75
is an average cross power density spectrum and Ex is the discrete Fourier transform of the
measured field Ex. The (*) symbol indicates complex conjugation. The two cross power
expressions above combine to yield
and
and expressions for Zyx and Zyy are obtained in a similar way.
The surface impedance is usually expressed as apparent resistivity and impedance phase and
they are calculated from the surface impedance components as
ij
ij
ij
Z
f
Z
1
2
0
2
2
.
and
ij
ij
ij
Z
Z
tan
Im
Re
1
whether they are based on scalar or tensor calculations.
Z
E H
H H
E H
H H
H H
H H
H X
H H
xx
x
y
y
x
x
x
y
y
x
y
y
x
x
x
y
y
*
*
*
*
*
*
*
*
Z
E H
H H
E H
H H
H H
H H
H X
H H
xy
x
y
x
x
x
x
x
y
y
y
x
x
y
x
x
y
*
*
*
*
*
*
*
*
