TITLE:
On the Generalization of Seismic Tomography Algorithms
AUTHORS:
Mihály Dobróka, Hajnalka Szegedi
KEYWORDS:
Robust Tomography; Conjugated Gradients; SIRT; Cauchy-Steiner Weights
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.1,
February
27,
2014
ABSTRACT: 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.