Seismic ray tomography using L 1 integral norm

Abstract

Seismic ray tomography methods are usually associated with substantial computer processing time. The reason for this is that at each step of the iterative inversion process defined by the tomographic method the two-point ray tracing problem must be solved for each source-receiver pair. In order to resolve this, an Euclidean norm (L 2 vector norm), commonly used in error functions which are to be minimized in inversion procedures, is substituted by an L 1 integral norm, which enables the estimation of model parameters by minimizing the area between observed and calculated traveltime curves that are interpolated (or adjusted) to the data points. Relatively simple mathematical developments and numerical experiments with two-dimensional compressional seismic wave velocity field models show that L 1 integral norm saves an enormous amount of processing time with no significant loss of accuracy. Occasionally, parameters of the model can be better estimated using L 1 integral norm than the L 2 vector norm that is traditionally utilized in seismic inversion tomography.