Laboratories, Stanford University ... MI CUPI1 Y CLASSIVI-CATION Oft THIS PA. ..... (1 -ITM)/(. 1 P- ITM~lTM). I(Y. -2Yd. r1TM. 1 Y0)/(Yj + Y0)) e. K1TM. L~v.1 -.
STANFORD UNIECROISIY STANFORDCATO9430
SCOMPENDIUM OF THE ULF/ELF ELECTROMAGNETIC 00
by
A. C. Fraser-SmithI D. M. Bubenik
Technical Report E71 5-1
January 1980
Sponsored by The Office of NavalI Research through Contract No. N0001I4-77-C.0292 Task Area NR 089-121
I
h ocumont an for public rol.,.*a~
W.A
I
T
44
I
Reproduction in whole or in part i': permitted for any purpose of the U.S. Government.
The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Office of Naval Research or the U.S. Government.
I.•
4-1
',
.....
UNCLASSIFIED___________________ 51'CURITIY
OF THIS PAGE fWihen Date Entered)
Ct.AFSIFICATInN
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DCUMNTATON AGEBEFORE 1..2, GOVT ACCESSION NO.
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Tech. Report No. E715-1 4.TTE(ln
tlitts
LTYPE
RPOT'
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nccnicat Jul.&78-3,fJundW79 06 u
Compendium of the ULF/ELF Electromagnetic Fields Generated above a Sea of Finite Depth by Submerged Harmonic Dipoles
SEL 79-025
7ýAUTHOR~)
A. L./Fraser-Smith Z.M/uel
Aý,~~j
N#014-77-C-#292"'9
0.PEFOMIOOAA~ZAIN NAME AND AODDRESS1
Radioscience Labora tory, Stanford El ectronics " Laboratories, Stanford University Stanford. California 94305
AREA
Task Area NR 089-121
800 North Quincy Street Arlington, Virginia 22217 14. MONITORING AGENCY NAME &AOORE5SS(It
EEMNT, LOAM PROJECT, TASK LINr? NUMBERS
& wORMK
UCASFE
diff. hroni Controlling Office)
1S. OCLABBIFIC:ATIONYDOWNGRAt)INQ
.
Approved for public release; distribution unlimited. 10~.flISTAIpLTION StATr.MENT
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NOTES
11) I'I. Y WURDS-(Clntnu ini tareprta sidi
if noeess'ry aridIdentify hy bulock mriifi.rnb)
ULF/ELF Electromagnetic Fields VMD, VED, HED, HMD Submerged Dipoles Undersea/Air Communication Seafl oar tii
ABIIMI tAC I ICumiti'~
ti
loiol 't',
til,' if nPrommury Andl d10111t1Vfly Wr iork ritanrthall
,.I*- thi s report iwr ex tend$ earl ier computat ions of the ampl itudes of the quasi-static electromagnetic fields produced on and above the surface of a sea of finite depth by a submerged vertically directed harmonic magnetic dipole (VMD) to other dipoles. Specifically, .4'inow presentitiddta for the fields produced by a submerged vertically directed harmonic electric dipole (E)and by submergind horizontailly directed magnetic and electric dipoles
DDI
JAN
31473
EDITION OF 1 NOV 65 IS OEISOI.ETE
UNCLAS5IFIEDMI CUPI1 Y CLASSIVI-CATION
Oft THIS PA.LtnvI
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UNCLASSIFIED S•LJMITY 19
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CLASSIFICATION Of
KEI Y W(.)
