Development of the software of three-dimensional interpretation for electromagnetic tomography

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During the investigation of the applicability of the finite-element method (FEM) to 3-D modeling of electromagnetic tomography, it is found that the accuracy can be degraded significantly when the conductivity contrast is very high, or when the frequency used is low. This is due to the fact that the assumption on the continuity of the electric field is violated in the conventional FEM.Thus, in order to improve accuracy we used the edge element FEM and the staggered-grid finite difference method, both of which can take into account the discontinuity of the electric field. The modeling results show that good accuracy can be obtained for 3-D models with high conductivity contrast if the frequency is above about 100 Hz, and that the system of equations is more ill-conditioned as the frequency is lower. It is also found that successive overrelaxation (SOR) method mainly used in this study is not an adequate solver for the system of equations at lower frequencies, and that the biconjugate gradient method with a preconditioning is promising. We are planning to incorporate the divergence condition into our formulation, which is expected to reduce the condition numbers of the system materix and make the iterative process of the solution more stable. After completing 3-D modeling programs which give desired accuracy regardless of the frequency used, we are going to work on the 3-D inversion.