STABILIZED ANALYTIC SIGNAL ALGORITHM IN 2D AND 3D DC RESISTIVITY DATA ANALYSIS

Abstract

The STATE OF ART in DC resistivity literature has revealed that the estimation of good quality of initial guess is problematic. As a result, the success of several mathematically rigorous nonlinear inversion algorithms is doubtful. Thus, the basic aim ofthe present thesis entails estimation ofstarting model from secondary potential data resulting from either 2D or 3D pole-pole DC resistivity survey. The DC conduction equation along with necessary boundary conditions are solved in 2D case by forward modelling. The Brewitt-Taylor and Weaver's discretization of conductivity scheme is used in the forward modelling exercise. Aspecific Finite Difference Mesh is opted after carrying out conventional convergence and validity tests. Thus, the forward modelling part of RES2AS has emerged. Due to lack of 3D resistivity forward modelling code at the start of the present effort in 1993, an analogy between boundary value problems concerning DC conduction and ground water flow under steady state conditions in the medium is revoked to adopt the existing Ground water modelling software (MODFLOW) for forward modelling purpose. Forthe analysis of secondary potential distribution at air-earth interface due to either 2D or3D conductive target (targets) emplaced in resistive half-space, an analogy between the boundary value problems of Electrostatics and Magnetostatics has been established by making use of Maxwell's equations. This analogy has allowed the import of Analytic Signal concept from Magnetics into DC resistivity method. It can be used in analyzing secondary potential data derived from 2D or 3D Pole-Pole resistivity surveys. The Analytic Signal computation in either 2D or 3D case involves derivatives of secondary potential data. In fact, numerical computation of derivatives of a given function resulting from an experiment means solving a Volterra type Integral equation of first kind of convolution, which belongs to the category of ill-posed problems. Hence, such a computation demands the use of some form of regularization to arrive at a stable Analytic Signal computation. So, Stabilized Analytic Signal algorithms, RES2AS and RES3AS are designed on the basis of Tikhonov's regularization concept in spectral domain as well as computationally effective FFT routines for tackling both 2D and 3D DC resistivity problems. The Analytic Signal and its associated terms estimate the body position, the lateral extent and depth of burial of conductive target(s) in both 2D and 3D cases. The stability character of RES2AS has been initially established in case of single as well as double conductive prism case. Further, the effectiveness of RES2AS is established in determining the key body parameters of different 2D targets from either error-free or error-prone secondary potential data derived from a series of numerical experiments. The utility of RES3AS in providing initial guess model in 3D case is checked in synthetic experiments involving single and multiple 3D conductive prisms emplaced in resistive half-space. However, for clarity sake the results concerning one intricate 3D model are included in this thesis. The stability of RES3AS is also established with the chosen three conductive prism model. The 3D Stabilized Analytic Signal and its associated terms enable the determination of initial guess model (Depth to top, lateral extent of the body). The results obtained match fairly well with the actual parameters. The validity ofRES2AS in field conditions has been attempted in the vicinity of our University Swimming pool. The objective was to infer the position location and to define the diameter of a buried drain pipe carrying waste water from the swimming pool. The secondary potential distribution along the principal profile for two different current pole positions have been obtained. With the help of RES2AS, the twin objectives of the survey entailing the position location and the diameter of the pipe have been met with. However, a similar experiment could not be undertaken in case of 3D due to lack of proper field equipment.