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It has become popular to estimate the Biot parameters of poro-elastic media by using inverse methods. That is, measurements of absorption coefficient and/or transmission loss are used as inputs to an optimization procedure that adjusts the Biot parameters to match the measurements. Software packages are available to perform these operations. To be successful, the models used to match the data must accurately represent the physics of the measurement. However, existing software are based on transversely infinite, layered systems. Such models cannot represent data measured in standing wave tubes when the elasticity of the edge-constrained sample is significant. Here, an approach based on a finite element model of the sample in the tube will be described. It will be demonstrated that this approach makes it easier to estimate the stiffness parameters of a porous sample. Further, a technique involving singular value decomposition of a sensitivity matrix derived from a linearized representation of the absorption coefficient and transmission coefficient near the solution point will be introduced. This procedure gives a clear indication of how many parameters can be estimated from a given data set and gives guidance as to the type of data and the frequency ranges that give the best results.
Bolton et al. (Thu,) studied this question.