Seismic Wave Attenuation and Dispersion in Fluid-Saturated Rocks: A Unified Poro-Viscoelastic Model Incorporating Squirt Flow and Viscoelasticity into the Biot Equations

Seismic wave propagation in fluid-saturated rocks exhibits complex attenuation and dispersion characteristics across a wide frequency range, which are influenced by various mechanisms of energy dissipation. This study introduces an integrated poro-viscoelastic model that combines three primary attenuation processes: Biot global flow, squirt flow, and the intrinsic viscoelasticity of the solid skeleton. A comprehensive time-domain Biot-crack approach is developed by incorporating a one-dimensional squirt flow representation within the Biot framework. The squirt flow mechanism is described using a Generalized Zener Model (GZM), which approximates its core term through a rational function, with coefficients optimized via a genetic algorithm. Furthermore, the model is extended to the poro-viscoelastic medium by incorporating the standard linear solid (Zener) viscoelastic model to account for intrinsic frame losses. This unified methodology effectively identifies three distinct attenuation peaks across the frequency spectrum, each corresponding to a specific mechanism: intrinsic frame viscoelasticity at low frequencies, squirt flow at intermediate frequencies, and Biot flow at higher frequencies. Rigorous validation through finite-difference time-domain (FDTD) simulations in heterogeneous media confirms the model's reliability, which exhibits significant wave attenuation and velocity dispersion effects. This comprehensive framework enhances the characterization of wave behavior in fluid-saturated rocks, with important implications for reservoir characterization and seismic interpretation.