Some properties of the inverse operator for a tsunami source recovery

摘要

The application of an inversion method to the problemof recovering the initial water elevation field generating a tsunami isconsidered. This article addresses the usually ill-posed problem of thehydrodynamical inversion of remote measurements of water-level datawithout any a priori information on a source but its very general spatiallocalization. The tsunami wave propagation is considered within thescope of the linear shallow-water theory. The ill-posed inverse problemat hand is regularized by means of the least square inversion usingthe truncated SV D approach. Some properties of inverting operatorin the context of retrieving a tsunami source are studied numerically.The goodness of the inversion is defined by the relative errors of thetsunami source reconstruction. As the result, we find the dependence ofthe goodness of the inversion in terms of the number of receivers, theirazimuthal coverage and the frequency band. The applied approach allowsone to control the instability of the numerical solution and to obtain anacceptable result in spite of the ill-posedness of the problem and makesit possible to predict a probable quality of the inversion by a certainobservational system. This result should be kept in mind when designinga tide-gauge network to study a tsunami source.