Three‐dimensional regularized Gauss‐Newton inversion algorithm using a compressed implicit Jacobian calculation for electromagnetic applications

Abstract

We present a compressed implicit Jacobian scheme for the regularized Gauss-Newton inversion algorithm for reconstructing three-dimensional conductivity distribution from electromagnetic data. In this scheme, the Jacobian matrix, whose storage usually requires a large amount of memory, is decomposed in terms of electric fields excited by sources located and oriented identically to the physical sources and receivers. As a result, the memory usage for the Jacobian matrix reduces from O(NF NSNRNP) to O [NF (NS +NR)NP], in which NF is the number of frequencies, NS is the number of sources, NR is the number of receivers, and NP is the number of conductivity cells to be inverted. Moreover, we apply the adaptive cross approximation (ACA) to compress these fields to further reduce the memory requirement and to improve the efficiency of the method. This implicit Jacobian scheme provides a good balance between the memory usage and the computational time and renders the Gauss-Newton algorithm more efficient. We demonstrate the benefits of this scheme using numerical examples including both synthetic and field data for both crosswell and surface electromagnetic applications.