A combined inverse tsunami problem

It is known that some of the parameters required for the direct simulation of tsunamis are the bottom relief characteristics and the initial perturbation data (a tsunami source). The seismic data about the source are usually obtained in a few tens of minutes after an event has occurred (the seismic waves velocity being about five hundred kilometers per minute, while the velocity of tsunami waves is less than twelve kilometers per minute). A difference in the arrival times of seismic and tsunami waves can be used when operationally refining the tsunami source parameters and modeling expected tsunami waves on the shore. The most suitable physical models related to the tsunamis simulation are based on the shallow water equations. We investigate three different inverse problems of determining a tsunami source using three different additional data: DART measurements, satellite wave-form images and seismic data. We investigate a gradient-type and SVD inverse problem solution and show that using a combination of three different types of data allows one to increase the stability and convergence of numerical inverse problem solution. Results of numerical experiments of the tsunami source reconstruction are presented and discussed.