Multiparameter identification of a lossy fluid-like object from its transient acoustic response - Scotti, T.; Wirgin, A. (Inverse problems in science and engineering, 2014)
A transient acoustic wave multiparameter inverse problem is studied. The aim is to simultaneously retrieve three constitutive parameters and one geometrical parameter of a lossy fluid-like cylinder by nonlinear full-wave inversion of synthetic data. Contrary to most publications treating this subject, it is assumed herein that the retrieval model is not identical to the data model, this being so because some of the parameters (priors) in the retrieval model are different (by the simple fact of being more or less unknown) from their true counterparts in the data model. This so-called model discordance, which is the usual situation in real-world inverse problems, is a source of errors for the retrieval of the other parameters. Moreover, it is a source of non-uniqueness and instability, a fact revealed by the employment of a properly-tuned Nelder-Mead downhill Simplex optimization algorithm, and which requires a second-order regularization for its resolution. Retrieval errors as a function of prior uncertainty are computed, and found to be large, for various model discordance scenarios involving one or two uncertain priors, for data with and without noise.