Weighting Factors in the Inversion of Seismic Data

Abstract

When using a generalized linear inversion technique, it is quite simple to allow input data to be weighted according to its accuracy or some other criteria. Weighting of data becomes desirable especially in the over-determined problem and also when mixed data sets are used such as a combination of stacking velocities and two-way travel times from an unmigrated stacked section of seismic data. However, the choice of the weighting factors for the various types of input data can have quite dramatic effects on the “solutions” obtained as illustrated in this paper using seismic data from the Gippsland Basin an area off-shore South-East Australia. In this study, the seismic line is divided into overlapping sections which are processed independently; the appropriateness of a set of weighting factors for the problem is determined by the criterion that it should enhance the lateral consistency between the solutions obtained all the way across the seismic line. Such an approach to the problem may be viewed as a very simple type of cross-validation technique; in this application, it is found that an appropriate choice of weighting factors can serve to regularize the problem.