A Numerical Investigation of Cross-Hole Seismoelectric Conversion

The seismoelectric method corresponds to the measurement of electromagnetic disturbances associated with the passage of seismic waves in a porous material. This coupling is due to the existence of the electric double layer at the solid/water interfaces. We consider the case of two parallel wells. A seismic source is triggered in the first well and sensors (electrodes/geophones) are inserted in the second well. Before the arrival of the seismic energy to the second well, electromagnetic disturbances can be recorded that are associated with electromagnetic conversion of the mechanical energy. This conversion occurs when the seismic wave reaches hetrogeneities located between the two wells. These hetrogeneities are characterized by discontinuities in the electrical or mechanical properties. Using the equations of poroelasticity (Biot Theory) and electrokinetic conversion (Maxwell equation in the quasi electrostatic limit), we model the seismoelectric conversion using the finite element method with Comsol 3.5. We developed also an inverse modeling algorithm to image the position of the hetrogeneities between the two wells through the use of the recorded seismoelectric signals recorded in the second well. To reach this goal, we use a source localization technique based on Tikhonov regularization with the use of compactness in the regularization term of the cost function.