No abstract

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Waveform (output least squares) inversion of seismic reflection data can reconstruct remarkably detailed models of subsurface structure, and take into account essentially any physics of seismic wave propagation that can be modeled. However the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is based on the Born approximation but is capable of correcting substantially erroneous initial velocities. Appropriate choice of objective (differential semblance) turns migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modeling concept links these two apparently unrelated approaches to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized (single scattering, Born) waveform inversion problem. Extended modeling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests that this new approach to nonlinear waveform inversion may combine the global convergence of velocity analysis with the physical fidelity of least squares.

Differential semblance optimization (DSO) is an approach to inversion of reflection seismograms which avoids the severe convergence difficulties associated with nonlinear least‐squares inversion. The method exploits both moveout and amplitude characteristics of reflections. We have implemented a version appropriate to plane‐wave (p‐tau) seismograms and layered constant‐density acoustic earth models. Theoretical and numerical analyses of this version of DSO indicate that stable and reasonably accurate estimates of both velocity trend and reflectivity can be derived. To test DSO further, we applied it to a marine data set from the Gulf of Mexico, where the method produced results which compare favorably to well‐log information. The method can be extended to incorporate laterally heterogeneous velocity models.

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