Seismic ray tomography using the method of damped least squares

Abstract

The well known problem with seismic tomography is that limitations of source receiver geometry mean that seismic ray coverage is incomplete. This is one cause of artifacts that disturb reconstructed velocity distribution images. In this paper, we attempt to reduce the occurrence of artifacts by means of the damped least squares method. In general, tomographic velocity models are obtained by dividing the area of exploration into a number of rectangular cells, and assigning slowness values to each cell. The reconstruction procedure generally used is the iterative method, in which ray tracing and modification of the model are carried out alternately. The damped least squares method is one way to obtain stable least squares solutions. It is an attempt by the authors to take into account irregularity of ray coverage by determining damping parameters for each cell from the number and directionality of rays passing through each cell. Numerical experiments showed that if appropriate damping parameters are selected, the damped least squares method can reduce the occurrence of artifacts. The method was also applied with good results to field measurements, taken at a dam site in an area of granite.