A differential semblance algorithm for the inverse problem of reflection seismology

AbstractThis paper presents an analysis of stability and convergence for a special case of differential semblance optimization (DSO). This approach to model estimation for reflection seismology is a variant of the output least squares inversion of seismograms, enjoying analytical and numerical properties superior to those of more straightforward versions. We study a specialization of DSO appropriate to the inversion of convolutional-approximation planewave seismograms over layered constant-density acoustic media. We prove that the differential semblance variational principle is locally convex in suitable model classes for a range of data noise. Moreover, the structure of the convexity estimates suggest a family of quasi-Newton algorithms. We describe an implementation of one of these algorithms, and present some numerical results