Forward calculation of 3D controlled-source electromagnetic responses based on joint application of secondary field and coupled potential formulations

Abstract

In the traditional framework of 3D controlled-source electromagnetic (CSEM) modeling, either the field formulation or the coupled potential formulation is implemented. We have developed an improved algorithm that can calculate the 3D CSEM responses based on a joint application of the secondary field and secondary coupled potential formulations. The vector finite-element method is implemented for the discretization of the curl-curl equation of the secondary field. The vector and nodal elements are implemented simultaneously for the discretization of the coupled potential formulation. We use the stiffness matrix resulting from the coupled potential formulation to construct an efficient preconditioner, which is used for the solution of the linear system of equations obtained based on the secondary field formulation. The linear system of the equations could be solved efficiently by the quasiminimum residual method within several hundred iterations with the constructed preconditioner. We compare different modeling schemes to calculate the CSEM responses for a horizontally layered earth model excited by an electric dipole and find that the iteration process of the improved algorithm converges faster on average than other modeling schemes for the frequency band considered. Thus, the least computation time can be obtained over the frequency band for the improved algorithm compared with other modeling schemes, with the same level of accuracy reached. We further verify the efficiency of the algorithm through a small-scale 3D earth model excited by a magnetic dipole. Finally, we illustrate the performance of the algorithm with two 3D subsurface models, including a land-based model and a marine disk model. By comparison with published work, it is illustrated that our algorithm can efficiently calculate accurate land-based and marine CSEM responses with the new constructed preconditioner implemented.