A Footprint-Guided Algorithm for 3-D Simulation Based on BEM of Topography Effect in Frequency-Domain Airborne Electromagnetic Method

Topographic undulations often have nonnegligible influence on frequency-domain airborne electromagnetic method (FAEM) exploration. To study this effect caused by complex topography, this article proposed a numerical simulation method based on the boundary element method (BEM) to calculate the 3-D topography EM field of frequency-domain magnetic dipole source with arbitrary inclination angle. First, according to the vector integral equations and boundary conditions of the EM field, the boundary integral equations are derived, which describes the coupled electric and magnetic fields that are integrated only for the 3-D surface. Then, the 3-D surface identified by the area of influence of the magnetic dipole source is used as the integration region (footprint) with unstructured triangular dissection, and the boundary integral equations are solved in this region using BEM. The EM field at the geometric center of gravity of each element on the surface is obtained by solving the dense linear equations using the conjugate gradients squared (CGS) method, and the influence of the 3-D topography on the magnetic field (secondary field) at the receiving coil can be calculated according to the magnetic field boundary integral equation in the upper half-space. The algorithm is then tested with synthetical models to validate its feasibility and evaluate its performance, where the response characteristics of the magnetic field with different model conditions are analyzed.