Numerical Simulation of the Effect of a DC Electric Field on Seismic Wave Propagation with the Pseudospectral Time Domain Method

We have modeled the effect of a direct current (DC) electric field on the propagation of seismic waves by the pseudospectral time domain (PSTD) method, based on a set of governing equations for the poroelastic media. This study belongs to the more general term of the seismoelectric coupling effect. The set of physical equations consists of the poroelastodynamic equations for the seismic waves and the Maxwell’s equations for the electromagnetic waves; the magnitude of the seismoelectric coupling effect is characterized by the charge density, the electric conductivity, the Onsager coefficient, a function of the dielectric permittivity, the fluid viscosity, and the zeta potential. The poroelastodynamic vibration of a solid matrix generates an electric oscillation with the form of streaming current via the fluctuation of pore pressure. Meanwhile, fluctuating pore pressure also causes oscillatory variation of the electric resistivity of the solid matrix. The simulated poroelastic wave propagation and electric field variation with an existing background DC electric field are compared with the results of a physical experiment carried out in an oilfield. The results show that the DC electric field can significantly affect the propagating elastic energy through the seismoelectric coupling in a wide range of the seismic frequency band.