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_
_
_
THIS PAGE (When OQta Fniered)
l
20 ABSTRACT (Continved)
l
mm
|iiiii
S~(HMD
and HED, respectively). The primary purpose of these computations is to determine the conditions under which an electrically conducting seafloor can produce significant changes in the fields, as compared with the fields • ~~produced on and above an infinitely deep sea fr frequenciesq n.otLLbj!/,JF bands (frequencies less then 3 kfz}. As in •a•earlter work,rl f I-f'-Bt '.even' Itcomparatively highly conducting seafloor (conductivity ofSQ,4.4s/m•) ?• ~can produce substantial changes in the field amplitudes for some source""-- . •:." ~receiver configurations, and, in the case of the horizontal dipoles (as ,/ •,• ~previously found for the VMD), alterations of two orders of magnitude or Smore can occur In the amplitudes on the sea surfa~ce for smaller values of •' ~ý5 w.,y•-.?e VED fields are more strongly affected byea seafloor, and some field • $-•q• -quah•Nites can be changed by over four orders of magnitude for of,_< 0.04 S/m. Reviewilhg the dipole field data as a whole, it appears that the vertical electric component produced by the HED in the plane of the dipole (0 • 0*)
• • • ••,..:i
This component. Is comparatively large, varies at large dlstancus as the inverse square of the distance, and tends to be enhanced by the presence of a seafloor. Finally, despite many differences In the fields and in the seafloor effects, we find that our previously derived criteria for estimating ' I when a seafloor effect is likely to occur for a VMD source are valid for all dipole sources. Thus, the largest seafloor induced changes occur when the...•i dipole is within I seawater skin depth (6) of the seafloor, and there is.... S~essentially no ýeafloor effect when the dipoles are more than 36 above the flDoor. deerin
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SEL 79-025
COMPENDIUM OF THE ULF/ELF ELECTROMAGNETIC FIELDS GENERATED ABOVE A SEA OF FINITE DEPTH BY SUBMERGED HARMONIC DIPOLES by
A. C. Fraser-Smith D. M. Bubenlk*
'i ,
Technical Report E715-1
January 1980
Sponsored by The Office of Naval Research through Contract No. N00014.77-C-0292
national,
address: S*Present Electromagnetic Sciences Laboratory, SRI Inter-
Menlo Park, California 94025.
I,-
-`W
ACKNOWLEDGEMENTS We wish to thank Oswald G. Villard, Jr., for many stimulating discussions and encouragement during the course of this work. We would also like to thank Sidney G. Reid, Jr., and R. Gracen Joiner of the Office of Naval Research for helpful discussions and for making the work possible. The invaluable assistance provided by Paula Renfro in tne preparation of the report is gratefully acknowledged. A preliminary presentation of some of the material in this report
T..
was made at the Workshop on Ocean Floor Electromagnetics held at the Naval Postgraduate School, Monterey, California, August 20-22, 1979. SuLpport for the work was provided by the Office of Naval Research through Contract No. N00014-77-C-0292.
I
I -
"i
-
l
-i
ABSTRACT In this report we extend earlier computations of the 6nplitudes of the quasi-static electromagnetic fieldc produted on and above the surface of a sea of finite depth by a submerged vertically directed harmonic magnetic dipole (VMD) to other dipoles. Specifically, we now present data for the fields produced by a submerged vertically directed harmonic electric dipole (VED) and by submerged horizontally directed mangetic and electric dipoles (HMD and HED, respectively), The primary purpose of these computations is to determine the conditions under which an electrically conducting seafloor can produce significant changes in the fields, as compared with the fields produced on and above an infinitely deep sea, for frequencies in the ULF/ELF bands (frequencies less than 3 kHz). As in our earlier work, we find that even a comparatively highly conducting seafloor (conductivity af 0.4 S/m) can produce substantial changes in the field amplitudes for some source-receiver configurations, and, in the case of the horizontal dipoles (as previously -
found for the VMD), alterations of two orders of magnitude or more can occur in the amplitudes on the sea surface for smaller values of Of. The VED fields are more strongly affected by a seafloor, and some field quantities can be changed by over four orders of magnitude for of < 0.04 S/m. Reviewing the dipole field data as a whole, it appears that the vertical electric component produced by th HED in the plane of the dipole (• =0) should be the most useful for undersea-to-air communication at large distances. This component is comparatively large, varies at large distances as the inverse square of the distance, and tends to be enhanced by the presence of a seafloor. Finally, despite many differences in the fields and in the seafloor effects, we find that our previously derived criteria for estimating when a seafloor effect is likely to occur for a VMD source are valid for all dipole sources. Thus, the largest seafloor induced changes occur when the dipole is within 1 seawater skin depth (S) of the seafloor, and there is essentially no seafloor effect when the dipoles are more than 36 above the floor.
v
.
TABLE OF CONTENTS Page . ......... . . .. .. .. .. .. ....... 1. INTRODUCTION........
-~
11. III.
METHOD OF CALCULATION...........
. .. .. .. .. .. .........
RESULTS. .. .. .......... ............ ............ ..... 13
IV. DISCUSSION. .. .... .............. ............ ......... 15 ............ ......... 21 V. REFERENCES. .. ...... ............ FIGURES FOR THE VERTICAL ELECTRIC DIPOLE..........
