Information Technology Reference
In-Depth Information
This mathematics sheds light on the physical mechanisms of the magnetotelluric
anomalies caused by near-surface three-dimensional inhomogeneities. Anomalies
of electric field include the induction and galvanic parts. At low frequency they
lose the inductive part and become static. Anomalies of the magnetic field are of
the inductive nature. At low frequency they vanish. The remarkable property of the
magnetic field is that with lowering frequency it gets free of near-surface distortions.
At what distance from inhomogeneity can we determine the true normal
impedance? Singer and Fainberg answer this question, using two criteria:
r
>>
λ
o
and
r
>>
λ
L
. Combining these criteria, they write
r
>>
max(
λ
o
,λ
L
)
.
(7
.
109)
λ
o
is an effective penetration depth
h
eff
derived from the Tikhonov-
Cagniard impedance
Z
of the two-layered horizontally homogeneous medium
underlying the inhomogeneous
S
1
−
Parameter
plane:
h
eff
=
Z
/
o
,
λ
o
=
(7
.
110)
where
o
2
tan h
=
−
o
2
h
2
.
Z
i
−
i
Parameter
λ
L
is a generalized adjustment distance
f
|
g
|
=
S
1
R
2
λ
=
o
S
1
h
2
|
,
(7
.
111)
L
|
−
1
i
where
g
and
f
are the galvanic and induction parameters defined by (7.21). Note
that Singer and Fainberg prefer to write
λ
L
as
R
2
S
−
1
1
Z
,
λ
=
(7
.
112)
L
+
o
h
2
is the low-frequency asymptotics of
Z
. The advantage of
(7.112) is that it allows to generalize the estimation of
where
Z
=−
i
L
to the multilayered mantle.
Let us come back to (7.102), (7.103), (7.104) and (7.105). Assuming that
r
>>
λ
λ
o
, we reduce
Q
1
,
Q
2
,
Q
3
,
Q
4
to the far-zone asymptotics and write
P
r
Z
N
1
1
e
−
r
/λ
L
1
1
S
1
Z
N
π
2
r
1
E
r
=
r
3
+
+
2
π
i
o
λ
o
λ
L
/λ
2
r
/λ
L
L
o
P
Z
N
2
e
−
r
/λ
L
(7
.
113)
1
1
rS
1
Z
N
π
2
r
E
A
=−
r
3
+
2
π
i
λ
o
λ
/λ
L
L
