Imaging using cross-hole seismoelectric tomography

We propose a new cross-hole imaging approach based on seismoelectric conversions associated with the transmission of seismic waves from seismic sources located in a borehole to receivers electrodes located in a second borehole. The seismoelectric seismic-to-electric problem is solved using Biot theory coupled with a generalized Ohm's law with an electrokinetic coupling term. The components of the displacement of the solid phase, the fluid pressure, and the electrical potential are solved using a finite element approach with PML boundary conditions for the seismic waves and boundary conditions mimicking an infinite material for the electrostatic problem. We have developed an inversion algorithm using the electrical disturbances recorded in the second borehole to localize the position of the heterogeneities responsible for the seismoelectric conversions. Because of the ill-posed nature of the inverse problem, regularization is used to constrain the solution at each time in the seismoelectric time window comprised between the time of the seismic shot and the time of the first arrival of the seismic waves in the second borehole. All the inverted volumetric current source densities are stacked to produce an image of the position of the heterogeneities between the two boreholes. Two simple synthetic case studies are presented to test this concept. The first case study corresponds to a vertical discontinuity between two homogeneous sub-domains. The second case study corresponds to a poroelastic inclusion embedded into an homogenous poroelastic formation. In both cases, the position of the heterogeneity is fairly well-recovered using only the electrical disturbances associated with the seismoelectric conversions. ?? 2011 Society of Exploration Geophysicists.