Poroelastic effect on the shear wave in the systems of alternating solid and viscous fluid layers: theory vs numerical modeling

Abstract

The attenuation and dispersion of shear waves in fluid‐saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov's exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long‐wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The new approach developed in this study enables an explicit analysis of solid/viscous fluid layers in a broad range of frequencies and of fluid viscosities. The model appears to be suitable for numerical testing using a viscoelastic modeling approach. The displacement‐stress rotated staggered finite‐difference (FD) grid technique is applied to solve the elastodynamic wave equation. Viscosity is implemented by using a generalized Maxwell body. The established numerical model and carried out computations show very good agreement with the theoretical dispersion curves. This numerical exercise demonstrates the capability of the developed method to simulate the poroelastic phenomena and opens new prospective for the applications in the digital core technology.