Geoscience Reference
In-Depth Information
propagating separately from every point in the bore-
hole and linearly recombine the resulting wave fields
and electrical potential fields to reflect delays that
would focus energy at a given point in the subsurface.
In this case, the experimental effort is proportional to
the number of sources in the boreholes, since we can
consider the computational effort to recombine the
electrical potential fields negligible.
In the numerical experiment shown in the following,
we use an even simpler method. We loop over all the
points located in the scanning area and inject an identical
pulse (Ricker wavelet) to generate wave fields propagat-
ing in the medium. We assume that we know the velocity
model with sufficient accuracy in order to predict correctly
the kinematics in the subsurface. Figure 6.14 shows an
example of wave propagation from a scanning point to
the receivers located in the wells. The seismic wave field
encodes the model heterogeneities and carries this infor-
mation to the boreholes surrounding the scanning point.
Then, we record these simulated seismic signals at the
receivers located in the wells (see the seismograms in
Figure 6.15), and we reinject the recorded seismograms
into the formation in order to focus the seismic energy
back at the chosen scanning point (Figure 6.16). As indi-
cated earlier, the recorded seismograms (see Figure 6.15)
could be generated by linear superposition of seismograms
generated separately from all points in the boreholes.
The backpropagating waves (Figure 6.16) generate
seismoelectric sources at every location where rapid
changes of physical properties occur in the medium
(Figure 6.17). The corresponding normalized electric
potential distribution is shown in Figure 6.18. The reason
for normalization of the potential map is that the source
we use is of arbitrary strength, and this in turnmeans that
the virtual electrode obtained by focusing is characterized
by a proportional potential. However, since the potential
normalization is done globally, that is, for all time steps,
the relative relationships between the potentials recon-
structed at different times and positions are preserved.
This simulation, shown in Figures 6.14, 6.15, 6.16,
6.17, and 6.18, illustrates the main difficulty of using
seismoelectric methods to investigate the subsurface:
relatively weak sources of energy are located everywhere
in the medium at all times. However, our method
addresses this issue. Instead of observing the seismoelec-
tric conversions at all times, we concentrate on only one
moment, that is, the time when the injected wave field
Water saturation
0.6
0.4
0.2
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130
140
Offset (m)
(a)
Conductivity (S m
-1
)
0.04
0.02
0
70
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Offset (m)
(b)
Location of water−oil interface
0.8
0.6
0.4
Scanned
area
0.2
0
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Offset (m)
(c)
Figure 6.11
Determination of the position of the oil water
interface using a set of beamforming points at the same depth
that cross the interface.
a)
Spatial distribution of water saturation
(snapshot #3) showing the position of the saturation front.
b)
Electrical conductivity distribution.
c)
Source intensity as a
function of offset. This shows that the strongest seismoelectric
conversions are generated at the position of the saturation front.
scanning domain). The entire procedure is summarized
in the chart shown in Figure 6.13.
There are two main ways in which we can implement
our procedure in practice:
1
First, we could consider a broad distribution of sources
located at all locations in the boreholes. These sources
are characterized by different phase delays but are syn-
chronized such that the generated acoustic energy
focuses at a specified location in the subsurface. Every
focus location requires a different physical experiment
with sources characterized by different phase delays.
The effort required by this experimental setup is pro-
portional to the number of scanning points in the
subsurface.
2
Second, we could consider a single source located
at different points in the boreholes. We simulate waves
