The inverse problem of the electroseismic conversion

Abstract:

In fluid-saturated porous media, electromagnetic fields couple with seismic waves through the electroseismic conversion. Indeed, at the contact interface of pore fluid and solid rock, an electrical double layer (EDL) is formed. When electric or magnetic fields impinge on the EDL, the electrokinetic phenomenon causes movement of the fluid relative to rock frame and thus emits seismic waves, which can be remotely detected.

Pride (1994) derived the governing model of electroseismic conversion, in which Maxwell's equations are coupled with Biot's equations through an electrokinetic mobility parameter. In 2005, White established a forward model for the electroseismic method by solving Maxwell's equations and the elastic wave equation sequentially, while the initial amplitude of elastic waves is calculated according to Pride's equations with a high-frequency asymptotic theory.

In 2007, Thompson et al. at ExxonMobil presented results of three field experiments of electroseismic conversion in Texas and Canada. By using specially designed electrical source waveforms, these tests showed that the electroseismic conversion at depth up to 1000 m can be detected with geophones placed on the surface. Their tests also succeeded in identifying several gas sands and delineating hydrocarbon accumulations.

In this project, we study the inverse problem for electroseismic conversion. We divide the inverse problem in two steps, the inverse source problem of Biot's equations and the inversion of Maxwell's equations with internal data. For the first step, with low frequency assumption, we derive a quantitative estimate of the Gassmann approximation and prove the Lipschitz-type stability of recovering the sources from the boundary seismic measurements. For the second step, we study the coupling effects between seismic waves and EM waves, and achieve a Lipschitz-type stability estimate of the reconstruction of electrical parameters. By combining these two steps, we obtain a stability estimate of recovering electric parameters from the surface measurements of seismic waves. Therefore, we conclude that, with particularly chosen electric sources, the inverse problem is well-posed.