Approximate methods for time-reversal processing of large seismic reflection data sets

Abstract

Seismic reflection data sets, whether collected on land or at sea, contain very large amounts of data even by modern standards. These data are typically sampled regularly in time but irregularly in space. So, temporal Fourier transforms are straightforward, but spatial transforms can be problematic, and very often require special efforts to resample the data onto a uniform grid in space. On the other hand, time-reversal processing of such data requires only the temporal Fourier transform, which is easy for these data. Accounting for data reciprocity, a complex square transfer matrix can be constructed at each frequency, and standard methods can then be used—at least in principle—to find singular values and singular vectors (SVD) of this large matrix. Once those singular vectors having the largest singular values are known, it is relatively straightforward to reconstruct the scattering surfaces giving rise to the data matrix. The biggest leap in this data processing scheme comes from the need to find the SVD for very large complex matrices. But iterative schemes using Krylov space methods can be applied to resolve this difficulty and produce a relatively small number of singular vectors containing the most relevant information.