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University of Portland Pilot Scholars Engineering Faculty Publications and Presentations Shiley School of Engineering 5-1986 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. Follow this and additional works at: http://pilotscholars.up.edu/egr_facpubs Part of the Electromagnetics and Photonics Commons Citation: Pilot Scholars Version (Modified MLA Style) 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. http://pilotscholars.up.edu/egr_facpubs/3 This Journal Article is brought to you for free and open access by the Shiley School of Engineering at Pilot Scholars. It has been accepted for inclusion in Engineering Faculty Publications and Presentations by an authorized administrator of Pilot Scholars. For more information, please contact [email protected]. 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. 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