A Hybrid Spectral-Element and Finite-Element Framework for Three-Dimensional Full-Wave Seismoelectric Modeling
Abstract
Seismoelectric responses generated in fluid-saturated porous media contain indirect geophysical information related to subsurface interfaces, material contrasts, and electrokinetic coupling. Many three-dimensional simulations adopt a quasi-static electromagnetic approximation, which neglects displacement-current contributions and cannot provide a complete description of full-wave electromagnetic propagation. In this study, we present a hybrid spectral-element and finite-element time-domain framework for three-dimensional full-wave seismoelectric modeling based on the Pride–Biot equations and the magnetic vector potential–electric scalar potential (A–ϕ) formulation. The poroelastic wavefield is first computed using a high-order spectral-element method, and the resulting relative fluid–solid velocity is introduced as the source term for the electromagnetic problem. An implicit backward-difference scheme is employed to accommodate the substantial difference between seismic and electromagnetic wave speeds. The coupled A–ϕ systems are solved using a flexible generalized minimal residual method with an upper-triangular block preconditioner based on an approximate Schur complement and algebraic multigrid cycles. This solver strategy is adopted as a practical treatment for the large, sparse, nonsymmetric, and strongly coupled systems generated by the three-dimensional formulation. The proposed framework is validated through numerical experiments involving half-space and layered media, a fault damage zone model, and a modified SEG/EAEG salt-dome model. The results reproduce the expected coseismic and interfacial responses and demonstrate the accuracy, numerical stability, and computational feasibility of the method in heterogeneous three-dimensional structures. The framework provides an effective forward-modeling tool for analyzing full-wave seismoelectric responses and for generating synthetic data for future subsurface sensitivity and joint-inversion studies.