IFIGURES
FOR THE HORIZONTAL ELECTRIC DIPOLE, 0
00.
................
23
39
FIGURES FOR THE HORIZONTAL ELECTRIC DIPOLE,
900... .. .. ..... 55
FIGURES FOR THE HORIZONTAL MAGNETIC DIPOLE,
0.. .. ......... 71 0*
FIGURES FOR THE HORIZONTAL MAGNETIC DIPOLE, (p 90c .. .. ..........87
vii
17
-
I
I,
Note:
In this report we use the abbreviation ULF (ultralow-frequencies) for frequencies less than 5 Hz. Pc 1 geomagnetic pulsations are observed in the upper part of this frequency range (0.2 to 5 Hz). ELF (extremely-low-frequencies)
is used to designate
frequencies in the range 5 Hz to 3 kHz, and VLF (very-low-frequencies)
is used for frequencies in
the range 3 to 30 kHz,
- r ." Viii
p9.Aw
I.
INTRODUCTION
In a recent paper [Fraser-Smith and Bubenik,
1979] we described the
ULF/ELF electromagnetic fields generated on and above the surface of a sea of finite depth by a submerged vertically directed harmonic magnetic dipole (VMD).
By comparing the field amplitudes produced in the presence
of a seafloor with those produced when no seafloor was present (i.e., an infinitely deep sea),
.
for
we showed that a seafloor could produce substan-
tial changes in the fields for certain source-receiver configurations. Further, our computations showed that these changes did not require a seafloor with an exceptionally low electrical conductivity: changes of up to an order of magnitude occurred in some field amplitudes when a seafloor was introduced with a conductivity (of) only one tenth of the In addition to conductivity of seawater (a ; where as E 4 Siemen/m). drawing attention to the existence of these potentially large seafloor effects,
the primary purpose of our paper was to present quantitative
data on the changes produced by a seafloor and to introduce criteria for estimating when spafloor effects were most likely to occur.
Sum-
marizing these criteria, we found that the seafloor effects were most
Smarked
in seas that were electrically shallow, i.e., for seas that were less than a few seawater skin depths (6) deep. More quantitatively, we found that the largest changes in the fields were produced when the VMD was within 16 of the seafloor, and there was essentially no seafloor effect when the VMD was more than 36 above the floor.
"Another purpose of the paper was to point out that seafloor effects would probably be important, or at least significant, at most sea locations if measurements were made at frequencies in the ULF range (frequencies less than 5 Hz).
This conclusion follows from the criteria
described above and from consideration of representative seawater skin In particular, because the skin depth at 0.01 Hz is depths (Table 1). nearly 2.5 km, a seafloor as deep as 7 km can produce perceptible changes in the electromagnetic fields produced on and above the surface by a submerged VMD operating at 0.01 Hz (or at lower frequencies). only very little of the world's seafloor area is located at depths
Since
I!I
II Table 1. Representative Skin Depths (for as a 4.0 S/m)
•
•
Frequency (Hz)
Skin depth (M)
100
25.2
1
251.6
80
28.1
0.8
281.3
60
32.5
0.6
324.9
40
39.8
0.4
397.9
56.3
0.2
562.7
10
79.6
0.1
795.8
8
89.0
0.08
889.7
6
102.7
0.06
1027.3
4
125.8
0.04
1258.2
2
177.9
0.02
1779.4
1
251.6
0.01
2516.5
S20
S.1 !
I,.
Frequency (Hz)
Skin depth (M)
'U
km, and then only in narrow trenches, the seas everygreater thin 7 where can be considered to be electrically shallow for electromagnetic signals with frequencies less than 0.01 Hz. The results we have just described could have application in geophysical prospecting or in the detection of wrecks on the seafloor, as noted by Fraser-Smith and Bubenik [1979]. Another possible geophysical application is in the derivation of effective seafloor electrical conductivities: a calibrated dipole source could be submerged at a known
,•,would !r: R
.Brock-Nannestad,
depth and its electromagnetic field measured on or above the surface; comparison of the measured fields with the theoretically computed values give the effective seafloor conductivity. (Other electromagnetic methods for obtaining seafloor conductivities have been suggested by 1965; Bannister, 1968; and Coggon and Morrison, 1970.) Specific Navy applications include submarine detection and undersea-toair communication. Because of these many possible applications, we have now extended the work of Fraser-Smith and Bubenik £1979] on the VMD to the remaining three major dipole categories: the horizontal magnetic dipole (HMD) and vertical and horizontal electric dipoles (VED and HED, respectively). To insure the general application of the new data, we have computed the amplitudes of all the relevant electric and magnetic field components for each dipole. Also, in the case of the horizontal dipoles (where the fields have an azimuthal variation), our field tomputations cover the two principal azimuthal angles 00 and 90 90. The primary purpose of this report is to present these new field data. As in our earlier work, we have used a parametric approach by measuring all distances in units of the seawater skin depth 6, where :(2/,,oli 0 s)I/12
:i.
