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ULF/ELF electromagnetic fields generated along
the sea floor interface by a straight current source of
infinite length
Aziz S. Inan
University of Portland, [email protected]
A. C. Fraser-Smith
O. G. Villard Jr.
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Inan, Aziz S.; Fraser-Smith, A. C.; and Villard, O. G. Jr., "ULF/ELF electromagnetic fields generated along the sea floor interface by a
straight current source of infinite length" (1986). Engineering Faculty Publications and Presentations. Paper 3.
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Radio Selene., Volume 21, Number 3, Pages 409-420, May- June 19R6
ULF/ELF electromagnetic fields generat.ed along the seafloor interface
by a straight current source of infinite length
A. S. l nan.' A. C. Fraser-Smiih. and 0. G. Vlllard, Jr .
Spaa. T1Uc01Mt1Ulk:4tioM or.d Radio>ei"1".u lAborotory, Sf.Olo/oril. L'nlotrlity, Cab/a""4
(Received March 15, 1985; revised-October 30, 1985, accepted October .JO, 1985.)
Prope.plion or ULF/ ELF elcctroma~etic fields along the seaftoor lntorfocc (aHumed to be a plane
bounUury acpa..ra~ing two rcmi-infinitc couducting media) is considered. Earlier expressions for the
elcctroma~etlc ftelds genera ted hy a straight current source or infinite length arc applied to the
•••/ocub<d 1111erface. The field com1xments are calculated nltrncrically um! arc compmi:d to the fiekl
c~mponenu In "~wnter of infinite extent. At 1he seanoor bouncl4ry, the fiel<11 c•n p1opa1010 longer
d1st11ncc• bec~ u •c of tho lower seabed conductivities. The M W horizontal component of the magnetic
Oeld gencru1ed ni ~ rosult of the existence of the sea/seabed interface bcco1110• lor11or thun the vertical
component or th< mB&n•tic fi<ld at large distances; it is also more sensitive to the conductivilv or tile
seabed ol low froqucncic1. The rCiulll indicate !.hat there i~ an optimol frequency Bl which 1w~ of the
field components lrnve a maximum field int ensity at a certain d iS10.nce Croni the llOun:e. Some practical
applications m dlscuncd.
INTRODUCTION
EI_ec tromagnetic wave propagation in conducting
media has been or practical interest since the beginning of this cenrury. T oward the end of the tirst
World War, limited e:tpcrimenud a.od theoretical
work focused on the generotion of electromagnetic
fields in, on, and above the sea by submerged cables
carrying alternating current [Drysdale. 1924; Butterworth, 1924]. T his work was motivated by the use of
cable-gen era ted electromagnetic fields for navigatio n
[Wright, 1953]. These fields hove olso become im porta nt for communicating with subma rines [M oore,
1951 , 1967]. Do~pi te the absorption of electromagne tic e nergy in seawater, elec tromagnetic signals
a: ELF a:e able to propagate to moderately great
d1sla.nces m the ocean and, as a result, they are a
possi ble means of con1munieation with deeply subm~ rg~d s u?marines [Wa/1, 1972). A more recent a pplication 1s geophysical prospect ing. A significant
amount of rei;earch has used electromagnetic techniqu es to study the strucn1re of the earth's crust
[Burrows, 1963; Walt arid Spies, 1972a, b, c]. Propagation of VLF signals through the earth has also
been of considerable interest for mine communi'Now a t Cngi.neerina Dcparuru:nl. San Fra!leiKo Stale University, California.
Copyril!hl 1986 by the American Geophysical Union.
Paper number SS08l 7.
0048-6604/86/00~S-08 l 7S08.00
409
cation; in the event of a mme disaster, telephone
wires and other normal links o f communication
could be interrupted, but communication with the
trapped miners could ~till be achieved through the
earth [ Wait a11d Spier, 1973) .
The first extensive theoretical study of electromagnetic wave prop11gotion between submerged stations in seawater was reported by Moore [1951), and
mosc of t he subsequent theoretical work <;e11tered on
a sea of infi nite ex tcnL [Wail, 1952; Kraichman,
1976] or on the effects of the sea s urface in a very
deep sea [ Moore, 1951; Wair and Campbell, 1953;
H ansen, 1963; Banos, 1966 ; Fraser-Smith and Bubenik, 1976 ; 81tnnister and Dube, 1977]. These studies
indicated that if the horizontal distance between the
source and o bserver is larger tha n several skin
depths, the energy relleivcd may follow an up-overdown mode above t he surface [Moore and Blair,
196J]. T his result led to the conclusion t hat near the
sea/seabed interface, the energy received may follow
an analogous down-under-up mode in a weakly conducting seabed under cettaio conditions [Bubenik
and Fraser-Smith, 1978).
