Specifications

University of Pretoria etd – Combrinck, M (2006)
of
rd
S
t
>>+ 2
2
0
µ
(where r now represents the small loop radius after reciprocity) and
simplifying equation 2.3 we have
()
()
loop[m].iver small rece the of radius
loop receiver inturns ofnumber
loop (large)r transmitte the ofmoment dipole magnetic
where
(2.5)
areaRx effective
H
(2.4)
z
=
=
=
=
+
−===
∂
∂
+
−=
r
n
S
t
M
d
S
M
rn
emfemf
t
d
Sr
M
emf
r
r
timelatetimelate
timelate
0
42
42
1
16
3
1
16
3
µ
τ
τ
π
π
τ
This is a very good approximation for the chosen system geometry as the radius of the
receiver loop is always in the order of one meter and the late time condition is always
satisfied under field conditions. The “late time” approximation of the S-layer response is
therefore directly proportional to
. This behaviour manifests as a straight line with a
slope of
m = –4 on a graph of log (emf) versus log (t).
4−
t
2.3.3
Finite conductor in a resistive host rock (half space)
The significance of having a confined target surrounded by an insulator is that there is
always some stage of time (“late time”) when the current distribution in the conductor
becomes invariant with time and the decay becomes exponential at a rate determined by
the shape, size, and conductivity of the body (McNeill, 1980). An intuitive feeling for the
general behaviour of isolated (confined) conductors can be developed from examining the
simplified case of a conducting sphere assumed to be in a region of uniform magnetic field
that is suddenly terminated. Immediately after termination of the primary current (early
time) the secondary currents flow on the surface of the sphere and are independent of its
conductivity (figure 2.4a). From then on the currents diffuse radially inwards, similar to the
smoke-ring propagation found in a half space. This stage of changing current distribution
is referred to as intermediate time (figure 2.4c). The late time commences when the
inductance and resistance associated with each current ring, have stabilized and from this
time onwards both the currents and their associated external magnetic field commence to
decay exponentially with a time-constant given by
11