Singular value decomposition of the velocity-reflector depth tradeoff, Part 1: Introduction using a two-parameter model

Abstract

A singular value decomposition (SVD) of a two-parameter model serves to introduce several characteristics of a raypath inversion of the standard reflection seismology recording geometry. Two important families of eigenvectors consist of constructive interference and destructive interference of velocity and reflector depth. The eigenvalue that corresponds to the velocity-reflector depth destructive interference is very sensitive to the maximum ray angle in the data. For a cable length equal to twice the reflector depth, the theoretical linear resolution is quite high. The relative weighting between velocity and reflector depth is not critical so long as the weight is near 1.0.