本文選題：頻譜激電法 + Cole-Cole模型��； 參考：《吉林大學(xué)》2017年碩士論文

【摘要】：頻譜激電法(SIP)也稱復(fù)電阻率法(CR)具有多參數(shù)解釋異常的能力,多個(gè)Cole-Cole模型參數(shù)可以為評(píng)價(jià)異常源的性質(zhì)提供更多的信息。由于Cole-Cole模型參數(shù)較多,各參數(shù)靈敏度不同,且SIP中既包含激發(fā)極化效應(yīng)又包含電磁效應(yīng),這些都制約著SIP反演問(wèn)題的研究。反演是解釋地電結(jié)構(gòu)的最終手段,研究一種基于同時(shí)考慮激發(fā)極化效應(yīng)和電磁感應(yīng)效應(yīng)正演、同時(shí)反演四個(gè)Cole-Cole模型參數(shù)的SIP反演算法對(duì)SIP的研究至關(guān)重要。本文首先基于既考慮激電效應(yīng)又考慮電磁效應(yīng)的一維SIP正演,實(shí)現(xiàn)了一維SIP最小二乘反演。本文采用利用SIP數(shù)據(jù)實(shí)部和虛部聯(lián)合反演的方法,將反演域從復(fù)數(shù)域變?yōu)閷?shí)數(shù)域,降低了反演的多解性。為了更好的反演靈敏度較低的頻率相關(guān)系數(shù)和時(shí)間常數(shù),本文提出實(shí)部和虛部加權(quán)反演的思想,在定義目標(biāo)函數(shù)時(shí)對(duì)實(shí)部和虛部的目標(biāo)函數(shù)進(jìn)行加權(quán),在反演不同參數(shù)時(shí),通過(guò)控制實(shí)部和虛部在反演中所占的比重來(lái)提高各參數(shù)的反演效果。為此本文推導(dǎo)了利用SIP數(shù)據(jù)實(shí)部和虛部聯(lián)合加權(quán)反演Cole-Cole模型參數(shù)的最小二乘反演算法。模型試算結(jié)果表明:這種反演方法不僅可以很好的反演零頻電阻率和極化率,還可以顯著提高頻率相關(guān)系數(shù)和時(shí)間常數(shù)的反演效果。三維反演方面,本文基于既考慮激電效應(yīng)又考慮電磁效應(yīng)的三維SIP有限差分正演,利用現(xiàn)今較為成熟的NLCG技術(shù),實(shí)現(xiàn)了同時(shí)反演四個(gè)Cole-Cole模型參數(shù)的三維SIP反演算法。三維反演采用電場(chǎng)實(shí)部和虛部聯(lián)合反演的方案,來(lái)降低反演的多解性。由于是電場(chǎng)實(shí)部和虛部聯(lián)合反演,故本文推導(dǎo)了三維反演電場(chǎng)實(shí)部和虛部目標(biāo)函數(shù)的靈敏度矩陣表達(dá)式,并給出利用擬正演求取實(shí)部和虛部靈敏度矩陣的方法,大大降低了計(jì)算費(fèi)用,避免了直接求靈敏度矩陣耗時(shí)過(guò)長(zhǎng)和內(nèi)存不夠等問(wèn)題。為了解決一些參數(shù)靈敏度低、反演難度大的問(wèn)題,在反演時(shí)采用對(duì)實(shí)部和虛部加權(quán)的方法,并設(shè)計(jì)理論模型進(jìn)行了試算,證明了算法的可行性、優(yōu)越性和穩(wěn)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.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P631.3

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