Layer‐Stripping direct traveltime inversion for seismic data

The problem of determining the velocity and depth structure of a layered earth model from surface seismic data is of considerable interest in exploration seismology, and many variations on ways to pose the problem and solve it have been proposed. One popular approach is based on layer stripping, in which it is assumed that all layers above a given layer whose parameters are to be determined have been inverted. This information is then used, together with seismic reflection data, to invert for the parameters of the given layer. This procedure is repeated until the entire section of interest has been inverted. The problem may be posed as a one‐, two‐, or three‐dimensional problem. The one‐dimensional case has received considerable treatment in the literature. The purpose of this paper is to extend a theoretical result and the corresponding analysis from the 1‐D to the 2‐D case. Specifically, it is shown that for a dipping plane layer 2‐D stratified earth, the depth/dip/velocity structure of the section can be determined by a direct layer‐stripping algorithm in which a system of nonlinear equations is solved for the unknown layer parameters using only traveltime data from three offset locations. This is the minimal information required to solve the problem. In practice, the solution is extremely sensitive to data errors and so a minimum norm implementation would usually be employed, utilizing the redundancy of data available from more than three offsets. It is the theoretical development which is of interest here. Its actual implementation may take many forms.