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The oddities of regularized inversion: Regularization parameter and iterations

Marie L. Clapp

marie@sep.Stanford.edu

ABSTRACT

Proper imaging in areas with complex overburdens can not be done effectively with an adjoint operator such as migration. To image in complex areas, we really want to apply an inverse operator, but most imaging problems can be represented by very large matrices that are difficult to invert directly. Therefore, many schemes to approximate an inverse operator have been developed. Regularized least-squares inversion implemented in an iterative scheme can be very effective in dealing with illumination problems when the imaging and regularization operators are well chosen. However, those aren't the only decisions that need to be made. Both the choice of regularization parameter ($\epsilon$) which balances the data and model residuals and number of iterations (niter) can have a significant effect on the quality of the final image. In this paper, I describe some of the issues that must be taken into account when choosing $\epsilon$ and niter for an imaging problem with poor illumination. I also examine their effects on a simple synthetic data example. These experiments show that the effects of $\epsilon$ and niter are related and must be considered when performing an inversion for imaging.



 
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Stanford Exploration Project
7/8/2003