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^{}.

- Introduction
- Review of Tikhonov's regularization
- Smoothing by regularization
- Shaping regularization in theory
- From triangle smoothing to triangle shaping
- Examples

- Conclusions
- Acknowledgments
- Bibliography
- About this document ...

2013-07-26