Computer algebra software for least squares and total least norm inversion of geophysical models

We consider the model inversion problem that arises in geophysical sciences. Whether it is formulated in a deterministic or stochastic framework, it can be solved by minimizing an appropriate loss function with respect to unknown parameters. In such an optimization the efficiency of local minimization is crucial but the complexity of involved models often restricts the applicability of derivative based techniques. We consider the application of modern computer algebra programs to automatically compute needed derivatives and we propose a computer shell developed under the MATLAB ® environment that can be used to efficiently solve these problems. The software can be used by users that do not have specific skills in numerical and symbolic computation techniques. In order to show the general applicability of the proposed procedure and the software tool, we report the application to two different, but simple, ground deformation models and to two solution techniques: the classical nonlinear least squares, that is the most used approach, and the L 1 structured total least norm approach, which has proved to be very effective in dealing with data characterized by large outliers. Experimental results from synthetic and real data are shown.