A Weighting Inversion Method of Spectrum Induced Polarization

Wu Yu Hao

doi:10.11648/j.earth.20190803.16

Abstract

The inversion results of complex resistivity method are four Cole-Cole model parameters. Among the four parameters, the frequency dependence and the time constant are more difficult to invert. It is necessary to study an algorithm that can invert the four Cole-Cole model parameters at the same time. In this paper, the least squares and OCCAM inversion algorithms are used to invert four Cole-Cole model parameters. In other words, two model constraints are added to the objective function. When inverting different Cole-Cole model parameters, the real and imaginary parts of the data are weighted to adjust the proportion of real part and imaginary part of data in inversion. Firstly, the formula of the algorithm is deduced. Then the theoretical models are designed for inversion trial calculation. In the inversion process, the inversion converges steadily by adjusting the Lagrange factor, and the inversion effect is improved by adjusting the weighting coefficients of real part and imaginary part. This method can get better inversion results by adjusting the proportion of the real and imaginary parts of the data in the inversion. The model trial results show that the weighting inversion algorithm significantly improves the results of the inversion of the four Cole-Cole parameters.

Highlights

Spectrum induced polarization (SIP), known as complex resistivity method (CR), is widely used in environmental and engineering, mineral and land pollution exploration, and based on the difference of electrochemical properties between rocks and ores
Cole-Cole model and its combination are used to fit the induced polarization and electromagnetic coupling, laying the foundation of SIP, and he thought that the frequency dependence c and the time constant τ could be used to distinguish mineral from non-mineral. put forward the theory that the approximate formula is used as the forward model to obtain the true parameters of SIP from a measuring point
On the premise of considering electromagnetic coupling, this paper studies the weighting inversion of real and imaginary parts of 1D spectrum induced polarization data, and draws the following conclusions: 1. The real part and imaginary part of apparent complex resistivity are sensitive to different Cole-Cole parameters

Summary

Introduction

Spectrum induced polarization (SIP), known as complex resistivity method (CR), is widely used in environmental and engineering, mineral and land pollution exploration, and based on the difference of electrochemical properties between rocks and ores. Ghorbani et al [1] used the real and imaginary parts of complex resistivity to directly invert the Cole-Cole model parameters on the premise of considering electromagnetic coupling. He inverted one-dimensional direct current sounding using the amplitude data of complex resistivity observed at low frequencies, and obtained the resistivity model is acted as the initial model of the resistivity in SIP inversion, after that, invert four Cole-Cole model parameters at the same time. The inversion algorithm is deduced, and test several theoretical models show on the stability and superiority

Damped Least Squares Inversion Theory

Damped Least Squares Inversion Results and Analysis

Conclusion