Randomly distributed unit sources to enhance optimization in tsunami waveform inversion

In tsunami waveform inversion using the conventional Green's function technique, an optimal solution is sometimes difficult to obtain because of various factors. 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. We utilize a genetic algorithm that further enhanced by a pattern search method to find an optimal distribution of unit source locations prior to the inversion. Unlike the conventional method that characterized by equidistant unit sources, our method generates a random spatial distribution of unit sources inside the inverse region. This leads to a better approximation of the initial profile of a tsunami. The method has been tested using an artificial tsunami source with real bathymetry data. Comparison results demonstrate that the proposed method has considerably outperformed the conventional one in terms of model accuracy.

Tsunami Waveform Inversion of the 2007 Peru (Mw8.1) Earthquake

An earthquake shook the central-southern coast of Peru on August 15, 2007, as a coseismic effect a tsunami was generated, which flooded some villages and beach resorts and killed 3 people. From the analysis and signal processing of 10 tidal records, we obtained the parameters of the seismic source and the initial coseismic deformation through an inversion modeling, in which the synthetic signals are compared with the observed signals by a non-negative least square method. The maximum slip located on the southern part of the rupture geometry is 7.0 m. The calculated scalar seismic moment isM0= 1.99 × 1021Nm, equivalent to a magnitude ofMw8.1. We used these parameters to obtain a heterogeneous seismic source model, which was used as initial condition to simulate the tsunami propagation and inundation. We used the field survey observations to validate our source model.

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.