Seismic dispersion, attenuation and frequency-dependent anisotropy in a fluid-saturated porous periodically layered medium

The White model is generally used to quantify seismic dispersion and attenuation caused by interlayer wave-induced fluid flow. However, this model derives P-wave dispersion and attenuation only in the direction perpendicular to the layer. Thus, in this study, we derive the exact analytical solutions for full effective stiffness coefficients of a fluid-saturated layered porous medium so as to calculate the angle-dependent seismic dispersion and attenuation and frequency-dependent anisotropy. The analytical solution for fluid pressure is derived using Biot's equations of quasi-static poroelasticity. Then, the mean stress or strain is obtained through its relationship with fluid pressure, and the stress-strain value is used to derive the effective stiffness coefficients. This is followed by the calculation of the angle-dependent seismic dispersion and attenuation and frequency-dependent anisotropy. Our results show that the layered medium with alternating gas- and brine-saturated layers having the same matrix is isotropic at all frequencies. However, the layered medium with periodically distributed highly porous, thin layers shows significant frequency-dependent anisotropy. In the case of P wave, the largest magnitudes of dispersion and attenuation are observed in the direction perpendicular to the layer, while those for SV wave occur at the incident angle of around 45 degrees. When our model is compared with the previous models, the low- and high-frequency limits of our model are found to be identical to the poroelastic Backus averaging. In addition, the widely used single relaxation function approximation is found to be a good approximation of our exact solutions. Our proposed model is easy to use and can be applied in the seismic exploration of the layered earth.