3D Wavelet Finite-Element Modeling of Frequency-Domain Airborne EM Data Based on B-Spline Wavelet on the Interval Using Potentials

Abstract

We present a wavelet finite-element method (WFEM) based on B-spline wavelets on the interval (BSWI) for three-dimensional (3D) frequency-domain airborne EM modeling using a secondary coupled-potential formulation. The BSWI, which is constructed on the interval (0, 1) by joining piecewise B-spline polynomials between nodes together, has proved to have excellent numerical properties of multiresolution and sparsity and thus is utilized as the basis function in our WFEM. Compared to conventional basis functions, the BSWI is able to provide higher interpolating accuracy and boundary stability. Furthermore, due to the sparsity of the wavelet, the coefficient matrix obtained by BSWI-based WFEM is sparser than that formed by general FEM, which can lead to shorter solution time for the linear equations system. To verify the accuracy and efficiency of our proposed method, we ran numerical experiments on a half-space model and a layered model and compared the results with one-dimensional (1D) semi-analytic solutions and those obtained from conventional FEM. We then studied a synthetic 3D model using different meshes and BSWI basis at different scales. The results show that our method depends less on the mesh, and the accuracy can be improved by both mesh refinement and scale enhancement.