Based On The Application Of Radial Basis Function Mesh-free Method In Two-dimensional Gravity, Magnetic And Electrical Survey Forward

With the rapid development of computer technology, the problems that mainstreamforward methods like finite element method, finite difference method can solve areincreasingly complex, which makes geophysical exploration have a mature application indeep geological structure study, metallic minerals search, oil and gas resourcesexploration, disaster prevention, and other areas. However, the traditional numericalmethods in the face of some complex models will face great meshing difficulties, such asground ups and downs, dramatic changes in physical parameters, any combination ofabnormal body, etc. This makes the forward calculation increase a lot of time andcomputational cost, and reduce efficiency.Meshfree method, setting a series of nodes in the computational domain andboundary to discrete the boundary value equation, avoids the mesh. Firstly, starting fromthe radial basis function interpolation theory and by studying a series of specific issuessuch as the configuration-central nodes set, the shape parameters’ selection, the disposeof boundary conditions, the discrete of differential equations, the matrix equations’solution, etc, this paper introduce the meshless method to gravity, magnetic, electric two-dimensional forward modeling. In dealing with boundary conditions, the first boundarycondition with a radial basis function approximation can be made directly to a highaccuracy, while the second type of boundary conditions need to add Hermite derivativeconditions and couple polynomial basis functions in order to improve the boundaryprecision.Then, through writing meshfree algorithm for single abnormal model, thecombination model of gravity, magnetic, electrical field was carried forward calculation.In order to verify the accuracy of the meshfree method, respectively using threetechniques, which are compared with the analytic solution, the traditional method offorward results and the inversion results.Validation results showed that at the samemesh size, the calculation accuracy of meshless method is higher than finite element,finite difference forward. In addition, compared to the grid method,meshfree method also has the advantages of node set flexible, programming easy, dimension insensitive,ease of solving high-dimensional problems and so on.But the meshfree method based on radial basis function also has its own deficiencies:since the radial basis function is a global-type basis functions, the formed matrix is a fullmatrix, unsuitable for solving large problems. In the discrete process of differentialequations, there exists a big magnitude difference between the second derivative of thebasis function and the first derivative, resulting coefficient matrix’s huge number ofconditions, which also reduces the computational accuracy. Finally, researchingtriangular grid-based rapid mapping of scattered data, and writing a computer program,can avoid the cumbersome mouse operation of third-party software.