Time-Domain Modeling of Anisotropic Poro-Viscoelasticity: A Unified Framework for Biot and Squirt Flow Mechanisms

Summary

Modeling seismic wave attenuation and dispersion in fluid-saturated porous media is essential for reservoir characterization; however, significant challenges remain in accurately capturing the effects of anisotropy. Unified theoretical frameworks that combine Biot and squirt flow mechanisms have often been limited by two key factors: they are typically based on the isotropic assumptions and rely on oversimplified physical models for squirt flow. Consequently, a time-domain numerical implementation for advanced, physically-based anisotropic squirt models has been lacking. This study presents a unified theoretical and numerical framework that, for the first time, integrates Biot’s theory of anisotropic poroelasticity with a state-of-the-art model for anisotropic squirt flow based on one-dimensional fluid pressure diffusion in cracks partially connected to spherical pores. The core innovation is a time-domain implementation achieved through a semi-analytical conversion of the complex, frequency-dependent frame moduli into a Generalized Zener Model representation. With parameters optimized via a genetic algorithm, the system is expressed as a set of differential equations with memory variables, enabling efficient finite-difference time-domain (FDTD) simulations in complex heterogeneous media. Our numerical results demonstrate that the model accurately captures frequency- and angle-dependent velocity dispersion and attenuation in VTI media due to squirt flow in the seismic-to-sonic frequency band. The FDTD algorithm is rigorously validated against analytical solutions, and simulations in heterogeneous media highlight its capability to capture spatially-varying anisotropic attenuation effects. This framework bridges a critical gap between advanced rock physics theory and practical wavefield simulation, providing an accurate forward modeling tool for interpreting seismic data to characterize complex reservoir rocks.