Homogenization of Porous Thin Layers With Internal Stratification for the Estimation of Seismic Reflection Coefficients

Abstract

Stratified thin layers often present a prominent mechanical contrast with regard to the embedding background and, hence, are important targets for seismic reflection studies. An efficient way to study the reflectivity response of these thin layers is to employ their homogenized viscoelastic equivalents. We aim to homogenize a simple, yet realistic, thin-layer model, which is composed of a finite non-periodic sequence of homogeneous porous strata embedded in a background deemed impermeable at the seismic frequencies. The overarching objective is to reproduce the reflectivity response of such stratified thin layers. However, the estimation of the equivalent moduli is inherently affected by the boundary conditions (BC) associated with the embedding background. Therefore, classical homogenization procedures, which assume the existence of a periodic structure, are not readily applicable. We, therefore, propose a novel homogenization procedure that incorporates naturally the appropriate BC. To this end, we consider a sample that includes both a part of the background and a section of the thin layer, to which we apply classical oscillatory relaxation tests. However, we estimate the average of stress and strain components only over the thin layer section of interest. To test the accuracy of the method, we consider a sandstone composed of two strata saturated with different fluids embedded in impermeable half-spaces. After estimating the corresponding equivalent moduli, we compare the resulting P-wave reflectivities with those obtained using the original model. Our results show that the inferred viscoelastic equivalent closely reproduces the reflectivities of the stratified thin layer in the seismic frequency range.