Such a mode has been investigated io a somewhat
different context by a number of researchers [Wheeler, 1960; Burrows, 1963; Mort and Biggs, 1963 ; Wait
and Spies, 1972a, b, c; King and Smith. 19SI). These
studies suggested that a waveguide may exist under
both the sea and continents a nd that i t m11y become
a usable communication lmk if o ther above-ground
communications are di ~ rupted; it would also h ave
410
!NAN ET AL: EM FIELDS GENERATED ALONG TRE SEAFLOOR
much lower noise levels. In an electrically shallow
sea, the sea-surfllcc and seabed modes may ex.ist
simultaneously. Weaver [ 1967] analyzed the fields of
electric dipoles submerged in seawater, and Ramaswamy et al. [1972) considered a subme rged horizontal magnetic dipole, both taking a sea of one skin
depth deep. Ramaswamy a lso computed the field
components when both the source and recei ver are
located at the sea/seabed interface as a function of
seawater induction number varying from O to 3. N umerical data [Bu benlk and Fraser-Smith, 1978;
Fraser-Smith and Bubentk, 1979) of the electromagnetic fields produced by a vertical magnetic
dipole submerged in a sea of :finite depth teveal the
effects of a sttongly conducting seabed. Other electromagnetic methods for obtaining seabed conductivities have been proposed [Brock-Nannestad, 1965 ;
Bannister, 1968a, b; Coggon and Morrison, 1970].
Bamiister [1968a] observed thnt the conductivity of
the seabed may be determined by measuring only the
horizontal componenl of the magnetic field produced
at the sea/seabed interface by a long horizontal line
source located at the air/sea interface. Coggon a11d
Morriso11 [1970) considered a vertical magnetic
dipole s ubmerged in seawater and analyzed the electromagnetic fields over various ranges of seawater
induction nwnbers and seabed conductivities. A
recent active-source electromagnetic sounding experiment on the oceao floor [Young and Cox, 1981) intr oduced new possibilities for studying the electrical
conductivity of the ocean crust.
This work considers an electrically deep sea and
calculates the electromagoetic fields produced b y a
long straight insulated cable when the source and
receiver are both located on the seafloor. The effects
of the sea surface are neglected because attenuation
on the paths of propagation from the cable t o the
receiver via the sea surface is larger. Both the sea and
seabed are assumed to be isotropic, homogeneous,
and time-invarianl conducting media separated by a
plane interface-the seafloor. Frequencies in the
ULF/ELF band (less than 3 kHz) are considered because only ·signals in these bands will propagate 10
ranges of interest before being significantly a ttenuated. The displacement current terms in botb media
are neglected, and this assumption is well justified in
these frcqut:ocy ranges. IL is assumed that both media
are nonmagnetic, with permeabilities equal to t he
free-space permeability (µ 0 == 41t x 10 - 1 H/ m). The
conductivity of t he seawater u. is assumed to be 4
S/ m and the conductivity of the seabed varies.
If the length of a long straight insulated cable lying
at the plane interface of two conducting media is
longer than the longest of all o ther physical dimensions, it is known as an "inlinite~ cable. There is an
alternating current 1 cos wr flowing in the cable
which is assumed to be uniformly distributed, and
this assumption is jus tified at sufficiently low frequencies [Wait, 1952; Sunde, 1968]. The cable is oriented along the x-axis, and the plane interface of the
two media is z == 0. The direction of the current is
out of the paper at t == 0. Everything is invariant in
the x-direction, as illustrnted in Figure l.
