Frequency Domain Controlled Source Electromagnetic 3D Finite Element Modeling Based On MPI

For frequency domain controlled-source electromagnetics (FCSEM), 3D interpretation of FCSEM data is necessary for a better understanding of the subsurface structure, due to the complexity of the sources, EM fields and measuring systems. The Karnia apparent resistivity used commonly in the MT problem can be distorted for the FCSEM data at the nearby and transitional region. Thus, the following work is carried out in my thesis.The ID forward methods and calculation of all time apparent resistivity of the FCSEM for a bipolar source are presented. For the forward problem, the bipolar source can be discretized into a sequence of dipole source, and its excited fields are given by summation of the response of each dipole source calculated by Hankel filtering. The all time apparent resistivity can be calculated as the apparent resistivity of the half-space model, equivalent to the overall apparent resistivity of the underground complex structure. The all time apparent resistivity for both bipolar and dipole source are solved for several typical 1D models. Comparison shows that the former one can model the underground structure more accuarately.Then the 3D modeling of FCSEM with FEM is presented. From the Maxwell equations, its boundary value problem is derived, and then transformed into variational form from which finite-element linear equations are derived. The introduction of zero divergence conditions for the electric field outside the source avoided the spurious solution. By using the field of the electric dipole source in homogeneous half-space as the outer boundary conditions, difficulties in loading the 3D boundary conditions was solved. The pseudoδfunction was adopted to simulate the electric dipole source, which avoids the singularity of the solution, and enhances the stability of the equations. For large sparse matrix, Row Compressed Storage (CSR) method was deployed to handle the resulting large sparse matrix. The SSOR-PCG method was used to solve the linear equations. For the computational intensity of 3D modeling, MPI was applied to parallel the computation for different frequencies. The 3D modeling for several models with different geologic setting, are illustrated, which shows the EM responses are modeling properly, and the all time apparent resistivity, can correct the distortion of Karnia apparent resistivity at the nearby region.