Electrical and electromagnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 309

Table 5.4 Values of the power-law constant ( k ) for the thin layer

and half-space responses, and for current ( I ) -channelling within

Overburden

them, for horizontal ( ) component

measurements. Note that the decay in the horizontal components
is faster than that of the vertical component.

X and Y ) and vertical ( Z

Step response

Step Impulse

Impulse
response

X and Y Z X and Y Z

Thin layer 4 3 5 4

Halfspace

I-channelling 4 5

Log delay time (ms)

Half-space 2 1.5 3 2.5

Figure 5.79 The power-law decays of conductive overburden (a thin
surface layer) and conductive basement (a half-space) for the step
and impulse responses. Actual decay constants (slope values (k)in
Fig. 5.78a ) are given in Table 5.4 .

I-channelling 2.5 3.5

In this case eddy currents are induced into the conduct-
ive layer at the conductivity interface of its upper surface
( Fig. 5.75b ). Diffusion is con ned to within the layer and,
for a homogeneous layer of in nite lateral extent, the
current system is free to quickly expand laterally. It is an
uncon ned conductor with response decaying as a power
law ( Fig. 5.78a ) with decay constant (k) larger than that of
a half-space, i.e. the decay is faster than that of a half-space.
The decay in a thin layer is controlled by the product of its
conductivity and thickness, but not by these parameters
separately,

the overburden, becomes apparent. Further aspects of
near-surface conductive material and its responses are
described in Section 5.7.6.1 .

5.7.2.3 Confined conductor
When a homogenous subsurface contains a discrete zone
of contrasting conductivity, two eddy current systems are
created when the primary field is turned off ( Fig. 5.75c ) .
One current system is induced in the background material,
as described in Section 5.7.2.1 , and the other induced in the
discrete conductor. Those in the conductor try to repro-
duce the primary

thickness product, also
known as the conductance (see Section 5.2.1.2 ) . Values of
k for a thin layer are shown in Table 5.4 .
As the thickness of the layer increases, the diffusion
begins to experience vertical migration downward, as well
as outward, from the upper interface (closest to the source
loop), and the response approaches that of a homogeneous
half-space. Where the subsurface is multi-layered, induc-
tion occurs simultaneously in each conductive layer and
their decaying responses interact. Their conductance and
depth, and the spacing between the layers, determine the
amplitude of their responses and the resolution of each in
the measured decay. Thin resistive layers tend to be invis-
ible compared with the stronger, more slowly decaying
responses of conductive layers.
Figure 5.79 shows the responses measured in the pres-
ence of conductive overburden. The relative decay rates of
the thin layer and half-space responses means that at early
delay times the response is chiefly due to the conductive
overburden, so early-time measurements are necessary for
resolving the rapidly decaying overburden response. At
later times when the overburden response has diminished,
the slower-decaying response of the deeper eddy current
system in the half-space, i.e. from the basement underlying

i.e. the conductivity -

field in the vicinity of the conductor, then
immediately begin to diffuse over and through the body
with their expansion being con ned by its boundaries,
which have a signi cant in uence on the nature of the
transient decay. It is known as a con ned conductor, also
referred to as a discrete conductor.
When the conductor is in a high-resistivity environment
and there is no interaction with its surroundings, the initial
surface eddy current flow is dependent in a complex way
on the geometry of the conductor. With time the current
system migrates through the body and, for an electrically
homogeneous body, the late-stage decay is exponential.
The amplitude (A) as a function of delay time t for the
step response is then given by:

A 0 e t = τ

A ð t Þ¼ ð 5 : 24 Þ

and for the impulse response by:

1
τ

A 0 e t = τ A ð t Þ¼ ð 5 : 25 Þ

where A 0 is the apparent initial amplitude of the exponen-
tial decay which is dependent upon the conductor ' s shape,