Meshfree Method Applied To Geophysical Forward Two-dimensional Magnetotelluric Forward As An Example

Magnetotelluric (MT) sounding is an important geophysical means to study the Earth electrical structure using the natural EM field as it’s source.It does not need artificial power supply, low cost, and facilitate to the work. Without high resistance shielding, and the exploration depth varies with the frequency of the electromagnetic field, light can be tens of meters up to hundreds of kilometers deep, therefore It has receive a wide range of applicationsIn the forward problem to solve the Magnetotelluric (MT), finite difference method and finite element method are the main numerical methods. But these issues are grid-based numerical methods, such as the finite element method:the solution domain is partitioned into a finite number of units, each unit of the grid nodes are connected together. Meshing is the basic features of the existing traditional numerical methods. Although these methods have achieved a great success, it has its own limitations:1)The division unit is a very tedious job, their workload is often compared with finite element analysis for complex three-dimensional problem, and doesn’t to adapt to the changing of the grid.2) finite element (FEM) calculation accuracy depends on the shape and size of the element meshing, and thus not suited to mesh distortion occurs due to large deformation.A major cause of the above-mentioned problems is that these methods are based on the basis of the meshing to the establishment the discrete system equation. To overcome these difficulties, the non-grid method (Meshfree) is an important supplement to the finite element (FEM)Over the past decade, the non-grid method (Meshfree) as a new numerical calculation, based on the finite element make a great development. But different from the finite element method, the approximation functions of meshless method is based on a series of discrete nodes. Although the Meshfree Method has been widely studied in mechanics, reservoir seepage problems, electromagnetics, the theory in solving geophysical forward problem and cite studies is yet to come. Using Matlab, we will discuss the problem from the following aspects related in this paper,First, from the Maxwell equations, we deduces the medium of two-dimensional Magnetotelluric (MT) boundary value problem corresponding to the integral equation and then use a series of discrete nodes discretized the area. Based on the discrete nodes, we get the meshfree shape function. The introduction of the moving least squares method to construct the shape function to deduce the shape function of the strike, combined with the two-dimensional Magnetotelluric exploration. Last we give the relevant parameters, such as the influence domain, the domain of weight function to determine.Due to the use of least squares the idea, some point is not satisfied with the delta function, and thus using special methods to make these points to meet Delta, in this paper, we use the penalty function method and the Lagrange multiplier method to deal with essential boundary conditions.The program is verified by comparison with the analytic response of a symmetrical ladders model and with finite difference results of laterally inhomogeneous model and topographic model.