing field of sea waves). According to i
Table 2, in this case the field strength of the jet is considerably great-
er than the field outside the fluid. ~
We note in conclusion that the computations made relate formally not only
to disturbances created hy sea movements, but also circumterrestrial plasma. I
Therefore, observations from aircraft and artificial earth satellites with j
superconducting apparatus on board can be a convenient tool for studying i
the spatial and temporal variations of the geomagnetic field of both hydro- i
spheric and ionospheric origin. ~
The authors express appreciation to Professor B. Ya. Levin for discussion i-
of the results. ~
BIBLIOGRAPHY ~
i
l. Shuleykin, V. V., FIZIKA MORYA (Marine Physics), "Nauka," 1968. I
2. Solimar, L., TUNNEL'NYY EFFEKT V SVERKHPROVODNIKAKH I YEGO PRIMENENIYE I
(The Tunnel Effect in Superconductors and its Use), "Mir," 1974. ~
3. Kulik, I. 0., Yanson, I. K., EFFEKT DZHOZEFSONA V SVERKHPROVODYASH~i:IKH ;
TUNNEL'NYKH STRUKTURAKH (Josephson Effect in Superconducting Tunnel ;
"Nauka " 1970. ~
Structures), ,
_ i
30 ~
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4. Weaver, J. T., JGR, 70, 1921, 1965.
5. Leybo, A~ B., Semenov, V. Yu., GEOMAGNETIZM I AERONOMIYA (Geomagnetism
~ and Aeronoury), 15, 231, 1975.
~ 6. Podney, W., JGR, 80, 2977, 1975.
~
~ 7. Gorskaya, Ye. N., Skrynnikov, R. G., Sokolov, G. V., GEOMAGNETIZM I
~ ~ AERONOMIYA, 12, 153, 1972.
'
I 8. Kontorovich, V. M.~; DOKL. AN SSSR (Reports of the USSR Academy of Sci-
i ences), 137, 576, ~1961.
~ 9. Burtsev, G. A., IZV. AN SSSR, FIZIKA ATMOSFERY I OKEANA (News of the
~ USSR Academy of Sciences, Physics of the Atmosphere and Ocean), 11,
~ 1084, 1975.
~
; 10. Tikhonov, A. N., Sveshnikov, A. G., IZV. AN SSSR, S~R. GEOFIZ. (News of
! USSR Academy of Sciences, Geophysical Series), No 1, 48, 1959.
~ 11. Landau, L. D., Lifshits, Ye. M., ELEKTRODINAMIKA SPLOSHNYKH SRED (Elec-
: trodynamics ci Continuous Media), Moscow, 1959.
!
j 12. Dorman, L. I., VOPROSY MAGNITNOY GIDRODINAMIKI I DINAMIKI PLAZMY (Prob-
! lems in Magnetohydrodynamics and Dynatnics of Plasma), AI1 LatvSSR, 63,
! 1962.
;
13. Korn, G., Korn, T., SPRAVOCHNIK PO MATEMATIKE (Mathematics Handbook),
~ "Nauka," 1974.
;
~ 14. Kamenkovich, V. M., OSNOVY DINAMIKI OKEANA (Principles of Ocean Dynamics),
"Nauka.," 1973.
i 15. Goodman, W. L., Hesterman, V. W., Rorden, H., Goree, W. S., PROC. IEEE,
; 61, 20, 1973.
