# On constraints imposed on a transversely isotropic elasticity tensor

## TL;DR

This paper examines physical constraints on transversely isotropic elasticity tensors, focusing on stability and seismology-based restrictions, and explores their effects through numerical examples.

## Contribution

It provides a detailed analysis of how stability and seismological constraints influence the properties of TI elasticity tensors, with numerical illustrations.

## Key findings

- Stability conditions impose fundamental restrictions on TI tensors.
- Seismology-based restrictions affect the range of feasible elasticity parameters.
- Numerical examples demonstrate the impact of these constraints on known elasticity constants.

## Abstract

We discuss several physical constraints imposed on elasticity parameters of a transversely isotropic (TI) tensor. There are three types of restrictions we investigate; a fundamental one of stability conditions, and two additional ones, commonly considered in seismology. The first commonly considered restriction comes from an assumption of a wave with a greater speed in the horizontal than vertical direction. The second constitute the assumption that quasi-P wave is faster than quasi-S waves. We show several numerical examples to examine how these restrictions affect a TI tensor with known values of certain elasticity constants that could be acquired from the vertical or horizontal measurements.