Contraction pre-conditioner in finite-difference electromagnetic modelling

Nikolay Yavich, Michael S. Zhdanov

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


This paper introduces a novel approach to constructing an effective pre-conditioner for finitedifference (FD) electromagnetic modelling in geophysical applications. This approach is based on introducing an FD contraction operator, similar to one developed for integral equation formulation ofMaxwell's equation. The properties of theFDcontraction operatorwere established using an FD analogue of the energy equality for the anomalous electromagnetic field. A new pre-conditioner uses a discrete Green's function of a 1-D layered background conductivity.We also developed the formulae for an estimation of the condition number of the system of FD equations pre-conditioned with the introduced FD contraction operator. Based on this estimation, we have established that the condition number is bounded by the maximum conductivity contrast between the background conductivity and actual conductivity. When there are both resistive and conductive anomalies relative to the background, the new pre-conditioner is advantageous over using the 1-D discrete Green's function directly. In our numerical experiments with both resistive and conductive anomalies, for a land geoelectrical model with 1:10 contrast, the method accelerates convergence of an iterative method (BiCGStab) by factors of 2-2.5, and in a marine example with 1:50 contrast, by a factor of 4.6, compared to direct use of the discrete 1-D Green's function as a pre-conditioner.

Original languageEnglish
Pages (from-to)1718-1729
Number of pages12
JournalGeophysical Journal International
Issue number3
Publication statusPublished - 2016
Externally publishedYes


  • Electromagnetic theory
  • Magnetotellurics
  • Marine electromagnetics
  • Numerical approximations and analysis
  • Numerical solutions


Dive into the research topics of 'Contraction pre-conditioner in finite-difference electromagnetic modelling'. Together they form a unique fingerprint.

Cite this