Compute SVD of a Very Large Matrix in the Context of Geological Prospection

SVD methods are nowadays at the heart of solving and analysing inverse problems in geophysic. Although the SVD analysis of large size problem is very expensive, there are different ways to overcome this limitation. The major of them are using HPC cluster parallelization algorithms, some limitation of input model and simplify the input model. In this paper, we present SVD low-rank approximation algorithm. It can be used to make SVD analysis of the linearized problems namely inversing seismic data in Born approximation. High performance of proposed algorithm is based on the fast decreasing singular values of Born matrix and on applying the adaptive cross approximation (ACA) technique. Performance of intermediate steps is improved by using BLAS and LAPACK components from Intel Math Kernel Library (Intel MKL) that is optimized for Intel architecture and parallelized via OpenMP. Validation tests showed that proposed Low-rank SVD approximates singular values and spaces spanned on the major singular vectors very well. Performance tests showed more than ten time performance on one-thread system. Algorithm has large opportunity for parallelization both on shared memory systems (using OMP parallelization) and on distributed ones (MPI parallelization)