Solving Large Linear Inverse Problems in Geophysics by means of Eigenvalue Calculations

This paper discusses the computation and utilization of singular values and singular vectors in the solution of very large inverse problems that arise in the study of physical models for the internal structure of the Earth. In this study, the Earth is discretized into layers and the layers into cells, and travel times of sound waves generated by earthquakes are used to construct the models. The underlying numerical models correspond to sparse matrices with dimensions up to 1.3x10-by-3x10. Singular values and singular vectors of these matrices are then computed and used in the solution of the inverse problems and to estimate uncertainties. The paper outlines the formulation adopted to model the Earth and the strategy employed to compute singular values and singular vectors, shows results for two models that have been studied, and comments on the main computation issues related to the solution of these problems on high performance parallel computers.