Correlation imaging with seismoelectromagnetic waves
N. Grobbe, C.P.A. Wapenaar and E.C. Slob
Department of Geotechnology, Delft University of Technology, Stevinweg 1, 2628 CN, Delft, The Netherlands
Niels Grobbe, Evert Slob and Kees Wapenaar
Introduction
Seismic interferometry is the passive seismological imaging
technique which makes use of the cross-correlation of responses at
different receivers in order to obtain the Green’s function between
these receivers. Using correlation to retrieve the Green’s function
response between two stations is in principle not limited to seismic
systems but holds for a wide class of phenomena, including seismoelectromagnetic effects (K. Wapenaar, E. Slob and R. Snieder, PRL
97, 234301 (2006)). The aim of this project is to identify and
characterize the potential of correlation imaging with seismoelectromagnetic waves in well-controlled laboratory experiments
and with theoretical modeling. It is a Shell-FOM project and a joint
project between the University of Amsterdam and Delft University
of Technology (the Netherlands). The experimental part is executed
in Amsterdam, whereas in Delft the theoretical part and numerical
modeling is performed. The combined set-up of the project is
useful because the theoretical Green’s function retrieval model can
be used to understand the experimental results and, in the
opposite way, the experimental results provide a physical validation
for the theory. The validated model can then be used in the
upscaling process from laboratory scale to field scale.
Numerical Example of 1D Green’s
Function Retrieval
In this project, correlation imaging with seismo-electromagnetic
waves will be investigated in 3D. The numerical examples of the 1D
Green’s function retrieval (S. de Ridder, E. Slob and K. Wapenaar,
GJI 178, 1289-1304 (2009)) have already shown how well the
interferometric representation retrieves the exact results. Below,
an example of this study is shown for a two-layered earth with a
vacuum half-space on top of it.
The two top figures at the left show the geometry of the
numerical experiments and the ray paths of events in the
seismoelectric Green’s function Gs(xB, xA, t). Red rays
represent EM ray paths, whereas blue rays depict shear
wave ray paths.
The equation in the middle represents one element of the 1D
version of the Green’s function retrieval for coupled EM and
seismic wavefields. The LHS represents the exact solution,
whereas the RHS is the interferometric representation. The
RHS consists of a summation of cross-correlated recordings
due to sources at the boundary and sources distributed
throughout the domain. It is desirable to be able to ignore
the domain sources, because they are not likely to exist in
practice.
Seismoelectric effect
The bottom left figure shows the exact and retrieved Green’s functions. The figure in the bottom middle
represents the separated contributions from the domain integral and the boundary sources.
The bottom right figure represents the correlation gather (the cross-correlation results for different positions in
the domain integral). When this correlation gather is summed, the result is the domain integral contribution
visible in the bottom middle figure.
The Green’s function of this situation contains 10 primary events (see the second figure above). In addition, it
has an infinite number of multiples and free surface ghosts. As visible in the graph of the correlation gather, no
strong spurious events occur in the positive time window of the retrieved signal containing GE,f(xB, xA, t). In
order to be able to deal with the large amplitude differences between the events, use has been made of a
colour scale which represents the logarithm of the absolute value of the signal.
From: Shaw, dissertation (2005)
From: http://www.liag-hannover.de
The origin of the seismoelectric effect lies in the electric double layer
in the pore wall of a porous medium. Due to adsorption there is
excess positive charge in the fluid. When there is a seismic or an
electromagnetic (EM) disturbance, coupling can take place at two
locations:
• Present in the waves (coseismic effect)
• At interfaces
an independently propagating EM or seismic
wave is generated (called the seismoelectric and electroseismic
effect, respectively)
Seismoelectric interferometry
As already mentioned in the introduction, interferometry makes use of
the cross-correlation of responses at different receivers in order to
obtain the Green’s function of the field response between these
stations. In other words, it is the active response from one station to
the other. Below, a possible seismoelectric interferometry setting is
sketched:
Cross-correlation of electric (Ex) and acoustic signals
(Vz) from sources:
• located at the surface (a)
• or located in the bulk (c)
direct acoustic response of a current source (Jxe)
generating an electroseismic wave (b)
Possible applications
The results will identify the feasibility of this novel method in e.g.:
• Prospecting of aquifers/reservoirs
• Diagnostics of borehole conditions (well logging)
• Monitoring of hydrocarbon production
Contact
Delft University of Technology
Faculty of Civil Engineering and Geosciences
Department of Geotechnology
Section of Applied Geophysics and Petrophysics
[email protected]
[email protected]
[email protected]