, COPYRIGHT: Izdatel'stvo "Nauka," "Geomagnetizm i aeronomiya," 1979
~ [495-5303]
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� ,
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~
I
, UDC 550.373
ELECTROMAGNETIC FIELD OF SEA WAVES IN AN ELECTRICALLY STRATIFIED SEA
. I
Moscow GEOMAGNETIZM I AERONOMIYA in Russian Vol 19, No 4, 1979 pp 715-721 ~
[Article by V. P. Smagin and V. N. Savchenko, Far Eastern State University, '
submitted for publication 30 May 1978] ~
I
Abstract: The authors formulate and solve '
the problem of an induced electromagnetic
field of_sea wind ~zaves in an electrically
. stratified,,sea of finite depth. Sea conduc-
tivi.ty.is s,tipulated as a function exponen- '
tially decr'easing ~rith depth. Electric field
strengtfi...ind the field of magnetic induction ~
are found''from solutions of the equations ,
for scalar potential. ~
[Text] Introduction. The problem of the influence of electric stratifica-
tion of extended conductors of finite thickness on the form of the vari-
able electromagnetic field inside and outside these conductors is of great {
importance for geophysics [1, Z). As noted in [3], the electric stratif- j
ication of the earth is important for study of both electric currents in i
the ocean and the conductivity of bottom rocks. But in that study there ~
was no discussion of the role of electric stratification of the ocean it- ,
self. However, exper.imental data on conductivity of the acean throughout i
its thickness indicate its sharp change, especially in the surface layer ;
with a thickness of 1 km [4]. This circumstance encourages development of '
a variant of the theory of electromagnetic induction in the ocean which '
would take into account the nonuniformity of conductivity in the ocean, ~
i.he diversity of types of wave movement of the sea medium (potential or ~
eddy) and an arbitrary';'choice of an electric model of the bottom. This ;
pi�oblem has not been sr~lved in the studies known to us (see reviews [3-5]). ;
i'
E uations for electric and ma netic fields and electric ~
Q g potential in an el- ;
_ ectrically stratified ocean. For solving problems related to electromagnetic j
induction in the ocean we will select a system of Maxwell equations in a i
quasistationary approximation, which is adequately substantiated [6, 7] for ~
the range of characteristic frequencies of sea waves, taking into account I
i
. ~
32 ;
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the low conductivity of the sea medium. However, for deriving the equations
of magnetic induction and an electric field, taking into account the nonuni-
formity of conducCivity c?'(r) of the sea medium, in the initial system of
equations for the electromagnetic field we retain the displacement cur-
rents which we will neglect after completing derivation of the mentioned
equations.
We will use the following Maxwell equations (in a practical system of units);
rotI3=�(j-}-~7U/~t), rotE=-aB/~t, divl)=p, divB=O, (1~
supplemented by the system of relationships
D~=eE, B=�H, j=6(I:-f-[vXB]). ~2~
Hencef.orth the sea medium is assumed to be nonmagnetic, that is,
wher.e � ~ is the magnetic permeability of a vacuum. In Ohm's law (2) v is -
the velocity of movement of the fluid, to be more precise, the velocity of
movement oi its particles. The B field includes the permanent geomagnetic
field and the induced magnetic field, which is considerably less than the
geomagnetic field, as a result of which in [v x B] (2) we will retain only
the term [v x F).
We will also assume that sea waves of all types contain an oscillating tem-
poral factor exp (-ic,~t) whic~h also contains electromagnetic values. We
will make partial use of this circumstance in the derivation of equations
f or B and E.
For B we ob tain an equation in a quasistationary approximation
~B-4-grad ln aXrot B-�Q~B/8t=-�o (F � V) v, ~ 3~
for E, on the other hand:
DE-I-grad(E�gradlnQ)-�Q ~E=-grad{Frotv-I-[vXr]gradlna}. (4)
Equations (3) and (4) must be supplemented by boundary and boundary-value
conditions, without which it is impossible to attain unambiguity of the
solution. First we will assume the disappearance of all fields at infinity.
The boundary conditions for the fields of conductors formed from sectors of
different conductivity are well known within the framework of a quasistation-
ary approximation [8]. Due to the nonmagnetic na.ture of the sea medium there
is a continuity of the magnetic induction vector B on all the conductivity
discontinuities. The continuity of the tangential component B-~ leads to a
continuity of the normal component (rot B)n or a continuity �~(E +[v x F])n.
~ The continuity of the normal component Bn leads, in accordance with (1), to
continuity of the normal component (rot E)n or a continuity of the tangen-
tial component E.~.
33
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~ I
Without analyzing equations (3) and (4) and without seelcing merhods for ~
their solution, we wi11 go in the direction of a further simpllfication
of the conditions of the problem, as.suming that it is possible to neglect ~
the effect of self-induction in equations (1), as has been done in other
~ studies [9-11]. The latter assumption leads to a restriction on the range
of the frequency spectrum of sea waves (and the electromagnetic field) by
, the inequality k2~ N o'w, which is easy to obtain from a comparison of the
Laplace operators d and - �o-a / a t af ter their effect on a plane mono-
chromat:tc wave (i:n hydrodynamics a surface progressive wave), propagaC- '
ing in tl:e direction of the x-axis.
