DC resistivity modelling with a Gaussian quadrature grid

Abstract

We present a new numerical scheme for 2D/3D direct current resistivity modelling. This method co-operatively combines the solution of the variational principle of the partial differential equation, Gaussian global quadrature abscissae and local cardinal functions so that it has the main advantages of the finite element method and the spectral method. The formulation shows that the method is close to the spectral element method, but it does not require the element mesh or the element integrations, and it makes it much easier to deal with geological models having a 2D/3D complex topography than the traditional numerical methods. It can achieve a similar convergence rate to the spectral element method. We show it transforms the 2D/3D resistivity modelling problem into a sparse and symmetric linear equation system, which can be solved by an iterative or matrix inversion method.