基于局部准线性近似的频率域航空电磁法三维正反演研究

发布时间：2018-06-09 17:53

本文选题：频率域航空电磁法 + 积分方程　；参考：《中国地质大学(北京)》2017年硕士论文

【摘要】：频率域航空电磁测量(AEM)能够在地面电法不能到达的偏远地区获得大量的电磁数据。典型的航空电磁测量每隔几米一个采样点,故可能包含上万个采样点,甚至更多。这些大规模数据的定量计算是十分耗时,并极具挑战性。正演是反演的基础,因此快速而精确的正演数值模拟计算是反演取得良好成果的关键。积分方程(IE)法作为数值模拟中的一种有效的方法,因为其只对异常体区域进行剖分,故具有计算速度快的优势。然而,积分方程技术的主要困难在于线性方程矩阵的大小,如果线性方程矩阵过大,则将需要消耗大量的内存,计算时间也增大很多。积分方程技术的这一限制在反演问题中变得更加严重,因为反演时对于不同的迭代模型参数需要多次正演计算。为了解决这个问题,一些近似的解法被引进全积分解中。国外学者Zhdanov和Fang (1996a,1997)开发出了基于电反射系数的准线性近似算法(QL近似)。在这种近似的方法中异常区域内的异常电场通过一个电反射张量λ与背景场Eb成比例。通过求解一个基于散射电流的积分方程的最小值问题得到这个电反射张量λ。这种方法的优点在于如果想要简化和加速计算,电反射张量能够被假定为标量或者对角张量来取代全张量。然而,QL近似的一个问题是其电反射张量λ需要在每一个新的激发源情况下重新计算一次。这就意味着这个近似方法不适合用于多源排列的反演方案里,尤其是这些数据的三维反演方法变得极度不切实际。为解决这个问题,Zhdanov等基于所谓的“局部”电反射张量又开发出了一种新的准线性近似(QL)方法,该方法具有源独立性。这种新的方法被称作局部准线性近似(LQL)方法,它结合了局部非线性近似(LN)和原始的准线性近似(QL)方法的思想。本文就是将这种局部准线性近似(LQL)的方法应用到频率域航空电磁法的合成数据反演中,反演结果显示了在解决多源排列的频率域航空电磁法中,这个方法是稳定和有效的。
[Abstract]:Frequency domain airborne electromagnetic measurements (AEMs) can obtain large amounts of electromagnetic data in remote areas not accessible by surface electricity. Typical aero-electromagnetic measurements can contain tens of thousands or more of sampling points every few metres. The quantitative calculation of these large-scale data is time-consuming and challenging. Forward modeling is the basis of inversion, so fast and accurate forward numerical simulation is the key to obtain good results. As an effective method in numerical simulation, the IE) method has the advantage of fast calculation because it only dissects the abnormal body area. However, the main difficulty of integral equation technique lies in the size of linear equation matrix. If the linear equation matrix is too large, it will need a lot of memory and the calculation time will be much longer. This limitation of the integral equation technique becomes more serious in the inversion problem because the inversion requires multiple forward calculations for different parameters of the iterative model. In order to solve this problem, some approximate solutions are introduced into the total integral solution. The QL approximation algorithm based on the electric reflection coefficient has been developed by the foreign scholars Zhdanov and Fang / 1996 / 1997. In this approximate method, the anomalous electric field in the anomalous region is proportional to the background field E b through an electric reflection Zhang Liang 位. By solving the minimum value problem of an integral equation based on scattering current, the electrically reflected Zhang Liang 位 is obtained. The advantage of this method is that if we want to simplify and accelerate the calculation, the electrically reflected Zhang Liang can be assumed to be scalar or diagonal Zhang Liang instead of the full Zhang Liang. However, one of the problems of QL approximation is that its electroreflection Zhang Liang 位 needs to be recalculated in the case of each new excitation source. This means that this approximate method is not suitable for multi-source array inversion, especially the 3D inversion of these data becomes extremely impractical. In order to solve this problem, a new quasi-linear approximate Zhang Liang (QL) method is developed based on the so-called "local" electroreflection (Zhang Liang), which is independent of the source. This new method is called the local quasilinear approximation (LQL) method, which combines the local nonlinear approximation (LN) and the original quasilinear approximation (QL) method. In this paper, the local quasi-linear approximation (LQL) method is applied to the synthetic data inversion of the frequency domain aero-electromagnetic method. The inversion results show that the method is stable and effective in solving the multi-source array of frequency-domain aero-electromagnetic method.
【学位授予单位】：中国地质大学(北京)
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.326

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