Abstract: With the increasing requirements for reservoir precision in oil and gas exploration, the traditional seismic wave propagation theory based on the pure elasticity assumption can no longer effectively describe the dispersion and attenuation characteristics exhibited by seismic waves during propagation caused by rock viscoelasticity and pore structure in complex media. Seismic forward modeling in poro-viscoelastic media has become an important research tool for accurately characterizing such coupling effects, among which the generalized standard linear solid model and its memory variable approach reduce computational complexity by introducing auxiliary differential equations to replace convolution integrals, thus realizing effective simulation of frequency-dependent attenuation. However, under the conditions of complex reservoirs with strong nonlinearity and strong attenuation, traditional algorithms still face the dilemma of balancing computational accuracy and efficiency. This paper introduces the generalized recursive convolution method to convert the time convolution term in the constitutive equation into a high-order recursive formula, directly updating the wavefield state recursively in the time domain, avoiding the global storage of historical data and repeated integral operations, and significantly reducing computational complexity and memory consumption. Numerical experiments show that in the homogeneous model, the proposed method in this paper improves computational efficiency by approximately 9% compared with the traditional memory variable method while achieving higher wavefield amplitude fidelity; In the two-layer anisotropic model, it can depict interlayer reflection and wave mode conversion more clearly than the memory variable method, significantly improving the accuracy of wavefield simulation; And in the complex heterogeneous Marmousi model, this method can effectively simulate the wavefield interference and slow-wave attenuation characteristics under strongly undulating interfaces.

Key words: poroelastic medium, seismic forward modeling, seismic wave propagation, generalized recursive convolution, numerical simulation, wavefield simulation