A general forward solver for 3D CSEMs with multitype sources and operating environments

Abstract

To determine the electromagnetic (EM) fields of different three-dimensional (3D) controlled-source electromagnetic methods (CSEMs) using the same parameters of the forward solution, by explicitly considering the commonalities, we present a general 3D forward modeling solver for CSEMs with multitype sources and operating environments. The commonality of the solver is reflected in two aspects. First, the solver is based on a frequency-domain (FD) vector Helmholtz equation for determining the scattered electric field. The different types of sources are imposed on the right-hand term of the equation, expressed as background Green’s function. Second, sources of any CSEM can be composed of electric dipole (ED) or magnetic dipole (MD) superposition. Thus, the focus of the 3D forward modeling of CSEMs is reduced to determining the EM fields of ED or MD sources for the background medium. The quasi-minimal residual (QMR) method is used to solve the large sparse complex linear system. Once the FD EM fields have been calculated, the time-domain (TD) response can be obtained using the cosine/sine transformation. The numerical results show that the relative error is less than 5% between the 3D numerical and analytical solutions, which verifies the accuracy of the solver. We further study the difference between the real (bent) and theoretical (straight) wires. We suggest that the shape of the source must be considered for TD and FD CSEMs with a wire source during data processing and inversion. The last example investigated the characteristics of FD EM fields from a finite-length wire and TD EM fields from a rectangular fixed loop on the same conductive tilted disk model buried in resistive sediments. According to the numerical results, we recommend FD CSEMs with a wire source for detecting deep anomalies.