,
Sl2(1)
and w --2'rf, where f is the frequency, and l0 is the permeability of free space (4-m x lO- H/m). The seafloor conductivities are normalized to the conductivity of seawater. It is not difficult to convert the parametric field data into the actual electric and magnetic field amplitudes. To assist in this conversion, and in the Interpretation
4
3
4
of the data, representative skin depths for seawater (we assume as 4.0 Sienien/m, where the unit Siemen/m is identical to the older mho/m unit of conductivity) are listed in Table I. We assume that both the sea and the seafloor are nonmagnetic, i.e., that their permaabilities are the same as the permeability of free space. It seems clear that the ULF/ELF electromagnetic fields of submerged harmonic dipoles are influenced predominantly in practice by the electrical conductivities of the sea and seafloor, as described in this report, and that the effects of a magnetic seafloor can generally be neglected. However, studies of the electromagnetic properties of the at ULF/ELF frequencies are in their infancy, and there may be special circumstances in the future where a knowledge of the effects produced by a weakly magnetic (or even strongly magnetic) seafloor would be of interest. Our field data provide no information about these effects, but the field equations presented in the following section can be simply modified to include permeabilities differing from 10" (The equation for Zn is changed to Zn s wiPn/Yn, and the =
Sseaflonr *,
110 in the equations for the HED and HMD becomes the permeability of the layer containing the dipole sources, in accordance with our notation convention.) The data in this report, when taken together with our previous data for the VMD, prnvide moderately complete information about the ULF/ELF electromagnetic fields produced on and above a sea of tinite depth by submerged harmonic magnetic and electric dipoles.
.L I4
1 -**
METHOD OF CALCULATION
II.
Figure 1 shows the geometry used in the field calculations. The harmonic dipoles of moment m (magnetic dipole) or p (electric dipole) and angular frequency w are located at the point (-d,O,O) in a cylindrical coordinate system (r,,,z). The sea surface is the plane z - 0, and the seafloor is the plane z =-D. The region z > i is free space, while the region z < -D is a homogeneous conducting half-space corresponding to the seafloor. Using the notation of Fraser-Smith and Bubenik [1979), the air, water, and floor regions have been labeled +1, 0, and -1, respectively, and the surface and floor boundaries are correspondingly denoted +1 and -1. In Figure 1 the HMD source is directed along the x axis. We will use this particular geometry for both the HMD and for the HED. Our approach in this respect differs from that of Kraichman [1976], who oriented his HED along the x-direction and his HMD along the y-direction. The expressions for the electromagnetic field components produced by the VED, HED, and HMD at a point P (r,ý,z) in the space above the sea have been derived using a method adapted from Morrison et al. [1969], and Kong [1975]. The same method was used in our earlier work to obtain expressions for the VMD field components. The field expressions for the three dipole types are:
Sthe
Vertica* Electric Dipole
Er
22rrr
•Ez
2
0 0
F2M dX
f.f FIMX2
(2)
dX
(3)
,
l
i
5
1'2,
r
I
-,i
I
*.
I
II
z
EZ
BE
pBE
P< (a8.T)
+1
+1
D
0Ox
Id
D VED
0
___
x
*
I ;HMD
Figure 1. The geometry employed in computing the electromagnetic field components Er, Ez, and Bý (VEt) source; left) or Br, Bz, Býpand Er, Ez, Eý, (HMD source; right) produced at P on and above the surface of a sea of finite depth 0 by dipole sources located at a depth d (d ý.D) below the surface.
