Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples1

Abstract

AbstractSeismograms predicted from acoustic or elastic earth models depend very non‐linearly on the long wavelength components of velocity. This sensitive dependence demands the use of special variational principles in waveform‐based inversion algorithms. The differential semblance variational principle is well‐suited to velocity inversion by gradient methods, since its objective function is smooth and convex over a large range of velocity models. An extension of the adjoint state technique yields an accurate estimate of the differential semblance gradient. Non‐linear conjugate gradient iteration is quite successful in locating the global differential semblance minimum, which is near the ordinary least‐squares global minimum when coherent data noise is small. Several examples, based on the 2D primaries‐only acoustic model, illustrate features of the method and its performance.