Specifications

University of Pretoria etd – Combrinck, M (2006)
electromotive force (emf) is directly proportional to
2
5
−
t for an ideal step function
excitation. This behaviour is described as a power-law decay with time and manifests as a
straight line with a slope of
m = –5/2 on a graph of log (emf) versus log (t). The horizontal
component of the emf can be shown to exhibit the same behaviour (Kaufman and Keller,
1983); the only difference being that it shows a time-decay proportional to
in the late
time. In terms of the smoke-ring analogy, the “late time” for profiling commences when
the equivalent current filament is so far away that any receiver position can be
approximated to be at the centre of the smoke-ring. With the central-loop system (as used
in this study) this is always the case and it is easy to see why the late time approximations
are particularly useful for this survey geometry.
3−
t
2.3.2 Thin, conductive sheet (S-layer)
Parameters used in the conductive sheet model are shown in figure 2.2.
Transmitter loop
Receiver loop
r
d
T
hin, conductive sheet with conductance Siemens. S
Figure 2-2 Conductive sheet parameters.
The equivalent current smoke-ring behaviour for an S-layer (originally solved by Maxwell)
is described by Nabighian and Macnae (1991). With the primary field termination currents
are induced in the S-layer, once again representing the geometry of the transmitter loop.
As time passes the equivalent current filament retains it original size and intensity and only
appears to migrate downwards with a velocity related to the conductance of the S-layer as
(figure 2.3). This is an exact solution for velocity (v).
-1
ms
0
/2 µ Sv =
9