# Estimating the material parameters of an inhomogeneous poroelastic plate from ultrasonic measurements in water

## TL;DR

This paper introduces a Bayesian approach using Markov Chain Monte Carlo to estimate multiple inhomogeneous poroelastic parameters from ultrasonic water measurements, providing reliable uncertainty quantification and revealing material heterogeneities.

## Contribution

It presents a novel Bayesian inverse problem framework for estimating numerous poroelastic parameters with uncertainty quantification from ultrasonic data.

## Key findings

- The Bayesian method accurately estimates inhomogeneous poroelastic parameters.
- Uncertainty quantification reveals heterogeneities in the material.
- The approach improves reliability over traditional least squares methods.

## Abstract

The estimation of poroelastic material parameters based on ultrasound measurements is considered. The acoustical characterisation of poroelastic materials based on various measurements is typically carried out by minimising a cost functional of model residuals, such as the least squares functional. With a limited number of unknown parameters, least squares type approaches can provide both reliable parameter and error estimates. With an increasing number of parameters, both the least squares parameter estimates and, in particular, the error estimates often become unreliable. In this paper, the estimation of the material parameters of an inhomogeneous poroelastic (Biot) plate in the Bayesian framework for inverse problems is considered. Reflection and transmission measurements are performed and 11 poroelastic parameters, as well as 4 measurement setup-related nuisance parameters, are estimated. A Markov chain Monte Carlo algorithm is employed for the computational inference to assess the actual uncertainty of the estimated parameters. The results suggest that the proposed approach for poroelastic material characterisation can reveal the heterogeneities in the object, and yield reliable parameter and uncertainty estimates.