Finite difference modeling of electroacoustic logging response in fluid-saturated porous formation

Acoustic and electromagnetic (EM) waves are coupled in fluid-saturated porous media because of electrokinetic effect. Electroacoustic (E-A) logging describes the acoustic response to an EM source in a fluid-filled borehole surrounded by a porous medium. In this work a finite difference method is proposed to model the axisymmetric acoustic field of E-A logging in a horizontally stratified formation. Using the assumption that the reverse influence of the acoustic field on the EM field in the formation is negligible, the EM and acoustic fields are decoupled and the EM field can be calculated firstly. When the formation is horizontally stratified, the solution of the EM field with low frequency can be derived by ignoring the existence of the borehole. Then the acoustic field can be finite difference modeled through adding an electrokinetic source term derived from the primary EM field. In order to verify this method, we give an example of simulating the acoustic waveforms of E-A logging in a homogeneous porous formation for comparison with those obtained by the analytical method in Hu et al. (2007). It is concluded from the comparison of waveforms that the finite difference method is feasible and can be contributed to E-A logging in a horizontally stratified formation.