On inhomogeneity parameters for Backus average

TL;DR

This paper examines five inhomogeneity parameters for layered isotropic media, revealing their insights into intrinsic inhomogeneity and conditions for isotropy in Backus averaging.

Contribution

It introduces and analyzes five inhomogeneity parameters, highlighting their effectiveness over Thomsen parameters and establishing the condition for isotropy in Backus averages.

Findings

Backus average of isotropic layers is isotropic iff γ=0.

Zero δ and ε do not imply isotropy.

Five parameters provide deeper insight into inhomogeneity.

Abstract

In this paper, we discuss five parameters that indicate the inhomogeneity of a stack of parallel isotropic layers. We show that, in certain situations, they provide further insight into the intrinsic inhomogeneity of a Backus medium, as compared to the Thomsen parameters. Additionally, we show that the Backus average of isotropic layers is isotropic if and only if $\gamma=0$. This is in contrast to parameters $\delta$ and $\epsilon$, whose zero values do not imply isotropy.