A Hybrid Spectral-Element and Finite-Element Framework for Three-Dimensional Full-Wave Seismoelectric Modeling in VTI Porous Media

Assessing the contribution of electrokinetic effects to seismic electromagnetic signals requires forward methods capable of simulating coupled responses in anisotropic formations and complex geological models. We extend a three-dimensional hybrid spectral-element–finite-element time-domain framework to vertically transversely isotropic (VTI) porous media, incorporating directional stiffness, permeability and tortuosity. After decoupling Pride’s equations, the framework solves Biot’s equations using explicit time discretization to obtain the filtration-velocity field, which supplies the current source for an implicit time discretization of Maxwell’s equations to calculate the coseismic electric field. The sequential scheme permits separate time steps for the poroelastic and electromagnetic calculations. After verifying the accuracy of the implementation, we evaluated the framework through half-space simulations and a modified salt-dome example. The half-space results show that elastic anisotropy changes seismic waveform shape and the corresponding electric response even when electromagnetic transport coefficients remain unchanged. In the controlled comparisons, one axial parameter at a time is reduced by 20%: drained stiffness, permeability or tortuosity. Permeability and tortuosity changes produce displacement differences below 0.16%, with electric-field differences of 0.97–1.57% and 1.75–4.97%, respectively. These electric-field differences exceed the electric-waveform variations in the U0 case with the tested mesh and time-step refinements. Hydraulic perturbations therefore produce small displacement changes accompanied by more pronounced changes in the coseismic electric field. The modified salt-dome example simulates an irregular porous inclusion within a VTI background, showing localized electric responses and out-of-plane electric-field components where the corresponding displacement components are weak. A matched isotropic/VTI background comparison further quantifies the electric-waveform changes in the same salt-dome geometry. These comparisons characterize 20% single-parameter finite changes at one receiver for the prescribed model and source. The salt-dome results illustrate the spatial response of a complex model; quantitative field application requires calibration and comparison with observations using site-specific material parameters, source information and instrument responses.