Seismic wave propagation in biphasic viscoelastic TTI media Part I: theory

Abstract The biphasic viscoelastic tilted transversely isotropic (TTI) model provides a comprehensive framework for characterizing the viscoelastic behavior, stratification, and anisotropic fracture development in subsurface porous media. Previous research has established the governing equations for the biphase viscoelastic TTI media and conducted forward simulation to capture the essential wave propagation characteristics. However, the detailed behavior of slow compressional (P) wave and the influence of anisotropy on the biphase of the media is still not well understood. To address this, this paper derived a set of wave equations for describing biphasic viscoelastic TTI media by integrating the Carcione’s viscoelastic and anisotropy systems of solid skeleton with the Biot’s poroelastic theory. A high-order staggered grid finite-difference method is then used to simulate seismic waves for the first-order velocity-stress equations of biphasic viscoelastic TTI media. Compared with previous studies, this paper derives the wave equation of a new form of biphase viscoelastic TTI media. Numerical simulations demonstrate excellent consistency with classical Biot theory predictions while effectively capturing the combined effects of viscoelasticity and TTI anisotropy. These results confirm the physical relevance of the model parameters and enhance the understanding of wave propagation in complex biphasic media.