Geoscience Reference
In-Depth Information
Conductivity (S/m)
a)
10
-4
10
-3
10
-2
10
-1
10
0
10
1
Early-stage
decay
Late-stage
decay
10
-1
10
0
A
1
log(
A
2
)
log(
A
1
)
log(
t
2
)
-
log(
t
1
)
-
k
=
10
1
A
2
10
2
t
1
t
2
Delay time
10
3
Approximate conductivity
range of near-surface materials
b)
A
0
10
4
Permafrost
Conductive
regolith
Early-stage
decay
Late-stage
decay
Figure 5.77
Diffusion depth for electrical conductivities found in the
geological environment and for the range of delay times used in EM
surveying.
t
2
-
t
1
2.3 [log(
A
1
) - log(
A
2
)]
A
1
t
=
A
2
For a given half-space conductivity, diffusion depth is a
function of the square-root of t. It is plotted in
Fig. 5.77
as
a function of the half-space conductivity. Diffusion depth
is larger for more resistive ground because the current
system diffuses faster into it. A receiver at the surface
senses the smoke ring attenuating quickly, i.e. a rapid
decay in signal amplitude as the distance to the moving
smoke ring rapidly increases. In resistive ground it is
necessary to make measurements at early delay times in
order to detect the rapidly expanding smoke ring. Its
velocity decreases with increasing conductivity; in other
words, diffusion is a slow process in conductive ground.
As a consequence, measurements made at early delay times
pertain to shallower depths in conductive environments
than in resistive ones. Note that without the conductivity
being known, delay time is an unreliable indicator of the
depth to which particular measurements pertain.
t
1
t
2
Delay time
Figure 5.78
TDEM secondary decay for (a) power-law response
plotted on log
-
log axes with decay constant k and (b) exponential
response plotted on log
-
linear axes with time constant
τ
. A
1
and A
2
are the amplitudes of the secondary field at delay times t
1
and t
2
respectively.
A graph of the logarithm of the signal amplitude on the
vertical axis versus the logarithm of the delay time on the
horizontal axis shows the power-law decay as a straight
line with slope equal to the decay constant (
k)(
Fig. 5.78a
).
The value of k depends upon whether an impulse or step
response is being measured and on the component of the
secondary magnetic field measured, and is independent of
the conductivity. Values of k for a half-space response are
shown in
Table 5.4
. Note that the late-stage response of a
half-space is the same everywhere, so it does not matter
where the receiver is in relation to the transmitter loop.
-
Late-stage response
As described in Diffusion depth above, the current system
initially expands rapidly. At late times when it has diffused
to a very large distance from the transmitter loop, the
current system limits its own expansion and its position
changes very slowly, i.e. its velocity decreases to a low
value. This creates a large region where the secondary
eld
is vertical and of fairly constant amplitude everywhere.
This is known as the late-stage response of the half-space,
and the amplitude of the secondary
field decays with a
power law, i.e. the signal varies with delay time at the rate
of t
-
k
where k is the power-law constant.
5.7.2.2
Thin layer
A thin
flat-lying layer with higher conductivity than the
surrounding rocks is a commonly occurring conductivity
structure in the geological environment that couples well to
a horizontal loop. It commonly takes the form of a surface
layer, referred to as conductive overburden (see
Section
the loop is close to it.
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