lt is assumed that all the fields varv with rime as
exp (jaic). The electric a nd the magnetic field components for the infinite cable aie calculated fro m explicit expressions and numerical integration [Wait,
1953; ltran et al., 1982). Most or 1he data arc presented in dimensionless form by measuring all distances
in terms of the skin depth of the seawater 8, defined
as
fJ, - (2jWfloC1J 1i '
where w is the angular frequ.e ncy related to frequency
/ by the relation w = 2rrf. Seabed conductivity is normalized to seawater conductivity by u' = arfu.,
where a' is the normalized seabed conductivity. The
skin depth in the seabed is related to the skin depth
in sea water by {IJ ~ u,/(11') 112, and the wavelengths
~.,11 in both media nre proportional to the skin
depths, sioce
Ji>./! ~
2n<l,o.Jl
In conducting media, field intensity varies with an
exponential term e- m (wbere d is the distance from
the source) representing 55 dB/wavelength attenuation [Hansen, 1963) , and it is lhis attenuation that
.limits the range of Ihe electromagnetic signal. Figure
2 is a logarithmic plot of skin depth, wavelength, a nd
exponential attenuation in sea water as a function of
freq uency.
The numerical resulls obtained in this work can be
used to determine effective sea-bed conductivities in
I'
I
I
r
I
I
!SEA WAT ER)
! ty. O,z )
I
/
SEA
flOO'i
O',. 1.f4o
:
£..!~ P OJ
' " 0 77T////.1~f~1~(77:>/////:,
t
CTf, '*f•l'-o
(SEA BEOI
Fig. I.
CA3lE
ln6nitc cable located al the <e.1/ 0oor interface. Note the
symmetry with m pecr 10 the x·al<is.
JNAN ET AL.: EM FIELDS GENERATED ALONG UJ.E SEAFWOR
smooth regions of the seafiooc. Stretches of the abyssal plain in the western North Atlantic have been
measured to be smooth within 2 m over distances of
100 km [Pickard and Emery, 1982]. It is also assumed that the seawater shields the seafloor from
atmospheric noise and, because the region of interest
is far from the shore, the possibility of atmospheric
and power-line noise propagating through the earth's
crust can be neglected. This is important because atmospheric noise is especially strong in the ULF/ ELF
frequency ranges [Liebermann, 1962; Soderberg,
1969]. The only other likely source of noise is the
interna l noise of the receiver; the o ther natural electromagnetic sources of noise will not be as significant
[Chave and Cox, 1982].
2.
FIELD COMPONENTS
Following Wait's [1961] work, the field components produced by an infinite cable lying along the
x-axis can be written
l"' .-.,,
Ii"'"
-jwµ 0 I
- -
E,,, = -
-µ-0a,,, = tr
0
0
B,,, = -µ - I
u$ +
-
cos (.ly) dJ.
" cos (J.y) di.
- ·e-'·
-u.1 + u1
- --
o
uJ +u1
.le' '•'
(1)
"f
l""
1f
with B,.,. - E,,,
- -
o
tr
sin (~y) dJ.
(2)
0
u.s
2
1ta S
Ef,. = - ' -' E,,, ~ - Jim j2
(
··-·
r} = jwµorr1
./i.ttf>,
.
Br,• = - B,. = Jim .fi.
11 1
,,_
0
0
10
102
Fig. 2. Skin dep th. wavelensth, and exponential attenuation
in seawater with a cooducti>ity of·4 S/m (bas..'<! on Figure A.3 by
Krnl chman (19 76)).
0
u, + u,
i"'
u' a' --"""
- cos (.l'y') d).'
u~
+
i"' - -
uJ
(5)
i,'e" •I •' '
u; +it1
0
(4)
,
~m ().'y')
a.r
(6)
where
u; = ./x 2 + j2,
and z' = z/o,, y' = yjo,, A.' = .lo., and o" = a1 /a, .
When the receiver is located at the interface z = 0,
two of the field components cao be expressed in an
explicit form derived by W ait [1953, 1962] as
}Wl'of
'J
nyr2 - v, Y2
E, ,., = (
1
B.,, = ( /" 2)
3
[1,,yK,{·1',,V) - Y1 YK1(Y I y)]
[2y,yK,(y,y)
(7)
+ YtY 2 Ko(Y,Y)
- 211Y K 1(V1Y) - ~Jy 2 Kh1Y)]
(8)
where K 0 and K, are the modified Bessel functions
of the second kind oi order zero and one with complex arguments. The horizontal component of the
magnetic field B,,, does not have an explicit expression. When w = 0, both E,.• a nd B,,1 become
zero and the vertical magnetic field component simplifies to
3.
FKEOUENCV ( H r i
i-oo -,--,
e -"1 ''
cos (A'y') d.l.'
