# Sensitivity of Love and quasi-Rayleigh waves to model parameters

## TL;DR

This paper investigates how Love and quasi-Rayleigh surface waves respond to changes in model parameters like elasticity, frequency, and layer thickness, providing insights into their sensitivities for seismic analysis.

## Contribution

It offers a detailed sensitivity analysis of Love and quasi-Rayleigh waves without simplifying assumptions, including a novel derivation of the quasi-Rayleigh dispersion relation.

## Key findings

- Derived and plotted sensitivity coefficients for Love waves.
- Identified optimal frequency for layer thickness determination.
- Compared derivations of quasi-Rayleigh relation, highlighting discrepancies.

## Abstract

We examine the sensitivity of the Love and the quasi-Rayleigh waves to model parameters. Both waves are guided waves that propagate in the same model of an elastic layer above an elastic halfspace. We study their dispersion curves without any simplifying assumptions, beyond the standard approach of elasticity theory in isotropic media. We examine the sensitivity of both waves to elasticity parameters, frequency and layer thickness, for varying frequency and different modes. In the case of Love waves, we derive and plot the absolute value of a dimensionless sensitivity coefficient in terms of partial derivatives, and perform an analysis to find the optimum frequency for determining the layer thickness. For a coherency of the background information, we briefly review the Love-wave dispersion relation and provide details of the less common derivation of the quasi-Rayleigh relation in an appendix. We compare that derivation to past results in the literature, finding certain discrepancies among them.