Geoscience Reference
In-Depth Information
CHAPTER 6
The seismoelectric beamforming approach
As seen in Chapter 4, the seismoelectric conversion can be
rather weak with respect to the coseismic electrical fields.
“
For this purpose, we consider a 2D model with a porous
backgroundmaterial using constant mechanical, hydrau-
lic, and electrical properties. Two rectangular heteroge-
neities (labeled Anomalies 1 and 2) are embedded in a
homogeneous background (Figure 6.1). The background
and the two anomalies are characterized by the same
mechanical properties. They differ only by their hydraulic
and electrical properties, for instance, a change in water
saturation. Indeed, an increase of the nonwetting and
insulating fluid saturation (e.g., gas or oil) would decrease
the permeability of the water phase, thereby reducing the
electrical conductivity of the porous material. The material
properties used in this test are reported in Table 6.1. The
background material is supposed to be fully water satu-
rated (electrical conductivity of 1 Sm
−
1
). The anomalies
are more resistive (10
−
2
Sm
−
1
for Anomaly 1 and 10
−
3
S
m
−
1
for Anomaly 2).
Seismic sources are located in two wells. The seismo-
electric equipment (virtual geophones, seismic sources,
and electrodes) are set every 5m along the ground surface
and in the two wells (see Figure 6.1;19ineachwelland8
along the ground surface). The objective of this experi-
ment is to focus seismic waves at two specific points,
A and B (Figure 6.1), and evaluate whether seismoelectric
conversions due to the presence of a heterogeneity can be
recorded remotely at the electrodes located in the wells.
When the seismic energy is focused on a heterogeneity
such as an interface characterized by a drop in permeabil-
ity and resistivity, we expect to record a seismoelectric
conversion away from this interface (interface response).
allows for the
enhancement of the electrical field associatedwith seismo-
electric conversions over the spurious coseismic signals.
We present in this chapter the basic ideas of this method,
followed by numerical tests in piecewise constant and het-
erogeneous materials. We demonstrate how this method
can be used to improve cross-well electrical resistivity
tomography (ERT) through a technique called
“
image-
guided inversion.
Seismoelectric beamforming/focusing
”
The basic idea of image-guided inver-
sion is to use information from an image to impose the
structure in a way that shapes the model covariance
smoothness matrix that imposes this structural informa-
tion in the inversion of the geophysical data. Because
the computations performed for the examples shown in
this chapter are rather intense, we demonstrate this
method using the acoustic approximation only (see
Chapter 1 and its extension in partially saturated
conditions in Chapter 3). Nevertheless, the same general
idea can be applied to more general poroelastic wave
fields.
”
6.1 Seismoelectric beamforming
in the poroacoustic approximation
6.1.1 Motivation
Our first goal is to explain how the principle of seismo-
electric beamforming works with a simple example.