With the assumptions made the system of equations has the form:
rot B=~~j, rot E=0, div j=0, ~
(5) ;
divB=O, divD=p, j=v(E~-[vXF]), i
hence the electric field E can be st~;.,tlated through the potential: E_
-grad ~ . ~
Introducing U'= ~(z) and limiting ourselves only to the verttcal compon- ~
ent of the geomagnetic field F= kT', from the equation div j= 0 we obtain: ~
div E=-F rot v-E grad ln Q, '
and then for electric potential the equation: ~
Ocp+grad ln a grad cp=F � rot v. ~ 6~
i
In deriving the equations it was taken into account that [v x F] grad ln
p~- p , i
I
Now it is necessary to determine the nature of the wave movement of the sea
medium. The ocean will be assumed to have the constant depth H and to be ;
unbounded in the horizontal plane.
i
The system of Cartesian coordinates is situated on the undisturbed sea sur- ~
face; the z-axis is directed vertically upward, the x and y axes lie in the ,
horizontal plane. A sea wave, which is selected in the form proposed in [10], ;
has a component of the velocity of motion of fluid particles in the horizon- .
tal plane along the x axis and assumes a periodic change in the velocity of '
motion of fluid particles i~n the direction of the y axis. The finite length
of the wave crest is thereby taken into account. The horizontal velocity of ~
the fluid particles along the x axis is stipulated in the form;
(7) i
u=v(Z, k) cos (nx-wt) cos my,
;
where n= 2 st X; m= 2n / a y; aJ = 2 n/T, ~ X, ~ly are the wave lengths in
the directions of the x and y axes respectively; T is the period of oscil-
lations; k2 = n2 + m2. We will substitute the expression for velocity (7)
into (6), after which the right-hand side of the potential equation becc*nes
34 ;
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equal to mFv(.z, k) cos (nx -cJt) sin my. It is natural to seek solutions
of the equation hy the separa~ted var~.ables method
cp (x, y, z) (z, k) cos (nx-wt) sin m~,
As a result, the equation for poCential amplitudes is written in the form
~ ~
a ~ (Z, k) -1- d ln Q (z) d ~ ~Z, k) - k2W (z, k) =mFv (z, k> . ~8~
aZZ aZ aZ
Equation (8) is fundamental for further investigations. Assuming different
models of waves and conductivity, that is, stipulating the functions v(z,
k) and cT(z), using (8) it is possible to determine the electric potential,
and already on the basis of the potential the electric currents and mag-
netic fields in all media.
Equation (8) is supplemented by the continuity conditions for the normal com-
ponent of electric current density and the already noted continuity E,~ at
the conductivity discontinuities. ,
i Assume that solutions of equation (8) have been found (a specific example
j of the solution will be given in the next section). We will show that the
~ remaining electromagnetic parameters can be determined in the latter.
The electric field components are expressed most simply:
~
,
I Ex=-8c~(x, y, z)/ax=ncp(z, k) sin (nx-c~t) sin my,
~ Ey=-acp(x, y, !)18~=-m~(~, k) cos (nx-c~t) cos rn.y, (9)
i E,=-8~(x, a)laz=-[dcp(z, k)ldz] cos (nx-wt) sinna~.
~ Using Ohm's law, we will determine the components of the current density
j . vector j :
jz=aEx==na(a)cp(z, k) sin (nx-r~t) sin na~=
~ =jx(z) sin (nx-c~t) sinmy,
i jy=Q (F.y-vF) =-6 (z) [ mcp ( 2, k) -I-Fv (z, k) ] cos (nx- (10)
, -c~t) cos my=jy(z) cos (nx-c~t) cos nay,
i j:=6E:=-a(z) ldcp(z, k)/dz]cos (nx-c~t)sin m~=
=j= (z) cus (nx-wt) siii nty.
~ The induced current creates magnetic induction B(r), which we will deter-
; mine using the Biot-Savart law -
, B ~r~ �o J ~ ] ~r') X (r-r' ) ~ dr'.