6
(
20 * iWP.LEIP
J
Horizontal Electric Dipole
P. 9t2i~ p-
(X- yo)
j
FIE X dX +1 f[yOF4M + (x
-)
yF4
O3Xd
E
-X)
r-a~
f(
E0
(5)d
2E]
0
2
0 rO
+
yo+
Er
27
X
2E)d(8
r()
P-op Cos
-
B
())
xF 2 x d
f2E 0
7
1
Horizontal Magnetic Dipole
SE~~r = hsjjm 27rsin~ "
FIM •
-
.4
E
r -----
2
.
r
I*
Bz
where
.
•O
-
FE
d2M
rJ 00 1
FI
-- "M()-
+~h
O
.t B
rTM S -
F2M
•TM
3M
T
( 12)
F X
X
4
E
(12) (13) (13)
O
(14)
o+h) Orr
T
" (a)e-(yod+A'h)dlj FIM
) d]
0
0 F27t A ,
i]msnp
).:.;
r.
0
W0m Cos
,(l
dJ
-
'yo yO
iwJ~Om si n
YO + 4E
r
3 dX
TFM
""Er
+ X"F4E)dX E d F M YO YO
dA- -FrX
' r
(Yod+Xh)d B~=
F4
d=5
(~f
,
2
A(6
~jT
-
FlE
e-(Yod+Xh)3 (Ar) (b) F FMTMe .(a) -(Yod+Ah)j (r 0 TE
F2EF
F(a)e-(yod4Xh)j ITEe
F3 E
F(b)i-(Yod*9Xh )j(r r ~ ITE e
F
F(b)e-(yod+Xh)j (Ar)
F
and where F(a)
(
F(b) TM
(1
-ITM)/( 1 I(Y Y0)/(Yj
1
r1TM
L~v. 1 K1TM
F(b) TE
P-ITE
n
-2Yd
+
)/(Y
-
Y0 )) e .,~
fl
+2yo(d-D)
(1 + P-1TE)/'1
P-I.TEP1TE)
lTE)/( 1
P-lTEPITE)
(1 U EZ1
~1E
P-ITM~lTM)
*
y(a~
-
-
Z)/(Z1 + z0) e 2~
(Z1l - Z 0)/(Z 1l + 70)] e+2Y0(dD n
+1WE./ n /n
Zn
lJ0 /yf iW
2
2 2 A +k 9
.
.
........
~
kn
n
"
nn n
in
n,
or -
permittivity and electrical conductivity in region n, and
PO
41 x 10
n
H/m
Note that the expression for P-aTE differs from the one given by Bubenik and Fraser-Smith [1978] and by Fraser-Smith and Bubenik [1979].
*
The correct form of this expression is the one given here; this correct form was also used in our earlier computations, but it was reported incorrectly owing to a copy error. The equations listed above are valid at all frequencies. In our
*computations, however, we use the quasi-static approximation [e.g., Kraichman, '976), which isequivalent to neglecting most displacement current terms. Thus, with the exception of the iwpoeI factor multiplying the expression for the magnetic field component B produced by the VED, we set el a EO * _l - 0. This is a commonly used approximation, and it is applicable when the source-receiver distance is much smaller than a free space wavelength. Use of this approximation clearly implies a restriction on the frequency range over which our computations are valid. It was partly for this reason that we restricted the frequency range of applicability of the data derived in our earlier work either to frequencies between 0.1 and 100 Hz [Fraser-Smith and Bubenik, 1976] or to frequencies less than about 300 Hz [Bubenik and Fraser-Smith, 1978; Fraser-Smith and Bubenik, 1979]. More important, the restrictions were prompted by the fact that the specified frequency ranges were likely to be the most useful in practice for undersea-to-air and undersea-toundersea communication and for undersea detection. However, because of their possible use at frequencies above 300 Hz, we now point out that the data in 'his report and in the Bubenik and Fraser-Smith [1978] and Fraser-Smith and Bubenik [1979] articles are valid throughout the ELF and VLF ranges, i.e., they are valil, up to frequencies as high as 30
kHz. The actual validity of the parametric data depends specifically on the applicability of the quasi-static approximation at the largest
"1"
10
In this report, and in the last two articles source-receiver distances. cited, the largest source-receiver distance is only a little greater than 100 seawater skin depths (specifically, the greatest sourcereceiver distance occurs when d - 36, h - 106, and r - 1006, and the distance is 100.846). Assuming that "much smaller" than a free space wavelength means less than one tenth of a wavelength, the data in Table
2 show that in our case the quasi-static approximation begins to lose validity at frequencies above about 30 kHz. As in our earlier work we evaluated the full field expressions numerically, using the techniques described by Bubenik (1977]. We set 01" 0, and both the magnetic dipole moment m and the electric dipole 2 , and p - I Am), moment p are set equal to unity (m a I Am For dipQles of arbitrary moment the field values given in the figures should be multiplied by the moment to obtain the corresponding field magnitudes. We use the milligamma as our unit for the magnetic field (1 my * 1I picotesla), and the electric field data are presented In units of mi crovol ts/meter.
a, I
Al
iN .."
