2.5D electric resistivity forward modeling with element-free Galerkin method - Ma, Changying; Liu, Jianxin; Liu, Haifei; Guo, Rongwen; Musa, Bello; Cui, Yi-an (Journal of applied geophysics, 2019)
An element-free Galerkin method (EFGM) is proposed to perform the direct current (DC) resistivity modeling problems. The advantage of this method is the absence of elements, which makes nodes free from the elemental restraint. In this method, the moving least square (MLS) approximation is employed to construct the shape function. And the cubic spline function with high continuity is used as a weight function. Then, the boundary value problem and the corresponding variation problem of DC resistivity modeling problems are discussed. The discrete equations of two and a half dimensional (2.5D) DC resistivity modeling problems are obtained by using the Galerkin weak form formulation. Thereby, a 1D multilayered geoelectric model is adopted to verify the validity of the proposed EFGM. And the further tests of complicated geoelectric models illustrate that the correctness, good adaptability and flexibility of EFGM compared with the finite element method (FEM). The EFGM can conveniently simulate the undulating terrain and improve the simulation accuracy by refining nodes in local domain. In addition, the discretization of test models shows that EFGM is easy to handle the complicated geometrical geoelectric models by using arbitrary and irregular nodes. All these tests demonstrate that the EFGM is suitable to perform forward modeling for complicated geoelectric models. •An element-free Galerkin method (EFGM) is proposed to forward electric resistivity.•The moving least square approximation is employed to construct the shape function.•The numerical results of EFGM have higher accuracy than results of the finite element method.•The EFGM is more suitable than the FEM to simulate complex models.