On effects of inhomogeneity on anisotropy in Backus average

TL;DR

This paper investigates how inhomogeneity in layered isotropic media influences the anisotropy of the Backus average, revealing proportionality between inhomogeneity and anisotropy strength, with a special case leading to isotropy.

Contribution

It establishes a relationship between inhomogeneity and anisotropy in Backus averaging and identifies conditions under which the average remains isotropic.

Findings

Anisotropy strength increases with inhomogeneity.

Uniform rigidity across layers results in isotropic average.

Inhomogeneity and anisotropy are generally proportional.

Abstract

In general, the Backus average of an inhomogeneous stack of isotropic layers is a transversely isotropic medium. Herein, we examine a relation between this inhomogeneity and the strength of resulting anisotropy, and show that, in general, they are proportional to one another. There is an important case, however, in which the Backus average of isotropic layers results in an isotropic -- as opposed to a transversely isotropic -- medium. We show that it is a consequence of the same rigidity of layers, regardless of their compressibility. Thus, in general, the strength of anisotropy of the Backus average increases with the degree of inhomogeneity among layers, except for the case in which all layers exhibit the same rigidity.