II
-
wI.w-•
~&R~*
Table 2. Comparison of the 'free space wavelength (Akl)with one hundred times the seawater Aikn depth (1006) for various frequencies in the range 0.1-30 kHz. Seawater is assumed to have a conductivity of 4.0 S/rn.
It
Frequency
10065
Xl
(k~Z)
Ckin)
(kmi
il
0.1
2.52
3000
1190
1.45
1000
690
0.80
300
375
0.46
1N0
217
10
0.25
30
120
30
0.15
10
'10.3 L1 I3
12
67
111.
RESULTS
Our results consist of amplitude data for the radial and vertical • :;
components E., the total electric field ETOTAL. components Er Er and ~~TOALdEtettleeti il TTL and n the h total oa magnetic field BTOTAL (which also represents the azimuthal magnetic "field component B ) produced by the VED. We also present data for the three electric field components (Er, E0, Fz), three magnetic field components (Br, BS, B2 ), total magnetic field BTOTAL8 and total electric field ETOTAL produced by the submerged HED and HMD at the two principal azimuthal angles O and 900. Because of the sin 0 an,: cos 0 terms 0 appearing In the equations for the field components produced by the two horizontal dipoles (Equations 5-16), only one of the horizontal electric components (Er and E and one of the horizontal magnetic components (Br and B) are produced by each of the dipoles when 0 a 00 or 900. The vertical fields vanish at one or the other of these angles. The notation we use for these nonzero components 'Is EHORIZONTAL and BHORIZONTAL. Whether these components are radial or azimuthal can be determined quickly by noting the azimuthal angle and by referring to Equations 5-16. Alternatively, the form of the horizontal components can be determined by reference to the following list of nonzero magnetic and electric field quantities produced by each dipole type. VMD:
Br, Bz, Et; BTOTAL,
"VED: B,, Er HED, @ 0": iHED,
=90:
HMD,p= 0"': HMD, q = 90':
ETOTAL = E•.
; BTOTAL = B, ETOTAL. BEr Ez; BTOTAL = Bcc,ETOTAL'
EHORIZONTAL *Er,
Br, Bz, E4; BrTOTAL' BHORIZONTAL m Br'ETOTAL *E . Br, Bz, E
BTOTAL' BHORIZONTAL = Br, ETOTAL = 4E .
Bý, Ern Ez; BTOTAL ' B,, EHORIZONTAL ' Er, ETOTAL.
Note that for each dipole category there are only three basic magnetic and electric field components.'
13
r .;'
The presentation of the new field data is very similar to the one used for the results of our VMD computations (Fraser-Smith and Bubenik, 1979]. First, we present a series of curves that give the actual fields produced by a particular unit moment dipole when submerged in a sea of infinite depth. Next, we present additional curves that give the ratios of the fields produced by the dipole in a sea of finite depth D to the fields produced under otherwise identical conditions by the dipole submerged in the sea of infinite depth. These latter curves show clearly any seafloor effect that is present, since the absence of a seafloor effect is indicated by a ratio of 1.0. The curves for the infinitely deep sea are presented for three receiver heights (h/6 a 0, "1,and 10) and for four dipole depths (d/6 - 0.1, 0.3, 1.0, and 3.0). These data are then supplemented by the seafloor effect curves, which are drawn for four sea depths (0/6 - 0.1, 0.3, 1.0, and 3.0). Finally, to illustrate the effect of a change in the seafloor electrical conductivity, we consider two seafloor conductivities os a 0.1 of and 0.01 of, where we write a0 os (for seawater electrical conductivity), and
"rKi
0
,
s
f (for seafloor electrical conductivity). The subscript has been -l dropped from oa when this conductivity appears in the ordinate labels. The field data are presented in the following figures.
.
VED:
Figures 2-15. "HED, ý - 00: Figures 16-29. HED, ý - 90': Figures 30-43. HMD,
cp
00:
Figures 44-57.
