On the Generalization of Seismic Tomography Algorithms

The seismic tomography problem often leads to underdetermined and inconsistent system of equations. Solving these problems, care must be taken to keep the propagation of data errors under control. Especially, the non-Gaussian nature of the noise distribution (for example outliers in the data sets) can cause appreciable distortions in the tomographic imaging. In order to reduce the sensitivity to outlier, some generalized tomography algorithms are proposed in the paper. The weighted version of the Conjugate Gradient method is combined with the Iteratively Reweighted Least Squares (IRLS) procedure leading to a robust tomography method (W-CGRAD). The generalized version of the SIRT method is introduced in which the (Cauchy-Steiner) weighted average of the ART corrections is used. The proposed tomography algorithms are tested for a small sized tomography example by using synthetic traveltime data. It is proved that—compared to their traditional versions—the outlier sensitivities of the generalized tomography methods are sufficiently reduced.