Integrating the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) in the Biot viscosity extended framework

The viscosity extended Biot theory [Sahay, Geophysics (2008)] incorporates pore fluid viscosity in the constitutive relation of the classical Biot theory. The strain rate term due to pore fluid viscosity turns the zero velocity slow S wave mode into a diffusive process. In this framework, it is claimed that fast P and S waves bleed energy when the slow S wave is generated at an interface or at a discontinuity. On the other hand, the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) [Chotiros and Isakson, JASA (2004)] models the grain to grain contact as compression and shear relaxation processes and obtains a causal poro-elastic frame response. In this work, we incorporated the grain to grain contact physics in the constitutive relation of the Biot theory and integrated it into the viscosity extended Biot framework. With realistic parameters, the fast S wave phase velocity and attenuation in the integrated model show a significant difference over a range of frequencies when compared to BICSQS. Additionally, this integrated model may provide a more accurate match for the measured reflection coefficient.