HMD, f 9'o: Figures 58-71. The same basic arrangement of figures is used for each dipole category.
1 :14
II
9
IV.
DISCUSSION
At horizontal distances greater than 106 the curves for the fields produced by the dipoles in an infinitely deep sea begin linearly (see Figures 2, 3 [VED]; 16, 17 [HED. € • 00); 90']; 44, 45 [HMD, 0 = 00]; 58, 59 [HMD, 4 900]). use of logarithmic scales, the linear decline implies a decrease of the fields with distance. Further, because the linear portions of the curves are not all the some,
ii
to decrease 30, 31 EHED, Because of our power law the slopes of our data
indicate that the dipole fields for r > 106 decrease with distance as r-n, where the power n depends both on the dipole type and on the electric or magnetic field component under consideration. Since distance is an important factor in any communication or detection application of these data, we will examine the range of values assumed
by n. As previously described by Fraser-Smith and Bubenik [1979), the total magnetic and electric fields for the VMD had n - 4, and the two magnetic field components Br and B for this dipole had n a 4 and 5, respectively. These values of n, together with the values of n derived from our new data, are listed in Table 3. It can be seen than n ranges from 5, implying a very rapid decline of the field quantity with distance, down to 2, implying a comparatively slow variation of the field quantity with distance. These powers of n are all consistent with the distance variations in the approximate expressions for the fields tabulated by Kraichman [1976] for large source-receiver distances. Examining the field quantities with n = 2 in greater detail, we
*
observe that they are B (or, equivalently, BTOTAL) for the VED; E (or. equivalently. ETOTAL) for the HED, Q0; and E (or, equivalently, 0
ETOrAL) for the HMD,
- 90°. Although these three components would appear to have equivalent potential for long distance communication, we can dismiss the B component because, as Is clearly shown by the data in Figure 2, its amplitude is always very small. To illustrate, assuming r/6 = 100, h = 0, and d = 0.1, we have B 64a2 a 0.255 M8 lI-5 my at I Hz, for a unit moment or B,,, x 10- my x m2S
•..
15
r
N
~~~
*
*-
Table 3. Values of the power n occurring in the long distance variation rF observed in the fields produced by each
F
dipole.
is produced.
___component
•:
*1
An asterisk indicates that no field
MD VMD
VED
HEDHED,
VED
4
0,g
HMD,-
HMD,
0
--
BTOTAL
4
2
3
3
3
3
ETOTAL
4
3
2
3
3
2
Br
4
*
*
3
3
*
B
*
2
3
*
*
3
Bz Er
B
*
*
4
4
*
*
4
3
*
*
3
E
4
*
*
3
3
*
Ez
*
3
2
*
*
2
I1
16
! 0
k7
VED.
Under the same conditions, 62 = 0.128 my x m, or B. B, or
a unit moment HED (• - 00) would give 2.0 x my (Figure 16). •0 These
results apply to an infinitely deep sea; in a sea of finite depth the B amplitudes for the VED are reduced even further, as shown by the data in even-numbered Figures 4,...14. (The B¢ amplitudes for the HED, are mostly increased by the presence of a seafloor.) Comparing the Ez components produced by the HED, • - 0°, and the HMD, • 900, for an infinitely deep sea and for the configuration r - 1006, d - 0.16, and h = 0, we find (a) for the HED, = 00, 2 Ez x 63a a 0.204 x 102 PV/m X m S, or Ez = 3.20 x l0-7 uV/m at 1 Hz (Figure 17), and (b) for the HMO, 4 900, Ez x 4 = 0.288 x 102 PV/m 3S,or E 1.80 x 10 V/m at I Hz (Figure 59). This comparison is made for unit moment dipoles, of course. Without consideration of Sthe possibility that there may be practical reasons for preferring an HMD source to an HED, it appears from this comparison that using the vertical electric field produced by an HED source in the 4300 plane would be preferable for long distance communication to reception of the vertical electric field produced in the 4 - 900 plane by an HMD. In a sea of finite depth, our data show that the seafloor effects for Ez are predominantly positive (i.e., enhancements occur) for the HED ( 0), whereas the effects are predominantly negative for the HMD ( •*) 9 these results therefore lend additional support to the above conclusion. As we saw in the case of the B, component produced by the VED, it = 00,
is possible to have an r distance variation in a component, but still not to have sufficiently large amplitudes for measurements of the component to be useful in comparison to mc,:surements of some other dipole component with a more rapid decline of amplitude with distance. Comparing the amplitudes of the Ez component produced at large distances by the HED, . 0', with the amplitudes of all the other electric field components considered in this work, we find that under the same conditions in an infinitely deep sea the HED, 0°, component is larger in all cases. With the possible exception o t"' electric field components produced by the VED in a sea of finite depth, which will shortly be discussed, it appears unlikely that seafloor effects can produce 17
