Randomly distributed unit sources to enhance optimization in tsunami waveform inversion

Determination of sea surface deformation generated by earthquakes is crucial to the success of tsunami modeling. Using waveforms recorded at measurement stations and assuming that the rupture velocity is much faster than the tsunami wave celerity, sea surface deformation caused by a tsunamigenic earthquake can be inferred through an inversion operation using the Green's function technique. However, this inversion method for tsunami waveforms possesses a limitation, in that the inverse matrix does not always exist because of the non-uniqueness of the solution. In addition to the large number of unknown parameters, which might produce many local optima on the misfit function measure, the search towards optimality is confined by the uniform distance of unit sources used in the regular Green's function. This study proposes a new method to both optimize the determination of the unknown parameters and introduce a global optimization method for tsunami waveform inversion. The method has been tested using an artificial tsunami source with real bathymetry data. A significant improvement is achieved by stochastically searching for an optimal distribution of unit source locations prior to the inversion.