Geoscience Reference
In-Depth Information
Potential map
Filtered potential map
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Figure 6.21
Edge detection from the potential
map using an image sharpening filter in domain
ℜ
. This is done with the image processing
toolbox of MATLAB (function imsharpen). The
structural information contained in the filtered
potential map is used to impose textural
information onto the electrical resistivity
tomogram.
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Distance (m)
Distance (m)
(a)
(b)
value for the L2 scheme is on the range of 0.01
0.1 using
the L-curve approach. For our image-guided scheme,
we enforce a constant value for all iterations. Larger
values of the Lagrange parameter,
-
magnitude of the electrical field produced by the seismo-
electric coupling for three fundamental reasons:
1
We did not care about the amplitude of the electrical
potentials when we built a seismoelectric image.
Indeed, the only things that matter in building the
seismoelectric image displayed in Figure 6.20 are
the local variations of the electrical potentials that
map heterogeneities. Geometrical spreading could
be accounted for, but this was not done in building
Figure 6.20.
2
The conversions need only to be higher than the
background noise. Typically, the electrical noise is on
the order of 1
, enforce structural
similarity within each layer (conductivity values show
less variation within each formation) and have a negative
effect on the data RMS. We see clearly from Figure 6.25
that the texture of the resistivity tomogram is improved
and that the resistivity values are closer to the true resis-
tivity value by comparison with the tomogram obtained
in Figure 6.23. Such an improvement is very important
in order to be able to reliably apply petrophysical models
to be able to transform resistivity or complex conductivity
into relevant parameters such a saturation, salinity,
porosity, or permeability.
β
Vm
−
1
for the electrical field but can
decrease down to 1 nVm
−
1
at depth.
3
If electrical noise is high, stacking may be required.
One way to stack seismoelectric signals would be to
repeat the same seismic (Ricker wavelet) sources.
Another possibility would be to inject a harmonic pres-
sure source and to stack the resulting harmonic
electrical field over the number of cycles needed
to have a good signal-to-noise ratio. Therefore,
μ
6.3.3 Discussion
We have shown that by focusing seismic waves at set
of points, we can image the structural heterogeneities of
formations. However, we have not discussed the order of
in
