Solution of an unstable inverse problem: wave source evaluation from observation of velocity distribution

This paper illustrates how to estimate a wave source generating a wave system, including local waves, with the assumption of linear dispersive waves of two dimensions. The estimation of wave source is realized by using an inverse problem. Unfortunately, the inverse problem is ill-posed in the sense of stability, since the wave source information included in local waves diminishes as the distance from the wave source increases. In the area of applied mathematics, there are well-developed methods to tackle ill-posed problems, which are called regularizations. In this paper, three different regularizations which are well known in applied mathematics are introduced and investigated to learn whether they are applicable to the present problem of the estimation of wave source. From the numerical experiments, it is shown that the estimation is realized by the regularizations introduced in this study, so that they can be applied to the determination of a wave source generating a wave system including local waves. Received: June 6, 2000 / Accepted: February 7, 2001