基于拟线性积分方程法的三维复电阻率正反演研究

发布时间：2018-04-29 19:22

本文选题：积分方程 + 拟线性　；参考：《吉林大学》2016年博士论文

【摘要】：Cole-Cole模型作为描述岩、矿石频谱特征的经验公式广泛应用于复电阻率正、反演研究当中。与时间域激发极化法相比,频率域激电法(SIP)中包含了更强的电磁效应,SIP反演也因反演参数更多对正反演的效率提出了更高的要求。因此,了解并掌握大地介质中的电磁效应和激电效应的规律,提出并实现快速有效的SIP三维正反演算法,对SIP异常的解释至关重要。本文首先从理论上研究了大地介质的电磁效应和激电效应:通过理论分析和计算,剖析了大地介质电磁效应的特点,研究了其随频率、传播距离、介质电阻率变化的规律;通过三维数值模拟,研究和分析了在电磁效应存在时,激电异常随频率变化的规律。在此基础上,研究了接地导线源激发的电场空间分布规律,据此明确划分了复电阻率勘探的轴向区和赤道区,发现了视复电阻率畸变带,探究了畸变原因和规律。其次,对三维电磁模拟的积分方程近似算法进行了系统的研究,这些算法包括Born近似方法、非线性散射近似方法及拟线性系列近似方法,对它们的误差来源、适用范围、模拟速度进行了分析和对比。文中着重对比了对角拟线性近似法与标量拟线性近似法的计算精度,并通过反射系数分析了对角拟线性近似精度高的原因。通过利用格林函数的空间对称性和互换定理,压缩了格林系数的计算量,加快系数矩阵的生成速度,实现快速拟线性近似方法,为三维复电阻率反演研究打下良好的基础。最后,在三维复电阻率积分方程快速拟线性近似正演的基础上,本文提出并实现了三维复电阻率反演算法。为了改善反演的多解性,反演中加入光滑约束条件和Cole-Cole参数范围约束条件,提高反演结果的可靠性。通过对理论模型的反演试算,分析了算法的速度、稳定性和反演效果。结果表明:该方法计算速度快、稳定性高,对零频电阻率、极化率和频率相关系数的反演效果较好。论文还研究了中梯观测方式包含强列电磁效应的复电阻率反演,结果也表明:通过反演可以很好地恢复异常体的形态、位置及真实的模型参数,但噪音和初始模型的选择对反演结果影响较大。
[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.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P631.3

【引证文献】