.fi."h
BP = - ' B . = - lim .fi.
q•
J.J.c I
s.J
:--o
(3)
= E.., = 0, and where
y; " 1 = J).>+ yJ
'Y: = jcaµ
These expressions can also be written in the dimensionless form
"(J-y,y
u, =- .jJ..2 +
411
NUMERICAL RESULTS
This section presents the nwnerical data for t he
electric and magnetic field components at the interface of t he two conducting media. Two of these components E,... and B,.= have explicit expressions (equations (7) und (8)) that can be expressed in terms of
Kelvin functions [Young and Kirk, 1964] and their
derivatives. After some algebraic manipulations, their
amplitudes can be written in dimensionless form as
E'
I ,_. I
=
· [(c 1
M,o: IE,,..I = -(I--R')<x,
2_ _
1
-
Rc,) 1
+ (d 1 -
Rd,)1 ] 111
(9)
412
lNAN ET Al..: E).I F1ELOS GENERATED ALONG THE SEAFLOOR
and
B•
written as
I ,,,I
~ ,/2rr5, B
R
I ... I
µo l
,_ 1·-·· ;:
2_ _
(l _ R,)a}
_
_
-.- , sin (l'y') c/J.'
Bf.,= , /2
0
· [(t:x,(a, - 1<
2
ll 2) -
2(d1
+ («,(b 1 - R 2b,) + 2(c1 -
-
Rd2 ))2
Rc2)>1)'12
(10)
where
ktr 0 ~
a 2 * k~r0 21
b, - kli0 -i,
b, = kci0 ot 1
a,
as
c, • ker'0 a,
c~ - k~r'o «i
d,~kcf0 «,
d 2 "'kel0«1
"-1 ~Re;,,
..f2y•
R' ,. a' - <11/<r,
where a, and u.1 arc defined as the induction numbers
in the seawater and seabed Cdpeelively [Coggo" and
Morrison, 1970). The above expressions for the horirontal electric field component and 1be vertical magnetic field component can be calculaled numerically
by using tables or Kelvin functions and thei r derivatives [Lowell, 1959].
The o ther nonzero component at the interface is
the horizontal magnetic field component B..,. and it
can be computed only by numerical integration. The
expression for it (equation {5)) can be divided into
two parts.
B~, -
-,/2
f'- ' ~cos (l 'y') dl'
Jo u, + ll'r
u' e- •; r
Jim ../2
-'-,- cos (l'y') dJ..'
.. - o
..... u, + r1,
i
»
-
Two factors must be determined for nu01erical in tegration. T he first is .t;..,. It is assumed that the effective conductivity of the seafloor is smaller than
that of seawater (<1' < I). The value for A;... is chosen
such lha1 ~ » 2 aod, if this constraint is satisfied,
both 11~ and 111 can be approximated as
u'r
=).'
for .!' > ;.:,,..,.. Based on this approximation, the
second integral above can be replaced by 1111 explicit
·
term yielding
Bf, - - y r..L
l'-'
u'
-.-'-cos
(l'y') dl'
0
"·
+ u',
+ sin (l'~ y')
+ cos (l'
.._,y')
../2i
(12)
The above inl~1'fand s can be separated into their real
and imaginary parts and be numerically integrated as
real integrals. The data for the field components can
then be obtained by recombining these terms according to (I I) and (12). The second factor is the method
of integration. Both integrands arc welJ-bebaved
fun~tion.~ cx~ept for the cosine or sine term that may
osc1llntc rapidly at greater distances than the skin
depth of t he seawater [Hermance and l'elller, 1970].
Two techniques of numerical integration, Wedd!e's
rule [Computcntor1 Laboratory of Harvar·d University,
1949) and Filon's method [Tranter, 1956) were used;
and
:x, •
u.• + u,
(II)
.,/2y'
Similarly the integral expression for the vertical component of the magnetic field (equation (6)) can be
by selecting the in tegrat ion in terval small enough.
both produce sufficiently accurate results.
The computat.ions can be verified in several ways.
The first one is to compare the results obtained by
the two different numerical integration techniques.
The second is to compare the results obtained for B.,
through numerical integration using (l 2) to the res ults obtained for the same component using ( 10) and
tables of Kelvin functions. T he third is to check the
results by using the a pproximate expressions for the
lower and higher frequency ranges.