,
I
significant changes in this situation. We conclude, therefore, that the Ez field produced by an HED (0 = 00) source is likely to be the most attractive electric field component for possible long distance undersea-to-air communication or for undersea detection. Because of the great difference between magnetic field and electric field sensors, a comparison similar to those above of the possible advantages or disadvantages of rnagnetic field measurements versus electric field measurements is beyond the scope of th's work. Finally, we wish to point out the large seafloor effects that occur for the Er component and, to a lesser extent, for the Ez component producLd by the VED. Under certain conditions, the Er component can be increased by nearly six orders of magnitude (Figure 7; note the expanded ordinate scale in this figure and in Figure 5). None of the other electric or magnetic field components considered in this work are affected similarly; at most, enhancements or reductions of the field amplitudes by up to two orders of magnitude are observed. The Ez component is mostly reduced at short distances (r/6 < 1) and is largely unaffected at large distances (r/6 > 10), whereas the Er component tends also to be reduced at short distances before being enhanced at large distances. The total electric field, reflecting this behavior as well as the
•
differences in amplitudes of the two field components (Figure 3), is somewhat more stable than its components, but also exhibits a moderately large seafloor effect. Although it may not immediately appear to be true in the case of the VFD, all the criteria developed in our VMD study [Fraser-Smith and Bubenik, 1979] for estimating when seafloor effects are most likely to occur are valid for all the obher dipola categories. Thus, for each of the VMD, VED, HED, and HMD sources, we have the following criteria: (1) the seafloor effects are most marked in seas that are electrically shallow, (2) the largest changes in the fields occur when the dipole is located within one seawdter skin depth (6) of the seafloor, and (3) there is essentially no seafloor effect when the dipole is located more than S36 above the floor. The seafloor effects for the VED differ from the effects for the other dipoles only in their scale, nrt in the 18
S..
..
. . .. .
I
.
.
-
ii..
-
. . . .. ..
.
. . ..
r.
applicability of our criteria (l)-(3).
In particular, criterion
(2) appears to be most Important for the VED, with the largest seafloor effects occurring when the dipole is located on the floor.
IL 1*-'?
19
r-
,*
~19
V, REFERENCES Bannister, P. R., "Detemination of the electrical conductivity of the sea bed in shallow waters," Geophysics, 33, 995-1003, 1968. Brock-Nannestad, L., "Determination of the electric conductivity of the seabed in shallow waters with varying conductivity profile," Electron.
"Letters, 1, 274-276, 1965. Bubenik, D. M., "A practical method for the numerical evaluation of Son;erfeld integrals," IEEE Trans. Ant. Prop., AP-25, 904-906, 1977. Bubenik, D. M., and A. C. Fraser-Smith, "ULF/ELF electromagnetic fields generated in a sea of finite depth by a submerged vertically-directed harmonic magnetic dipole," Radio Scd., 13, 1011-1020, 1978.
7
Coggon, J. H., and H. F. Morrison, "Electromagnetic investigation of the sea floor," Geophysics, 35, 476-489, 1970. Fraser-Smith, A. C., and D. M. Bubenik, "ULF/ELF magnetic fields generated at the sea surface by submerged magnetic dipoles," Radio Sct.,
"11, 901-913, 1976. Fraser-Smith, A. C., and D. M. Bubenik, "UL*/ELF electromagnetic fields generated above a sea of finite depth by a submerged verticallydirected harmonic magneLic dipole," Radio Sci., 14, 59-74, 1979. Kong, J. A\., Theory of Electromagnetic Waves, 339 pp., Wiley-Interscience, New York, 1975. Kraichman, M. B., Handbook of Electromagnetic Propagation in Conducting Media, Second Printing, U.S. Government Printing Office, Washington, D.C., 1976. Morrison, H. F., F. J. Phillips, and D. P. O'Brien, "Quantitative interpretation of transient electromagnetic fields over a layered half ispace," Geophys ..
sP , 17, 82-101, 1969.
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