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 assum
ed throughout that only a finite set of data is known and some attenti
on is given to error-prone data. A moments approach to the solution of
this problem is outlined, together with associated error estimates. R
esults of numerical experiments on model problems are used to demonstr
ate the viability of the approach and the accuracy of the error estima
tes. The paper is restricted to two-dimensional problems, but the tech
nique remains applicable for higher dimensions.