本文選題：積分方程 + 擬線性��； 參考：《吉林大學(xué)》2016年博士論文

【摘要】：Cole-Cole模型作為描述巖、礦石頻譜特征的經(jīng)驗公式廣泛應(yīng)用于復(fù)電阻率正、反演研究當(dāng)中。與時間域激發(fā)極化法相比,頻率域激電法(SIP)中包含了更強的電磁效應(yīng),SIP反演也因反演參數(shù)更多對正反演的效率提出了更高的要求。因此,了解并掌握大地介質(zhì)中的電磁效應(yīng)和激電效應(yīng)的規(guī)律,提出并實現(xiàn)快速有效的SIP三維正反演算法,對SIP異常的解釋至關(guān)重要。本文首先從理論上研究了大地介質(zhì)的電磁效應(yīng)和激電效應(yīng):通過理論分析和計算,剖析了大地介質(zhì)電磁效應(yīng)的特點,研究了其隨頻率、傳播距離、介質(zhì)電阻率變化的規(guī)律;通過三維數(shù)值模擬,研究和分析了在電磁效應(yīng)存在時,激電異常隨頻率變化的規(guī)律。在此基礎(chǔ)上,研究了接地導(dǎo)線源激發(fā)的電場空間分布規(guī)律,據(jù)此明確劃分了復(fù)電阻率勘探的軸向區(qū)和赤道區(qū),發(fā)現(xiàn)了視復(fù)電阻率畸變帶,探究了畸變原因和規(guī)律。其次,對三維電磁模擬的積分方程近似算法進(jìn)行了系統(tǒng)的研究,這些算法包括Born近似方法、非線性散射近似方法及擬線性系列近似方法,對它們的誤差來源、適用范圍、模擬速度進(jìn)行了分析和對比。文中著重對比了對角擬線性近似法與標(biāo)量擬線性近似法的計算精度,并通過反射系數(shù)分析了對角擬線性近似精度高的原因。通過利用格林函數(shù)的空間對稱性和互換定理,壓縮了格林系數(shù)的計算量,加快系數(shù)矩陣的生成速度,實現(xiàn)快速擬線性近似方法,為三維復(fù)電阻率反演研究打下良好的基礎(chǔ)。最后,在三維復(fù)電阻率積分方程快速擬線性近似正演的基礎(chǔ)上,本文提出并實現(xiàn)了三維復(fù)電阻率反演算法。為了改善反演的多解性,反演中加入光滑約束條件和Cole-Cole參數(shù)范圍約束條件,提高反演結(jié)果的可靠性。通過對理論模型的反演試算,分析了算法的速度、穩(wěn)定性和反演效果。結(jié)果表明:該方法計算速度快、穩(wěn)定性高,對零頻電阻率、極化率和頻率相關(guān)系數(shù)的反演效果較好。論文還研究了中梯觀測方式包含強列電磁效應(yīng)的復(fù)電阻率反演,結(jié)果也表明:通過反演可以很好地恢復(fù)異常體的形態(tài)、位置及真實的模型參數(shù),但噪音和初始模型的選擇對反演結(jié)果影響較大。
[Abstract]:The empirical formula of the Cole-Cole model as the description rock and the spectral characteristics of the ore is widely used in the complex resistivity positive and inversion research. Compared with the time domain excitation polarization, the frequency domain excitation method (SIP) contains a stronger electromagnetic effect, and the SIP inversion also raises the higher requirements for the efficiency of the positive and negative performance because of the inversion parameters. The electromagnetic effect and the law of the excitation effect in the geodetic medium are mastered, and the fast and effective SIP three-dimensional positive and negative algorithm is proposed and realized, which is very important for the interpretation of the SIP anomaly. Firstly, the electromagnetic effect and the excitation effect of the geodetic medium are studied theoretically. The characteristics of the electromagnetic effect of the geodetic medium are analyzed by theoretical analysis and calculation. The law of variation with frequency, propagation distance and dielectric resistivity is studied. Through three dimensional numerical simulation, the law of abnormal excitation abnormality with frequency is studied and analyzed in the presence of electromagnetic effect. On this basis, the spatial distribution of electric field excited by grounding wire source is studied, and the axial zone of complex resistivity exploration is clearly divided. In the equatorial region, the distortion zone of the apparent resistivity is found and the causes and laws of the distortion are explored. Secondly, a systematic study of the approximate algorithm for the integral equation of the three-dimensional electromagnetic simulation is carried out. These algorithms include the Born approximation method, the nonlinear scattering approximation method and the quasi linear series approximation method, and the error sources, the scope of application and the simulation speed. The calculation accuracy of the diagonal quasilinear approximation method and the scalar quasi linear approximation method is compared, and the reason for the high accuracy of the diagonal quasi linear approximation is analyzed by the reflection coefficient. By using the spatial symmetry and Exchange Theorem of the Green function, the calculation amount of the Green coefficient is compressed and the coefficient matrix is accelerated. A fast quasi linear approximation method is realized and a good foundation is laid for the study of three-dimensional complex resistivity inversion. Finally, a three-dimensional complex resistivity inversion algorithm is proposed and realized on the basis of the fast quasi linear approximation of the three dimensional complex resistivity integral equation. In order to improve the multi solution of the inversion, a smooth constraint bar is added to the inversion. The reliability of the inversion results is improved by the constraint conditions of the part and the Cole-Cole parameter range. Through the inversion of the theoretical model, the speed, stability and the inversion effect of the algorithm are analyzed. The results show that the method has a fast calculation speed, high stability, and a better inversion effect on the zero frequency resistivity, polarizability and frequency correlation coefficient. The paper also studies the results. The observation mode of the middle ladder includes the inversion of the complex resistivity of the strong column electromagnetic effect. The results also show that the shape, position and real model parameters of the abnormal body can be recovered well by inversion, but the noise and the selection of the initial model have great influence on the inversion results.

【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：P631.3

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前2條

1 江飛;丘陵地貌條件下并行電法的勘探實踐研究[D];安徽理工大學(xué);2017年

2 王少博;三維大地電磁正演快速算法研究[D];吉林大學(xué);2017年

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本文編號：1821235