Optimal acoustic measurements (Q2706096)

Using the applied operator theory, the authors show how to find some information about an inaccessible half-space from acoustic measurements made in the accessible half-space. The basic concept is the so-called distinguishability (denoted by \(\varepsilon\)) of two operators \(A_1\) and \(A_2\) under a test field denoted by \(f\). The optimum \(f\) is defined as that for each \(\varepsilon\) is maximal. It is shown that there are three ways to get the optimum: the boundary map approach, the source approach, and the scattering operator approach. This last is used here to solve the problem. The authors propose an adaptive iterative method for producing the best fields including time-reversal mirror, and prove the convergence of this algorithm. Finally, some open questions are discussed.