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Hausdorff moments in two-dimensional inverse acoustic problems

This paper is concerned with the nonlinear inverse acoustic problem of the construction of the density/speed of sound distribution within a domain, given spectral data on the boundary of the domain. It is assumed throughout that only a finite set of data is known and some attention is given to error-prone data. A moments approach to the solution of this problem is outlined, together with associated error estimates. Results of numerical experiments on model problems are used to demonstrate the viability of the approach and the accuracy of the error estimates. The paper is restricted to two-dimensional problems, but the technique remains applicable for higher dimensions.