The shortest path method for seismic ray tracing in complicated media

Abstract

This thesis is concerned with the shortest path method for seismic ray tracing. The shortest path method is based on Fermat's minimum travel time principle and the theory on shortest paths in networks. To construct seismic ray paths in a complicated velocity model the relevant part of the Earth is covered by a large number of nodes that are connected when they are in a close neighbourhood of each other. Such a structure is mathematically referred to as a graph. It is turned into a network when weights are assigned to each connection. When the weights are chosen equal to the travel time of a seismic wave along them, the shortest paths in the network, defined as sequences of connections with minimum total weights, can be used to approximate seismic ray paths. The travel times along them can be used as approximations of the travel times between source and receiver pairs.