MODELLING OF 2D DC RESISTIVITY DATA USING IMMERSED INTERFACE METHOD

Abstract

The work presented in this thesis has focused on finding a better method to solve the forward modelling problems in Direct Current (DC) resistivity surveys. This work targets the 2D DC resistivity problem. The regular finite difference method, in general, gives a local truncation error of first order irrespective of the conductivity structure. Only in the case of continuous conductivity model, it is of second order. Immersed Interface Method is originally developed to improve the accuracy up to at least second order in the interface problems with sharp discontinuities. This method uses a local coordinate transformation and a modified undetermined coefficients method, which forces the local truncation error to be of second order at the points away from the interface and of first order at the points near the interface. This globally leads to a second order accuracy solution for problems even with the sharp discontinuities. Never before the immersed interface method is used to solve a resistivity problem. For the first time, in this study, IIM method is used to solve a 2D DC resistivity problem. In this thesis, initially Finite Difference algorithm is set to solve 2D DC resistivity problem and then the JIM scheme is set for the same. The algorithm is programmed using MATLAB. The program worked well for the homogeneous case and need further improvements to be applied for other models.