Seismic wave dispersion and attenuation resulting from multiscale wave-induced fluid flow in partially saturated porous media

Sedimentary rocks are typical heterogeneous porous media induced by fluid patches and pore fabric. It is well acknowledged that the wave-induced fluid flow (WIFF) at different scales will cause seismic wave dispersion and attenuation in a wide frequency range. Consequently, modelling wave dispersion and attenuation due to multiscale WIFF is of significance for reservoir characterization from multiscale geophysical measurement and interpretation. In this study, the multiscale WIFF in partially saturated porous media, including global, 3-D mesoscopic and squirt flows, are investigated. And we derive the wave equations by introducing the Rayleigh's spherical bubble oscillation and the porous grain models into Santos poroelasticity theory. Numerical simulations demonstrate that the multiscale model can interpret the transition of rock states as frequency increases and capture the broad-band seismic wave dispersion and attenuation characteristics, which are directly associated with the heterogeneity scale. Besides, the multiscale model can be degraded to a single- or dual-scale model under specific parameters. We validate the proposed model with board-band experimental data of partially saturated sandstones, confirming its comprehensive characterization of velocity dispersion and attenuation over a wider range of frequencies. Moreover, the model successfully interprets the unrelaxed state of partially saturated rock at ultrasound frequencies.