A Data-space Inversion Method For 2-D DC Resistivity Data

Direct current resistivity method is a branch method of the electrical prospecting, which is based upon the conductive difference between the rock and the ore. By observing and studying the stable artificial electric field, the method can be used to resolve geological problem and find the mineral. Direct current resistivity method has a very widely use, no matter used to general investigation on metallic or nonmetallic mineral, or used to research geologic structure, the method can reach a very good result. Moreover, its application is increasingly wider in the hydrology, engineering, and environmental geologic investigation and so on. To ensure its effect, efficient inverse method is necessary.So far, the mainstream inverse methods mainly includes: least square method, OCCAM's inversion, conjugate gradient inversion, relaxation inversion and several combinatorial optimization algorithms based on current optimization algorithms. OCCAM's inversion combines two required aspects: data misfit and smoothness constraint and gets the smoothest model fitting the data best. Weerachai Siripunvaraporn and Gary Egbert made improvements on the basis of the OCCAM's inversion. They transferred the progress of the OCCAM's inversion from model-space to data-space and realized the inversion of the magnetotelluric data in the spatial domain. Inversion in data-space lowers the order of the equation, which can decrease the calculated quantities and reduce the requirement of the memory of the computer and increase the efficiency of the inversion to a certain extent.In this paper we introduce the technology of the data-space inversion into direct current resistivity inversion, and combine the computation of Jacobian in wave spatial domain; we present a two-dimensional direct current resistivity inverse method in the data spatial domain. We have completed the algorithm about the two-dimensional direct current resistivity inversion method in the data-space by researching the follows: the 2.5-dimensional direct current resistivity forward problem in the wave-number-space, inverse methods in the data-subspace, and Jacobian matrix technology in the wavenumber domain. And we have tested the algorithm by using the synthetic data. At the end of this paper, we use data-space methods to inverse a set of field data, and we demonstrate the inversion results; this has further confirmed the inversion algorithm universal serviceability.We summarized the advantages and disadvantages of the algorithm at the end of the paper, and brought forward the image of three-dimensional inversion in the data spatial domain as the algorithm's research direction.