Specifications

University of Pretoria etd – Combrinck, M (2006)
Figure 2-1 The use of equivalent current filament concept in understanding the behaviour of
TEM fields over a conducting half space (after Nabighian and Macnae, 1991).
The quasi-stationary (derivative of) magnetic field transient response of a central-loop,
step-current system over a conductive earth is given by Kaufman and Keller (1985) as
() ()
[s], timet
loop[m]r transmitte the of radiusa
where
(2.1)
=
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
=
=
⎥
⎦
⎤
⎢
⎣
⎡
+−−=
∂
∂
∫
−
−
2
1
2
2
2
1
0
0
2
3
0
2
2
2
2
)(
23
2
3
σµ
πτ
τ
π
π
π
σµ
t
a
u
dxeuerf
euuuerf
a
I
t
H
u
x
u
z
with a late time asymptotic approximation of
(
)
(2.2)area)receiver(effective(emf) .
20
2
5
2
1
2
3
0
2
−
−=⋅=
∂
∂
t
Ia
t
H
z
π
σµ
In the “late time” (which can be achieved through either large values of t, or small values
of σ), it can be seen from equation 2.2 that the vertical component of the measured
8