1D And 2.5D Modeling And Inversion Of Complex Resistivity Data

Complex resistivity method(CR) is one of the geophysical prospecting methods that based on the complex resistivity characteristics difference of rocks and ores, the outstanding characteristic of this method is possessing the ability to reflect abnormal bodies with multi-parameter. But the inversion technique has not gotten better resolved, which has seriously affected the application and development of this method, therefore, it is of great research significance to carry out the study on 1D and 2.5D CR forward and inversion.On the premise of neglecting the electromagnetic coupling, the research work takes the Cole-Cole complex resistivity model into horizontal layered medium of DC resistance forward formula to realize one-dimensional CR modeling, then inducts and summarizes one-dimensional CR response characteristic with trials. From basic equations and boundary conditions that complex resistivity 2.5D point source potential satisfies, the variation equations about potential have been derived. And with binary tree(Bi-Tree)triangle element subdivision technique, linear and quadratic interpolation unit stiffness matrix expression were deduced. And the boundary adopts approximation method to make treated steel matrix has nothing to do with point source position but depends only on the power supply frequency and wave number; Meanwhile, with the matrix rearrangement and fill element analysis method based on graph theory and in combination with linear equation directly solving technology to finally realize 2.5D complex resistivity fast modeling. Furthermore, the accuracy of this algorithm was verified through 2.5D simulation of a horizontal layered medium model, on the basic of which, the typical complex resistivity models were simulated to reach the analysis and conclusion of 2.5D complex resistivity amplitude and phase response characteristic.In view of the inversion of complex resistivity, the regularization objective function was constructed, and the stable solution was implemented by Re-weighted conjugate gradient algorithms. In the process of one-dimensional inversion, we firstly determined one-dimensional resistivity model by fitting low frequency complex resistivity amplitude data, and then other Cole-Cole model parameters by fitting phase data, combining with theoretical example to verify the feasibility of this inversion strategy. In the process of 2.5D inversion, the complex resistivity amplitude and phase inversion objective function was constructed, and the sensitivity matrix calculation formula of Cole-Cole model parameters were derived with which was computed by reciprocity principle. In the inversion algorithm, we applied maximum smoothness stabilizing functional, parameters boundary-constrain and improved regularization factor automatically selected algorithm to improve the stability of inversion.