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.
Highlights
Accepted: 26 August 2021Airborne electromagnetic method (AEM) is an efficient and low-cost tool for geophysical exploration
We introduce the wavelet finite-element method (WFEM) to ameliorate the deficiencies in our airborne EM modeling
The first is that B-spline wavelets on the interval (BSWI) scaling functions can accurately hold the general information at a given scale, which means that the unknown field inside each element can be well approximated
Summary
Airborne electromagnetic method (AEM) is an efficient and low-cost tool for geophysical exploration. The edge-based finite-element method proposed by Nédéléc (1980) uses vector basis functions defined along the edges to approximate the electric field [50]. This guarantees the continuity of the tangential field component while allowing the discontinuity of the normal component at the same time. It can avoid the spurious modes because the construction of vector basis functions satisfies the divergence-free condition of the electric field in a source-free mesh. We verify the accuracy and demonstrate the advantages of our method via 3D numerical experiments
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