Computational methods for an inverse problem in acoustics

Abstract

The problem of computing normal velocities on the boundary of a region from pressure measurements on an interior surface is considered. The pressure satisfies the Helmholtz equation and is represented by a single layer potential. Once the density function is found, the normal velocities can be easily computed by applying a second kind of integral operator. The problem of solving for the density function from the interior pressure measurements is ill-posed. Regularization methods using the singular value decompostion and iterative methods, such as the conjugate gradient method for the normal equations, are compared for pressure data with noise. [Work supported by NSF and Cessna Aircraft Company.]