# On relations of anisotropy and linear inhomogeneity using Backus average

## TL;DR

This paper derives an analytical relationship linking anisotropy and linear inhomogeneity in layered media, using Backus average and seismological data to validate the theoretical model.

## Contribution

It introduces a new analytical system connecting anisotropy parameters with inhomogeneity, constrained by field data to ensure practical applicability.

## Key findings

- Derived a system of equations relating Thomsen parameters to inhomogeneity.
- Validated the analytical relationship using two seismological methods on field data.
- Provided insights into the anisotropy-inhomogeneity relationship in sedimentary layers.

## Abstract

The anisotropy of an equivalent medium resulting from the Backus (1962) average is induced by the vertical inhomogeneity among its constituent layers. The velocity field of the constituent isotropic layers increases linearly with depth, which is assumed to be a good seismological description of sedimentary layers Slotnick (1959). We derive an analytical relationship between the anisotropy, characterized by the Thomsen (1986) parameters, and the linear inhomogeneity parameters, which forms a system of three equations for nine unknowns. To obtain well-posedness, we constrain the problem by considering two seismological methods applied to field data. We use the results from the two methods, for a particular region of interest, to assess the validity of the analytical relation.