4n I r-r' I'
Here r is the radius-vector of the observation point; r' are the radius-
I vectors of the points of electric current sources. Integration is carried
' out for the entire region of electric currents.
i First we will find the vertical com~onent of magnetic induction:
I ~ ,~",y~ ~~~x~'y~'Z~)~y-~J~)-l~~x~ y~ z')(x-x')dx'dy'da'
' 'I~ .c a JJ~ , ,
4:c ((x-x')~-f-(y-y')=-f-(z-z')=]~~, � ~11~
~
~
i
~ 35
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r~ux ur~r'1C1AL U5E UNLY ~
~
We introduce the notations x' - x, y' - y, z' - z, after which ~
(11) assumes the form ~
i
Bj(x, y, a)=13=(z) sin (nx-wt) cos my, ~12~ ~
~
r r r jx (a') r~ sin mr~ cos n~-jv (z') ~ sin n~ cos m~ d~d~dz .
where B, z=- -J J J ~
~~~~"~s.~.~:~v,
(13) ;
In (13) we carry out integration for ~S and Y~, using [12]: ~
~ ~ ~ m
r r~ siu n~ cos mr~ cos mr~ d~ _
J J ~~2-E...,~Z~..~z~�~, d~d~1= f~ sin r~~d~ f~ sZ+~Z+~Z~>>.
~
~ .
= f ~sinn~[2m/(~z-f-~z)'~�~K,(my~z-1-~2)d~=
.
=4Yn%2m (n2+m2) -'''~'~'K-~~, (YnZ`in
~ ) _ (2~n/k) e-"~c~,
where K1(z), K-1/2(z) are cylindrical functions of a fictitious argument.
The other integral is computed in a similar way: ,
~ ~
f f r~ sin mr~ cos n~[~Z-f-r~2-t-~=]-'~� d~ dr~= (2~cm/k)e-"1L1.
As a result, formula (13~ assumes the form:
-s .
B=(z)=-(�o/2) f [(m/k)jx(a')-(nllc)iv(z'))e_"i:~,-=idz'. (14)
0
Substituting into (14) the expressions for electric currents from (10), we
ob tain
BZ (z) (�onFl2k) ~ Q(a') v(z', k) e-"~:'_:~ dZ'. (15)
. o
As can be seen from (15), BZ is completely determined by wave velocity and
the conductivity of sea water.
The horizontal components of magnetic induction BX and By can be determined
similar to BZ, but in a simpler approach. We will use equations (5) for mag-
netic induction: rot B= �.j , div B= 0 and the fact that
Bx(x, y, z) =Bx(z) cos (nx-~t) cos my,
. (16)
B~(x, y, a) =B�(z) sin (nx-c~t) sin my,
and we obtain the equations
nBy(z)-~-mBx(z)=�j:(z), B,'(z)-f-mB�(z)-nI3Y(i)=0,
which lead to a determination of BX(z), By(z):
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I
FOR OFFICIAL USE ONLY
i
B:~z) =~�om/k~)1=~a)-!'(n/k2)Bt'(z), ~1~~
I By~z) =~�on/k~)I=~a)-(m/kx)Bi'(z). (lg)
I
i
In particular, BX(z~ in the sea., that is, when -H?-e'") - 1 e~cs-t~ ~ezca-R~s_e-zca_R~,~
2 (a-I-k) 2 (a-k)
where B~ = �~v~F O'21/4.
' A numerical estimate of BZ at the sea surface, that is, with z= 0 and with -
the following values of the parameters: k~ 0.03 m'1, H= 103 m, v~ sh kH =
1 m/sec, ~"21 = 5 Cm, gives BZ(0) ~ 1.2 nT.
; The tangential components of the magnetic induction field are found using
formulas (17), (18). It is easy to determine the components of the electric
, field using formulas (9) and the components of the electric current using
formulas (10).
In r_onclusion it should be noted that the use of the exponentially decreas-
ing function (19) for electric conductivity of the sea with depth with the
, coefficients~xl N H-1 does not ensure the required marked decrease in con-
ductivity, especially at depths to 1,000 m, which, on the one hand, makes
it necessary to seek the functions most precisely approximating the experi-
mental variation of electric conductivity, and on the other hand, use a
multilayer electrically stratified model of ti~e ocean.