The first panels in F igures 3, 4, 5, and Figure 6
show the va.riations in the parametric amplitudes of
the three nonzero field components
arui
~:_. and the total magnetic field Bh with the induction number of seawater a,. Note that the paramelric
terms nu, 6;/ 1 and 2 ' 12rr.fJ./ µ 0 I appearing on the lefth and side depend on frequency f and not on receiver
distance y. T hese curves can be used for any frequency in the valid frequency range. The horizon1al
axis indicates the perpendicular distance of the
receiver from 1he axis of the cable along the seaftoor
in terms of skin depths of seawater. &!cb curve corre·
sponds to o different value of R (R - (u1/uJ1: 1 ); R
takes the values of 0.01, 0.03, 0. l , 0.3, and I except for
the B:,, component which is zero when R = I {oo
seaftoor). Bo th axes arc plotted on a logarithmic
scale.
The second panels in Figures 3 and 5 show the
variations of the amplitude ratio of E,.• and JJ,,, pro·
duced on the seafloor to those produced in a sea of
infinite depth as a fu nction of distance. T he second
panel in Figure 4 plots the variat.ion of tbe ratio of
the amplitude of B,., to the amplitude of B,,. as a
function of distance.
In F igurcs 7 and 8. the real amplitudes or the field
E:.•• B:.,.,
'S!
-
-111•1.
--- ·-·· A• O.l
....... A • 0.1
- - R • ll . OS
"5!-
-
~
·- " - 0 .01
-~
·:\
':"S'!
".\
~~
\.~\
".
--;;
ri
il
'·•.
'$!
-~
\ \..~~~~\
~
~~
\
"l?
\
\\\\
\\
'
\
!s-
10-·
1cf
10
"·
01,
Fig. 3. Variations in the amplitude of the elecuic field produced on the seafioor by ttn infinite cable and
variation of the ratio curves illustrating the changes in the tolaJ electric field in the case of au cl.ectrica.lly condllcting:
scah«i as a function of dis.tance. J.!ach curve corresponds to a dliferent scabc:d conductivity. The curves in the
second panel show the ratio of 1hc amplitudes of th.e electric field at the seafioor interface to the elcclric field in an
infinitely deep sea.
~
-
- R • I,
·-- · ·-- " .. 0.1
.............. 111. -
0. 1
- - R • O.CS
_
"S!
._111. .. o.c1
':'~·
~
~j~
~ :t
'1'2
~
~
'~
~
~
Fig. 4. Variation in the amplitude of the borir.ontal component of the magnetic ii.cld produced on lht: seafloor
by a n infinite cable and ••riation or the ratio of the amplitudes of the horizontal component to 111< vertical
component of the magnetic field , both produced on the seafl.oor by an infiuite cable in lhe ca.se of an elec...-ttically
conducting seabed. Each curve is n function of distance a nd corresponds to a different seabed conducti•ity.
INAN ET AL..: EM FIELDS GENERATED ALONG THE SEAFLOOR
414
·e
- - A • 1.
·--· · ·· f\ - O. t
•••"•··-··· Fl .. 0 . 1
- - _ i. - a.OJ
- -·-111 - 0.0 1
~
~
'S!
ii-
i.:;.
~ 'g
'e
'tg
"li,cr'
Ir/
1<1'
...
...
Fig. S. Variotion of the amplitude of the vertical component or the magnetic field produced on the scalloor by
an infinite cable 1.nd vllriatlon or the ratio ilhlS!cating the chAnges in the vertical component of the field in the cue
or an electrically conducting seabed as a function or distanet. Each curve corresponds 10 a different seabed
conductivity. Th• cu1v0$ in the second panel show the ratio of the amplitude< of the vertical component or the
magne1ic field prod uced on the $Cafloor to the .amc compo nent in nn inflnitoly deep sea.
- - ""' 0.1
'·
• •••• • • R ..
.... ..... . ,., ,. .. 0, 1
- - R • 4.01
-
'\
-;:-
~
~11
· - " '"' 110 1
:\~
.......
[13)
\\'\
'g
\\ \ \\\
~
\
\
2ity
IB•r.t>..J:.n;I -Jlo-I IB• AY.•.11 I
\\
'
\
\
\\ \ \\\
;
,.,,
components E,.x, B,,,, B,.• and the total magnetic
field B,,r arc plotted vs distance for an alternating
current sow ce with an amplitude of 1000 A and a
frequency of 1 Hz for the above seafl.o or conductivities. The units of the electric and magnetic fields
are milivolts/meter and picotesla, and distance is in
meters.
