Restoration of the ocean depth using recorded tsunami arrival times

Usually, the ocean depth is measured by the echo sounder in the course of a vessel cruise. However, there are a lot of areas in the World Ocean which are free of navigation. This means that by now there are no direct bathymetry measurements. For the numerical modeling of the trans-oceanic tsunami we need the digital bathymetry of the whole water area. The thus arising problem is to restore (at least, approximately) the depth values in the areas without reliable bathymetric data. This can be done in the process of the propagation of a real tsunami with the help of detectors used. Two algorithms for the depth restoration based on the tsunami arrival times are proposed. The algorithm has been tested on the depth restoration problem in the area with a sloping bottom, where the tsunami arrival times are known at the nodes of a rectangular grid.