Another important direction in the work should be related to solution of
equations (.3) and (4), making it possible to include electromagnetic fields
~ of inedium- and long-period waves in the system of computations.
' 39
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L Vl\ VL' 1' L~IlLIl! UJli Vl\LL I
BzBLxocxaPxY '
;
l. Trayman, R., GEOMAGNETIZM I AERONOMIYA (Geomagnetism and Aeronomy), 10, ;
478, 1970. ~
il
2. ELECTROMAGNETIC PROBING IN GEOPHYSICS, edited by J. R. Wait, The Golem
Press, Boulder, Colorado, 1971. ~
3. Cox, C. S., Fillouz, J. H., Larson, J. C., THE SEA, Vol 4, 1, 637, ~ ~
Wiley-Interscience, New York, 1971.
4. Bullard, E. C., Parker, R. L., THE SEA, Vol 4, 1, 695, Wiley-Intersci- ~
ence, New York, 1971. ;
5. Fonarev, G. A., Shneyer, V. S., MORSKIYE TOKI (Sea Electric Currents).
G~OMAGNETIZM I VYSOKIYE SLOI ATMOSFERY (Geomagnetism and High Layers
of the Atmosphere), No 2, "Nauka," 225, 1975. ~
6. Sanford, T. B., JGR, 76, 3476, 1971. ~
;
7. Larsen, J. C., PHYS. EARTH AND PLANET. INTER., 79 389, 1973.
8. Landau, L. D., Lifshits, Ye. M., ELEKTRODINAMIKA SPLOSHNYKH SRED (Elec-
trodynamics of Continuous Media), Chapter VIII, Gostekhteorizdat, 1957. i
j
9. Warburton, R., Caminiti, R., JGR, 69, 4311, 1964. ~
10. Leybo, A. B., Semenov, V. Yu., GEOMAGNETIZM I AERONOMIYA, 15, 236, 1975. ~
_ 11. Leybo, A. B., Semenov, V. Yu., Fonarev, G. A., GEOMAGNITNYYE ISSLEDO- ;
VANIYA (Geomagnetic Research), No 16, "Nauka," 30, 1975. ~
~
12. Gradshteyn, I. S., Ryzhik, I. M., TABLITSY INTEGRALOV., SUI~i, RYADOV I ,
PROIZVEDENIY (Tables of Integrals, Sums, Series and Froducts), Fizmat- ~
giz, 1963. '
i
COPYItIGHT: Izdatel'stvo "Nauka," "Geomagnetizm i aeronomiya," 1979
[495-5303J I
~
I
_ ~
j
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I
~
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UDC 551.46.01
I
~ ~ SYSTEMIC PRINCIPLES FOR ANALYSIS OF OCEAN OBSERVATIONS
_ ~ Kiev SISTENIIJYYE PRINTSIPY ANALIZA NABLYUDENIY V OKEANE (Systemic Principles
~ for Analysis of Ocean Observations) in Russian 1978 pp 2-3, 221-222
I
I [Annotation, introduction and table of contents from book by B. A. Nelepo
I and I. Ye. Timchenko, Izdatel'stvo "Naukova Dumka," 224 pages]
i [Text] This monograph is devoted to a systemic approach to the problem of
~ , predicting oceanic phenomena by means of automation of the data collection
~ and processing processes. On the basis of the theory of adaptive filtering
i of observations the monograph examines dynamic-stochastic models of pro-
cesses and fields in the ocean and validates the principles for combining
i hydroiiynamic problems in oceanography with statistical methods for the an-
alysis o� obs~rvations. As component parts of the systemic approach, a
I study is made of problems in the optimum interpolation of random fields and
the planning of ineasurements in the ocean.
