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Published as Geophysics, 72 , no. 2, R29-R36, (2007)

Shaping regularization in geophysical estimation problems

Sergey Fomel

Bureau of Economic Geology,
John A. and Katherine G. Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8972


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 general method for imposing constraints by explicit mapping of the estimated model 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 a better control on the estimated model in comparison with traditional regularization methods and, in some cases, leads to a faster iterative convergence. Simple data interpolation and seismic velocity estimation examples illustrate the concept[*].