  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.
