A Novel Integral Solution for Three-dimensional Direct Current Resistivity Problem with Topography
We develop a novel volume-surface integral formula for three-dimensional direct current (DC) resistivity forward modeling with inhomogeneous conductivities and an arbitrary homogeneous topography.First, a volume-surface integral formula is derived from its elliptic boundary value problem in terms of an artificial analytical function defined over the full-space.That leads to a volume integral accounting for underground anomalous regions and a surface integral over the surface topography.Then, tetrahedral grids are used to discretize the volume anomalous bodies and triangular grids are adopted to approximate the complicated surface topography.The usage of unstructured grids enables our volume-surface integral formula to deal with realistic Earth models with complex geometries and conductivity distributions.Furthermore, linear shape functions are assumed in both tetrahedral elements and triangular elements to obtain the final system of linear equations.In the final system matrix, singularity-free analytical expressions are developed for entries arising from volume integrals over tetrahedral elements;and Gaussian quadrature formulae are used to calculate surface integrals over triangular elements.To guarantee accuracies of final numerical solutions, direct solvers are used.At the end, three synthetic models are used to verify our newly developed volume-surface integral formula by comparison with published analytical solutions and finite-element solutions.Due to its high accuracy, solutions of our volume-surface integral approach can act as an efficient benchmark tool for other numerical solutions for complicated DC models with arbitrary homogeneous topographies.
Resistivity modeling Volume-surface integral formula Linear basis function Unstructured meshes Topography
Huang Chen Zhengyong Ren Jingtian Tang Feng Zhou
School of Geosciences and Info-Physics, Central South University, 410083, Changsha, China
国际会议
杭州
英文
295-298
2018-06-10（万方平台首次上网日期，不代表论文的发表时间）