Numerical Treatment and Evaluation of Inverse Problems

Abstract:- All regularization methods for computing stable solutions to inverse problems, involve a trade-off between the “size ” of the regularized solution and the quality of the fit that it provides to the given data. Though the appropriate choice of the regularization parameters is important, resolution and uncertainty analysis are as significant. Thus, we should also proceed to the resolution analysis in order to determine what scale features in the model can actually be resolved. In this work, we choose the proper values of damping and smoothing factors using two of the most well known regularization tools, the Picard condition and the L-curve [8], which generally provide a good estimation of the regularization parameters in combination with the standard maximum likelihood approach [3]. Additionally, the spread function as proposed by Menke [18] and a checkerboard test are applied in order to have an estimate of the resolution. The efficiency of the preferred methods is tested through a series of tests in real data from the area of Urals in Russia