频谱激电数据实部和虚部加权反演Cole-Cole模型参数研究

发布时间：2018-04-23 08:39

本文选题：频谱激电法 + Cole-Cole模型　；参考：《吉林大学》2017年硕士论文

【摘要】：频谱激电法(SIP)也称复电阻率法(CR)具有多参数解释异常的能力,多个Cole-Cole模型参数可以为评价异常源的性质提供更多的信息。由于Cole-Cole模型参数较多,各参数灵敏度不同,且SIP中既包含激发极化效应又包含电磁效应,这些都制约着SIP反演问题的研究。反演是解释地电结构的最终手段,研究一种基于同时考虑激发极化效应和电磁感应效应正演、同时反演四个Cole-Cole模型参数的SIP反演算法对SIP的研究至关重要。本文首先基于既考虑激电效应又考虑电磁效应的一维SIP正演,实现了一维SIP最小二乘反演。本文采用利用SIP数据实部和虚部联合反演的方法,将反演域从复数域变为实数域,降低了反演的多解性。为了更好的反演灵敏度较低的频率相关系数和时间常数,本文提出实部和虚部加权反演的思想,在定义目标函数时对实部和虚部的目标函数进行加权,在反演不同参数时,通过控制实部和虚部在反演中所占的比重来提高各参数的反演效果。为此本文推导了利用SIP数据实部和虚部联合加权反演Cole-Cole模型参数的最小二乘反演算法。模型试算结果表明:这种反演方法不仅可以很好的反演零频电阻率和极化率,还可以显著提高频率相关系数和时间常数的反演效果。三维反演方面,本文基于既考虑激电效应又考虑电磁效应的三维SIP有限差分正演,利用现今较为成熟的NLCG技术,实现了同时反演四个Cole-Cole模型参数的三维SIP反演算法。三维反演采用电场实部和虚部联合反演的方案,来降低反演的多解性。由于是电场实部和虚部联合反演,故本文推导了三维反演电场实部和虚部目标函数的灵敏度矩阵表达式,并给出利用拟正演求取实部和虚部灵敏度矩阵的方法,大大降低了计算费用,避免了直接求灵敏度矩阵耗时过长和内存不够等问题。为了解决一些参数灵敏度低、反演难度大的问题,在反演时采用对实部和虚部加权的方法,并设计理论模型进行了试算,证明了算法的可行性、优越性和稳定性。
[Abstract]:Spectral IP (complex resistivity method) has the ability to interpret anomalies with multiple parameters. Multiple Cole-Cole model parameters can provide more information for evaluating the properties of anomaly sources. Because of the large number of parameters in the Cole-Cole model, the sensitivity of each parameter is different, and the SIP includes both polarization effect and electromagnetic effect, which restrict the research of SIP inversion. Inversion is the ultimate method to explain geoelectric structure. It is very important for SIP to study a SIP inversion algorithm based on considering both induced polarization effect and electromagnetic induction effect and simultaneously retrieving the parameters of four Cole-Cole models. In this paper, the one-dimensional SIP least square inversion is realized based on the one-dimensional SIP forward modeling which considers both the IP effect and the electromagnetic effect. In this paper, by using the method of joint inversion of real and imaginary parts of SIP data, the inversion domain is changed from complex number domain to real number domain, which reduces the multiplicity of inversion solutions. In order to improve the frequency correlation coefficient and time constant with lower inversion sensitivity, the idea of weighted inversion of real and imaginary parts is presented in this paper. The objective functions of real and imaginary parts are weighted when defining objective functions. The inversion effect of each parameter is improved by controlling the proportion of real part and imaginary part in inversion. In this paper, the least square inversion algorithm for the parameters of Cole-Cole model is derived by combining real and virtual parts of SIP data. The simulation results show that this inversion method can not only invert the zero frequency resistivity and polarizability but also improve the inversion effect of frequency correlation coefficient and time constant. In the aspect of 3D inversion, based on the 3D SIP finite difference forward modeling which considers both the IP effect and the electromagnetic effect, a 3D SIP inversion algorithm for simultaneous inversion of four Cole-Cole model parameters is implemented by using the current mature NLCG technique. In order to reduce the multiplicity of inversion, the method of electric field real part and virtual part is used in 3D inversion. Because of the joint inversion of the real and imaginary parts of the electric field, this paper deduces the expression of the sensitivity matrix of the objective function of the real part and the imaginary part of the three-dimensional inversion of the electric field, and gives a method to obtain the sensitivity matrix of the real part and the imaginary part by using the pseudo forward modeling. The computational cost is greatly reduced, and the problems such as time-consuming and insufficient memory are avoided. In order to solve the problems of low parameter sensitivity and high inversion difficulty, the method of weighted real and imaginary parts is used in inversion, and a theoretical model is designed to test the feasibility, superiority and stability of the algorithm.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.3

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