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Shaping Regularization in Geophysical Estimation Problems

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Shaping Regularization in Geophysical Estimation Problems

By Sergey Fomel

Abstract:
Regularization is a required component of geophysical estimation problems that operate with insufficient data. The goal of regularization is to impose additional constraints on the estimated model. I introduce shaping regularization, a method for imposing constraints by explicit projection to the space of admissible models. Shaping regularization is integrated in a conjugate-gradient algorithm for iterative least-squares estimation. It provides the advantage of both improved efficiency and a better control of the estimated model. Simple data regularization and seismic velocity estimation examples illustrate the concept.