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.
Highlights
The classic geophysical tomography problem is solved to reconstruct the velocity distribution for the investigated portion of the Earth such that the projected data should agree with measurements
In this paper we report on generalization of two items, in that we apply Cauchy-Steiner weights (Cauchy weights with scale parameters automatically determined by using Steiner’s Most Frequent Values (MFV) method) in the original Conjugate Gradient tomography algorithm in order to minimize the weighted norm of the deviation vector
The generalization of the Simultaneous Iterative Reconstruction Technique (SIRT) is proposed and in the data space Cauchy-Steiner weights are used to calculate the weighted average of the Algebraic Reconstruction Technique (ART) corrections (W-SIRT)
Summary
The classic geophysical tomography problem is solved to reconstruct the velocity distribution for the investigated portion of the Earth such that the projected data (the traveltimes) should agree with measurements. Least squares problems in tomography have been solved by row action methods such as Algebraic Reconstruction Technique (ART) or Simultaneous Iterative Reconstruction Technique (SIRT) It was proved by [1] that the Conjugate Gradient (CG) method can be used even in large-scale tomographic least squares inversion with taking the advantage of the sparsity of the matrix of the problem. In this paper we report on generalization of two items, in that we apply Cauchy-Steiner weights (Cauchy weights with scale parameters automatically determined by using Steiner’s MFV method) in the original Conjugate Gradient tomography algorithm in order to minimize the weighted norm of the deviation vector. The generalization of the Simultaneous Iterative Reconstruction Technique (SIRT) is proposed and in the data space Cauchy-Steiner weights are used to calculate the weighted average of the ART corrections (W-SIRT)
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