A high-order finite-difference scheme for time-domain modeling of time-varying seismoelectric waves

Abstract

Simulation of the seismoelectric effect serves as a useful tool to capture the observed seismoelectric conversion phenomenon in porous media, thus offering promising potential in underground exploration activities to detect pore fluids such as water, oil and gas. The static electromagnetic (EM) approximation is among the most widely used methods for numerical simulation of the seismoelectric responses. However, the static approximation ignores the accompanying electric field generated by the shear wave, resulting in considerable errors when compared to analytical results, particularly under high salinity conditions. To mitigate this problem, we propose a spatial high-order finite-difference time-domain (FDTD) method based on Maxwell's full equations of time-varying EM fields to simulate the seismoelectric response in 2D mode. To improve the computational efficiency influenced by the velocity differences between seismic and electromagnetic waves, different time steps are set according to the stability conditions, and the seismic feedback values of EM time nodes are obtained by linear approximation within the seismic unit time step. To improve the simulation accuracy of the seismoelectric response with the time-varying EM calculation method, finite-difference coefficients are obtained by solving the spatial high-order difference approximation based on Taylor expansion. The proposed method yields consistent simulation results compared to those obtained from the analytical method under different salinity conditions, thus indicating its validity for simulating seismoelectric responses in porous media. We further apply our method to both layered and anomalous body models and extend our algorithm to 3D. Results show that the time-varying EM calculation method could effectively capture the reflection and transmission phenomena of the seismic and EM wavefields at the interfaces of contrasting media. This may allow for the identification of abnormal locations, thus highlighting the capability of seismoelectric response simulation to detect subsurface properties.

A Numerical Study of Electrokinetically Generated Pre-Earthquake Geoelectric Fields in Layered Porous Media

“…Numerical methods such as the finite element method, spectral-element method, and finite-difference method are capable of handling lateral heterogeneities and anisotropies. These methods have been developed to solve the 2-D modeling for dynamic scenarios, providing insights into the behavior of systems under varying conditions (Han & Wang 2001;Haines & Pride 2006;Gao et al 2019;Ji et al 2022). Therefore, extending them to the quasi-stationary case could be a promising future task.…”

Simulation of Seismoelectric Waves Using Time-Domain Finite-Element Method in 2D PSVTM Mode

“…However, the quasi-static approximation has errors in the accompanying electric field caused by the P-S wave. This is because the ability of the S wave to induce the electric field increases with increasing salinity, and errors will occur when ignoring the accompanying electric field of the S wave [37,38]. In summary, the quasi-static approximation method is effective only in the case of low salinity, while errors may occur in the case of high salinity.…”

“…Tohti et al, (2020) calculated the seismoelectric responses for an explosive source based on the time-domain FD (FDTD) algorithm [35], and Tohti et al, (2022) further expanded the seismoelectric coupling equations in 3D orthotropic media to simulate the seismoelectric signal propagating in orthotropic media [36]. Ji et al, (2022) proposed an adaptive time-step high-order FD scheme based on full Maxwell's equations for a time-varying EM field to simulate the seismoelectric responses in heterogeneous porous saturated media [37]. For the methods that solve the frequency-domain problems, a frequency-time conversion technique needs to be applied to calculate the time-domain responses, and the calculation accuracy is related to the selected frequency range.…”

Time‐domain finite element method based on arbitrary quadrilateral meshes for two‐dimensional SHTE mode seismoelectric and electroseismic waves modelling

“…Ji et al. (2022) proposed a time‐varying high‐order FDTD method based on the full Maxwell's equations to simulate the seismoelectric responses. Li et al.…”

“…Wang et al (2023) proposed a frequency-domain FE method to simulate 2D SHTE mode seismoelectric and electroseismic waves and applied this method in hydrocarbon exploration and monitoring of time-lapse pollutants. Ji et al (2022) proposed a time-varying high-order FDTD method based on the full Maxwell's equations to simulate the seismoelectric responses. Li et al (2023) proposed a time-domain FE (FETD) method based on the full-wave EM equations to simulate seismoelectric waves, which improved computational efficiency by a combination of explicit and implicit recursion.…”