I The authors give examples of the use of dynamic-stochastic models for the
I successive prediction of oceanic processes and fields. The monograph is
intended for professional geophysicists working on the problems of model-
ing and numerical analysis of physical processes and fields.
i �
~ Sixty-nine illustrations. Five tables. Bibliography (pp 213-220) 193 items.
i
- ~ -
I
~ Introductian. Pr.ediction of the state of the ocean as a medium is of great
~ scientific and practical importance for mankind. The knowledge accumulated
i by oceanology is evidence of the complex spatial-temporal variability of
the principal hydrophysical, hydrochemical and biological fields in the
ocean. As a result of the infinite diversity of the factors forming weather
in the ocean, in addition to the equations of hydromechanics, describing the
~ principal features of the dynamics of water masses, use is made of different
; stochastic methods for the modeling and filtering of observational data. The
~ problems arising with a combination of determined and stochastic approaches
~ to the investigation of oceanic phenomena remain virtua.lly unstudied. How-
~ ever, under conditions of automation of collection and processing of
i
41
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oceanological data such a research method (which ~oe have arbitrarily call-
ed the systemic approach to the analysis of a phenomenon) should be most ~
effective. Ttiis monograph is devoted to use of the systemic approach in
the problems involved in computing and predicCing oceanological processes ~
and fields on the basis of observa.tional data.
Due to the poor study of most of the considered matters, the book gives no ;
review of oceanological studies of stochastic modeling and analysis of ~
oceanic fields. Problems in objective and four-dimensional analyses of '
meteorological fields, similar in formulation, have been dealt with only ~ '
to the extent which was deemed necessary, taking into account their specific '
nature. Individual results of this study (for example, possible variants of '
oceanological data systems) must be regarded only as a formulation of the
problem for further investigation. ,
We consider it our pleasant duty to express deep appreciation to Academicians i
L. M. Brekhovskikh and A. M. Obukhov and Corresponding Member USSR Academy of ~
Sciences A. S. Monin for discussion of individual parts of the study and val- I
uable advice favoring an improvement in its content. !
I
i
Contents Page '
Introduction 3 ~
Chapter I. Prob.lems in Physics of the Ocean and Modern Systems Theory 4
1. Applied aspects of oceanological research 4
2. Automation of processes of collection and processing of oceanolog- 9 '
ical information
3. Systems approach to analysis of oceanic phenomena 16
4. Prob lem of prediction and filtering of processes and fields in the
ocean 22
_ 5. General principles for planning ocean observations 31
Chapter II. Optimum Filtering of Observations of Random Oceanological
Processes 37
6. Uptimum filtering of observation time series as a problem in control
theory 37
7. Algorithm for the optimum filtering of time series of oceanological
observations 45
8. ldentification of parameters of models of stationary hydrophysical
processes 48
9. Prediction of stationary hydrophysical processes by Kalman method 53
10. Piodeling of nonstationary hydrophysical processes 60
11. Automation of modeling and prediction, on an electronic computer,
of nonstationary hydrophysical processes 67
Chapter III. Objective Analysis of Spatial Random Ocean Fields 74
12. Statistical modeling of spatial random ocean fields 74
13. Optimum interpolation correla.tion algorithm 78
14. Construction of maps of hydrophysical fields by optimum interpolatior.
method 31
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15. Construction of maps of spatial distribution of oxygen based on
observations in the Tropical Atlantic 85
- ;6. Spectral optimum interpolation algoriChm 96
1;. Use of spectral interpolation algorithm in problems of construction
of maps of ocean fields 106
18. Statistical matching of oceanographic fields 113
~ 19. Refinement of map of oxygen field on basis of ineasurements of the
salinity field 122
Chapter IV. Sequential riethods for Predicting Ocean Fields 128
20. Use of inethods for four-dimensional analysis of observations in
meteorology 128
21. Formulation of problem of successive analysis of spatial-temporal
ocean fields 134
! 22. Spectral formulation of suc.cess.ive analysis method 141
23. Properties of algorithm for successive analysis of observations 143
' 24. Successive analysis of observations of vertical distribution of
~ current velocities 147
25. Prediction of vertical temperature profiles in upper layer of sea 156
26. Modeling and prediction of the vertical distribution of sea tem-
~ perature under expeditionary conditions 164
' Chapter V. Systemic Approach to Planning of Oceanographic Observations 174
~ 27. Measurement of oceanographic processes in relation to use of
, adaptive filtering methods 174
28. Planning of network of stations for measuring random spatial
oceanic fields 176
29. Rationalization of survey of spatial field of bottom relief 190
30. Measurement of. statistically related fields 195
31. Planning of observations of spatial-temporal fields in ocean 199
; 32. Organization of collection and processing of data in successive
analysis of oceanographic information 207
Bibl.iography 213
COPYRIGHT: Izdatel'stvo "Naukova dumka," 1978
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