The above results can be plotted in another parametric form in which the amplitude of the field components is written as
10'
'
(14)
Here, the terms on the left-hand side are nol functions of frequency but, instead, are functions of
receiver distance y. Figures 9 and 10 plot the variations of the field components in (t3) and (! 4), and
Fig. 6. Variat ion with distance of the amplitude of the total
magneiic field produced on 1hc scafloor by an infinit< cable. Bach
curve corresponds to a dilfercnt !C&bed cunductlvity.
!NAN ET AL.: EM FIELDS GENERATED ALONG THE SEAF'LOOR
__ ,..,,
415
~
.. .. _____ 1111;. Cl.3
.............. 1\ ~ O.t
1:!
- - f t • O.D,
.-ll't .. O,tJ1
<;l
'"2
Ol
'Si!0"'
1l
g
'\: .
~
E!l
""0
~
~
'\:.
~
'\:
~
.;?
0
~
\
11·.
~.
\\
\\
~
~\?
i<J
DISTANCE (METER)
io'
DISTANCE(METER)
Fig. 7. Va.riatioru in the amplitudes of the horizontal and vertical components of the magnetic field produced
on the scafioor by •n infinite cable earr;ing an al ternating current with an amplitude of JOOO A and a frequency of
l Hz: as a function of distance. Each c.-urvc corresponds. to a different seabed conductivity.
the horizontal axis shows the variation in frequency.
Note, once again, that each curve corresponds to a
different seabed conductivity and there is no horizont<il magnetic fie ld component for R = 1.
4.
DISCUSSION
All three field components produced at the i nterface can propagate farther when a seafloor is present
than can those produced in the absence of a seafloor
because of the assumed lower conductivity of the
seabed. The increase in range be<.-omes significant at
greater distances. For example, when f = 1 Hz, the
ampJjtude of the horizontal component of the electric
field E,,x becomes 1 nV/ m at a distance of y"" 3 km
for a' ~ 1 (infinitely deep sea), y"" JS km fm a'=
w - i, and y "" 90 km for a'~ io-... At 90 km, the
source cable must be much longer for it to be a n
infinite cable; for example, if it is 10 times longer (900
km), a uniform current distribution is still a good
assumption at 1 Hz [/nan et al., 1983].
The horizontal component of the magnetic field
B,,,,. is negligible when compared to the vertical component B"' near the cable; however, it becomes comparable to and la;ger than B.,, at greater receiver
distances (Figure 4). For example, if I = 1000 A,
f
= 1 Hz, and u' = 0.01, the amplitudes of the horizontal and vertical magnetic field components would
be I B,,, I o:: 0.70 x 106 pT and I B,,, J ""0.20 x io6 pT
at 10 m, 0.57 x 10 6 and 0.19 x 107 pT at 100 m, and
0.68 x 10' and 0.30 x 10' pT at l km. The amplitude of B,,, is also more sensitive to the conductivity
of the seabed than are the amplitudes of the other
two field components E,,,, and B,,,.
The horizontal component of the magnetic field
and the electric field are zero when (JJ = 0. They also
have optimal frequencies as observed in Figure 9 ; for
example, at a distance of I km, the electric field has
an optimal frequenC)' of approximately 0.15 Hz in an
infinitely deep sea [I nan ec al., J983].
S. APPLICATIONS
The numerical r esults obtained in this work could
be useful in the area of undersea communication. The
range of communication with submersibles in the
deep parts of the ocean is limited because of tM high
conductivity of the ~eawater. The seabed has an effective conductivity smaller than that of seawater
and, as a result, it may provide a new palh for the
signals along which there will be less atrenua.tion
compared to a signal propagating directly through
416
!NAN ET AL.: EM F1ELDS GENERATED ALONG TFm SJ!AFLOOR
'I!
<...
.,
-~
"'f<
1=!
"
~
'I!
0
~
<.:
~
0
t=:
~
0
~
~
~
"
'I!
-~
'I!
