Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Mathematical problems in geophysical investigations of solid Earth

In the non-homogeneous medium with the varying velocity of waves propagation it is not easy to find the wave-ray between two fixed points of the area. It is very difficult for computed wave-ray, which is started from the source point, to hit the small neighborhood of the distantly located receiving point. The method, which not uses the equations of wave-rays motion, is proposed in this paper. The main idea of this attempt consists in calculation of travel-times from the fixed source to all grid-points of the computational area. This can be done using numerical method, based on Huygence principle. When the algorithm calculates the travel-time to the point M of the computational area, it inputs into memory the grid coordinates of that neighboring grid-point, from which the wave most quickly reaches this point M. And so on for every grid-point from computational area. After this it is easy to find the ray from the source to any grid-point of our area. This method was used for tsunami wave-rays definition in two-dimensional areas of the Pacific. The method can be applied for the wave-rays definition in three-dimensional seismic problems.

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