Abstract
Inverse problems are in general ill-posed, in such a way that we have to deal with the aspects of existence, uniqueness and stability. In this work we deal with seismic traveltime tomography, which is a kind of inverse problem. We use the well known singular value decomposition (SVD) in order to obtain the slowness distribution from a given known set of traveltimes. When using SVD we face the problem of small singular values that should be avoided in the construction of the pseudoinverse matrix. We propose here a new methodology for the optimum selection of singular values. This methodology is based on the behavior of the singular values decay, the RMS error for data parameters, the RMS error for model parameters, the model parameters energy and the model parameters entropy. We applied this methodology in linearized seismic traveltime tomography, where the simulations with synthetic data provided good results.
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