.-.,
DISTANCE(MBTE8)
DISTANCE (METER)
Fig. 8. V•riatiollJ io the amphtud.. or the toial cl«:tric and magnetic fields produced on the ~oor by &n
lnllnlte cable carrying an alternating current with an amplitude or 1000 A and a frequency of l Hz as a fun~io• of
disuonc•. Each Ol!V• corresponds to u different seabed conductivity.
seawater; longer ranges can be achieved before the
signaJ becomes weal: and cannot be detected because
of extcnial and internal receiver noise. The seabed is
also a conducting medium and the exponential at·
ten uatioo of electromagnetic signals propagating
through rhc seabed is still significantly large at high
frequencies; therefore, operating frequencie s must be
low enough to reach long ranges. This limits the
bandwidth, and information cannot be transferred at
a high dnla rate.
New components at the seaftoor interface will increase tile ranges of communication.. For an infinite
cable carrying an alternating current of 1000 A at 1
Hz and assuming the minimum measurable magnetic
field to be OJ pT, the field on the seaOoor cao be
detected over a range of approximately 4 km before
its amplitude drops below O. l p T. The amplitudes of
the new horizontal component and the vertical component of the magnetic field along the interface are
0.24 and 0.09 pT at a receiver distance of 8 km for an
effective seabed conductivity of 0.4 S/ ro, and the total
magnetic field of 0.26 pT. If the seabed conductivity
is 0.04 S/ m, the two field components are 0.27 and
0.03 pT at a receiver distance of 20 km, and the total
magnetic field becomes 0.27 pT as a result of tbis
new component. These t wo components are abour
0.39 x l 0 3 and 0.22 x 102 pT at 20 Ian for a seabed
conductivity of 0.004 S/ m. These examples indicate
that Lbe range of electromagnetic fields along the sea·
floor increases significantly before their amplitudes
drop below the minimum measurable field value.
Arrays of long cables located on the seaftoor can
achieve longer communication ranges [Inan et al.,
1982]. The phases of the currents in each cable can
be adjusted to produce a maximum field amplitude
a t the receiver, which makes comm unication possible
over a much larger area. The separation distance of
the cables depends on the current amplitudes, fr1>
quency, conductivity of the seabed, sensitivity of IM
receiver, and background noise. With a series array
of cables, each carrying an alternating cunent of am·
plitude 1000 A and frequency I Hz and separated
from each other by 30 skin depths, the magnetic licld
produced al a point midway between the two cab!~
would be approximately 4 x 10 2 /{J, or 1.6 pT in an
infinitely deep sea; on a seabed with "i "' 0.04 S/m,
this field would be 4.6 x 103 pT. The results indicate
that the cables moved apan from a spacing of 3(]{>, to
1400, would yield th.c same field produced in an infinitely deep sea at that point. Large amounts of re-
! NAN ET AL: l!M FlELDS GENERATED ALONG THE SEAFLOOR
417
__.. ,
..... . . . " . 0.J
"~·-~···· · "' .. 0.1
- - - 11: .. 0.03
-
/
~~':,~\\
"!!
"""
...
~1~
-1'\ • G.0 1
":~
\
\
\
>I-11./;~\
'
\ \\
\
'
\
\ '.
\
I
I
\ \
\
'.,
I
\
~S?
\
\
1
1
\
- i~
,,----T'rf----r
'rf..l....-.;...._,.t'rf-'-...-~--./l'rf
1
'\\
\ \ \
\ \ ' \
\ \ \ .,
\
\ \ \ \
\
10
~.
\ \
I
~o
\
\ \ \\
"·
\ \\
\
1
10'
o,
o,
Fig. 9. Vari ationt in the amplitudes of the electric field and horizontal component of lhe magneUc field produced on U1e &eaftoor by an
infinite cabJc carryinp an alternate current as a runction of frequency. Each curve corresponds to a different seabed conductivity.
__,..,,
~
·g
. ....... " .. 0.J
....· - ··-· " '" 0 .1
- - - " "' O.ctl
-
·- " '"a.or
·g
~\\
rJ
=-1~
~
h
\
'i
N
';'!:?
~1!
\
\\,
\\
\ \\
~
'9
..
...~,
~
10•
VJ
...
1d
\
'
1'rf
'9
1~·
"'•
F ig. 10. Varintions in the amplitudes of the vertical compooail of the magnetic field and the tot•l magnetic field pcodua:d on the
se a.floor by ao infinj rc cable C3rrying an aJterualc current as a function of frequency. Each curve oormponds to a djfTcrcnt seabed
co n ductivity.
418
l"lAN ET AL.: EM FIELDS GENERATED ALONG THE SEAFLOOR
SEI.
