Ocean Electromagnetics 8.7 Magnetic and Electric Dipoles in a Bounded Ocean 191
Part A | 8.7
Table 8.1 Static VMD and HMD sources located at (0, 0, h) in an unbounded ocean
E x
E y
E z
H x
H y
H z
VMD
0
0
0
3m z x.z h/
4r 5
3m z y.z h/
4r 5
m z .2.z h/ 2 x 2 y 2 /
4r 5
HMD
0
0
0
m x .2x 2 y 2 .z h/ 2 /
4r 5
3m x xy
4r 5
3m x x.z h/
4r 5
where r D
p
x 2 C y 2 C .z h/ 2
Table 8.2 Static VED and HED sources located at (0, 0, h) in an unbounded ocean
E x
E y
E z
H x
H y
H z
VED
3p z x.z h/
4r 5
3p z y.z h/
4r 5
p z .2.z h/ 2 x 2 y 2 /
4r 5
p z y
4r 3
p z x
4r 3
0
HED
p x .2x 2 y 2 .z h/ 2 /
4r 5
3p x xy
4r 5
3p x x.z h/
4r 5
0
p x .z h/
4r 3
p x y
4r 3
where r D
p
x 2 C y 2 C .z h/ 2 and is the seawater conductivity
Table 8.3 In-water electric fields produced by the above-water images of submerged static VED and HED sources
(after [8.12])
E x
E y
E z
VED
3p z x.z C h/
4r
5
i
3p z y.z C h/
4r
5
i
p z .2.z C h/ 2 x 2 y 2 /
4r
5
i
HED
p x .2x 2 y 2 .z C h/ 2 /
4r
5
i
3p x xy
4r
5
i
3p x x.z C h/
4r
5
i
where r i D
p
x 2 C y 2 C .z C h/ 2 and is the seawater conductivity
Table 8.4 In-water magnetic fields produced by the above-water images of submerged static VED and HED sources
(after [8.12])
H x
H y
H z
VED
p z y
4r
3
i
p z x
4r
3
i
0
HED
p x xy
4 4
"
2
.z C h/.2.z C h/ 2 C 3 2 /
r
3
i
#
p x
4
(
x 2
4
"
2
.z C h/.2.z C h/ 2 C 3 2 /
r
3
i
#
1
r
2
i C .z C h/r i
)
0
where r i D
p
x 2 C y 2 C .z C h/ 2 and D
p
x 2 C y 2
Table 8.5 In-air electric fields from static VED and HED sources submerged at a depth h in a deep ocean (after [8.12])
E x
E y
E z
VED
3p z x.z h/
2r 5
3p z y.z h/
2r 5
p z .2.z h/ 2 x 2 y 2 /
2r 5
HED
p x .2x 2 y 2 .z h/ 2 /
2r 5
3p x xy
2r 5
3p x x.z h/
2r 5
where r D
p
x 2 C y 2 C .z h/ 2 and is the seawater conductivity. Note: A negative value for z is used for in-air computations
HED equations in Table 8.3 must be added to their
corresponding components from Table 8.2.
Likewise, the magnetic field formulations produced by the
jump in the surface current density has been computed in [8.12], and are listed in Table 8.4. Adding the
equations in Table 8.4 to their corresponding magnetic
Part A | 8.7
Table 8.1 Static VMD and HMD sources located at (0, 0, h) in an unbounded ocean
E x
E y
E z
H x
H y
H z
VMD
0
0
0
3m z x.z h/
4r 5
3m z y.z h/
4r 5
m z .2.z h/ 2 x 2 y 2 /
4r 5
HMD
0
0
0
m x .2x 2 y 2 .z h/ 2 /
4r 5
3m x xy
4r 5
3m x x.z h/
4r 5
where r D
p
x 2 C y 2 C .z h/ 2
Table 8.2 Static VED and HED sources located at (0, 0, h) in an unbounded ocean
E x
E y
E z
H x
H y
H z
VED
3p z x.z h/
4r 5
3p z y.z h/
4r 5
p z .2.z h/ 2 x 2 y 2 /
4r 5
p z y
4r 3
p z x
4r 3
0
HED
p x .2x 2 y 2 .z h/ 2 /
4r 5
3p x xy
4r 5
3p x x.z h/
4r 5
0
p x .z h/
4r 3
p x y
4r 3
where r D
p
x 2 C y 2 C .z h/ 2 and is the seawater conductivity
Table 8.3 In-water electric fields produced by the above-water images of submerged static VED and HED sources
(after [8.12])
E x
E y
E z
VED
3p z x.z C h/
4r
5
i
3p z y.z C h/
4r
5
i
p z .2.z C h/ 2 x 2 y 2 /
4r
5
i
HED
p x .2x 2 y 2 .z C h/ 2 /
4r
5
i
3p x xy
4r
5
i
3p x x.z C h/
4r
5
i
where r i D
p
x 2 C y 2 C .z C h/ 2 and is the seawater conductivity
Table 8.4 In-water magnetic fields produced by the above-water images of submerged static VED and HED sources
(after [8.12])
H x
H y
H z
VED
p z y
4r
3
i
p z x
4r
3
i
0
HED
p x xy
4 4
"
2
.z C h/.2.z C h/ 2 C 3 2 /
r
3
i
#
p x
4
(
x 2
4
"
2
.z C h/.2.z C h/ 2 C 3 2 /
r
3
i
#
1
r
2
i C .z C h/r i
)
0
where r i D
p
x 2 C y 2 C .z C h/ 2 and D
p
x 2 C y 2
Table 8.5 In-air electric fields from static VED and HED sources submerged at a depth h in a deep ocean (after [8.12])
E x
E y
E z
VED
3p z x.z h/
2r 5
3p z y.z h/
2r 5
p z .2.z h/ 2 x 2 y 2 /
2r 5
HED
p x .2x 2 y 2 .z h/ 2 /
2r 5
3p x xy
2r 5
3p x x.z h/
2r 5
where r D
p
x 2 C y 2 C .z h/ 2 and is the seawater conductivity. Note: A negative value for z is used for in-air computations
HED equations in Table 8.3 must be added to their
corresponding components from Table 8.2.
Likewise, the magnetic field formulations produced by the
jump in the surface current density has been computed in [8.12], and are listed in Table 8.4. Adding the
equations in Table 8.4 to their corresponding magnetic