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y ) H o y ( x o ,
y ) H o x ( x o ,
i
o
2 π
Y xx ( x
,
y o )
Y xy ( x
,
y o )
H o x ( x , y ) +
( x
dx o dy o = Y xx ( x , y ) Z N ,
x o ) 2
+
( y
y o ) 2
−∞
−∞
l Y yx ( x , y ) H o y ( x o , y o ) Y yy ( x , y ) H o x ( x o , y o )
i
o
2 π
( x x o ) 2
dx o dy o
H o y ( x , y ) +
+ ( y y o ) 2
−∞
−∞
= Y yx ( x , y ) Z N
1
.
(5
.
64)
H o x ( x
H o y ( x
y ) from this system of integral equations,
it suffices to know the admittance (impedance) tensor. Having determined the hor-
izontal components of the normalized anomalous magnetic field, we can compute
its vertical component. By virtue of (5.48)
To determine
,
y )
and
,
1
2
dx o dy o
H o z ( x
H o x ( x o ,
( x
,
y )
=
y o )
π
x
x o ) 2
+
( y
y o ) 2
+
z 2
−∞
−∞
(5
.
65)
1
2
dx o dy o
H o y ( x o ,
+
y o )
( x
z 2 ,
π
y
x o ) 2
+
( y
y o ) 2
+
−∞
−∞
where
H o z ( x
,
y )
H o z ( x
,
y )
=
.
H o y
Note that the anomalous magnetic field derived from (5.64) is readily trans-
formed in the anomalous electric field. Using (5.50), we get
i
o
2
dx o dy o
E o x ( x
H o y ( x o ,
,
y )
=−
y o )
( x
π
x o ) 2
+
( y
y o ) 2
+
z 2
−∞
−∞
(5
.
66)
o
2
i
dx o dy o
E o y ( x
H o x ( x o ,
,
=
( x
z 2 ,
y )
y o )
π
x o ) 2
+
( y
y o ) 2
+
−∞
−∞
where
E o y ( x
E o x ( x
,
y )
,
y )
E o x ( x
E o y ( x
,
y )
=
,
y )
=
.
H o y
H o y
To complete this consideration, we present the two-dimensional analogues of
(5.64), (5.65) and (5.66). Let x be the strike of the 2D model. Then, according to
(5.56b), (5.58) and (5.64), we have the integral equation for
H o y ( y )
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