Wave propagation model considering cross-scale attenuation mechanism and pressure influence

Abstract This study develops a wave propagation model for predicting seismic dispersion and attenuation that considers multi-scale attenuation mechanisms. The modeling approach comprises the following steps: First, substitute the rock physics parameters into the Biot-Rayleigh model to calculate the compressional wave velocity, subsequently the bulk modulus of rock skeleton is inferred from the velocity using Gassmann's equation, and thus the mesoscopic-scale attenuation mechanism of seismic waves is considered. Next, substitute the rock physics parameters into Gurevich's model considering the impact of pressure to calculate the bulk modulus of rock skeleton directly to integrate into the mechanism of attenuation occurred at microscopic scale. Then, the two bulk moduli are combined via a weighted summation, thereby obtaining an effective bulk modulus of rock skeleton that considers cross-scale attenuation mechanism. Finally, the effective modulus is incorporated into a dynamic system, where the framework of Biot's equations is employed. Based on plane wave analysis, dispersion and attenuation are predicted. The results reveal that the mesoscopic effect saturates quickly at low pressures, while the microscopic mechanism contributes more gradually over a broader pressure range. However, when both mechanisms are strongly activated, their interaction may suppress attenuation at high pressures, indicating a nonlinear coupling between the mesoscopic and microscopic attenuation mechanisms. This feature highlights the physical interpretability and adaptability of this approach in predicting the seismic wave attenuation characteristics at different scales, laying a foundation for high-precision seismic modeling and inversion in complex geological porous media.