WATE~
SEA - - . . ,
• LOOR
\
fig. 11. Otiomc:try for a seabed containing two conducting
layers.
sistive power will be lost, however, as tbe source current ftows io both the long cables and surrounding
conducting media. The advantage of this system is a
less noisy environment in which t he electromagnetic
signals propagate, because atmospheric noise at these
low frequencies will be shielded by the large de pth of
seawater [Mott and Biggs, 1963].
6.
RF.COMM b"NDATIONS
Throughout this investigation, it has been assumed
that the seabed is a homogenous medium; however,
it often contains layers of sediment with different
properties. This work could be extended to two or
more layers. For example. in the t wo-layer bed in
F igure 11, the first layer has a conductivity of <T1 ,
and extends from z = 0 to z = - h and the second
has a conductivity of q f l and extends from z = -Jr
to z = - co. Both the source and receiver arc located
at the sea/seabed interface. The conductivity of the
upper layer is in general larger than that of the lower
layer. For receiver dis tances smaller than the depth
of the first layer, the effects of the low-conductivity
layer should not be very significant. As receiver distances become larger titan the depth of the first layer,
however, the signal that follows the down-under-up
mode will be much stronger than the signal that directly propagates from the source to the receiver
using the sea/seabed boundary, a nd the lower layer
will be im portant. This means tha t, depending on the
location of the observer, the signal at the receiver will
carry information about the pro perties of dillerent
layers of the seabed.
The length of the straight cable was assumed to be
infinite. This is a good assumption for a receiver located in the vicinity of the cable (where the perpendicular distance to the receiver is much smaller than
the actual length of the straight cable) and not close
to the ends of the cable. A uniform current distribution along the cable was also assumed. Although
this is not true in an iufinite cable, the fiel ds produced at the receiver will be the result of the middle
portion of the cable because the contribution from
the portions toward the ends (not necessarily carrying the same cu.rrcnt) will be negligible. As the receiver distance increases, however, a longer portion of
the cable must be considered and the uniformcurrent assumption may no longer be valid. O ne extension of this work wou ld be to calculate the distribution of the current along a long straight insulated
cable located at the ~eafioor interface.
In practice, it may not be possible to locate the
receiver precisely at the interface. Another extension
would be to place the receive< some dist.a nce above
the sea/seabed interface and then calculate the fields
in this configuration. The integ rals for the field expressions will then require an additional term e-•,,
representing t he exponential attenuation as the signal
is propagating the vertical distance between the
source and receiver in the seawater. As a result, th~
fields produced at some vertical distance above the
seatloor wiU generally be smaller in amplitude than
the fields produced on the scatloor.
In concluding, we s hould comment on the dispersion that is likely to be involved in the propagation
of ULF/ ELF fields along the seafloor. Because of
their conductivity, both the sea and seabed are dispersive and there will therefore be a limit on the
achievable transmission bandwidth (i.e., on the
amount of information that can be transmitted). lo
illustrate, let us consider a carrier frequency of 100
Hz modulated at 1 H z, 10 Hz, and 100 Hz (i.e., with
1%, 10%, and !00% bandwidths). We will assume,
for simplicity, that the amplitudes of all t he frequency
components that fall into t his frequency bnnd arc
equal and attenuated at the same rate. The phase
difference between the two extreme frequency components (the upper a nd the lower sidebands) propagating through seawater becomes 180° at distances of
15.8 km, 1.58 km, and 152.7 m , respectively. If the
carrier frequency is I kHz with the same percent
bandwidths, the phase difference becomes 180° at distances of 5 km, 500 m, and 48.3 m, respectively.
These results show that the transmission range must
be reduced as the bandwidth is made larger if the
effects of dispenion are to be minimized. Another
related conclusion fo llows irnm.ediately from the f l''
dependence of phase velocit y on frequency: if the
carrier freque ncy is decreased the bandwidth also
mus t be reduced if an increase of dispersion is to be
avoided. Finally, propagation through the seabed has
a decided advantage over propagatio n through the
sea from the point of view of reduced dispersion as
well as increased range. Once again taking an illus-
!NAJS ET AL.: EM FIELDS GENERATED ALONG THE SEAFLOOR
trative example, suppose the seabed conductivity is
0.04 S/m and we apply the conditions in the example
above to pro pagation through the seabed instead of
the sea. In the seabed the ranges are all ten times
greater than those in seawater.
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