本文選題：頻率域航空電磁法 + 積分方程��； 參考：《中國(guó)地質(zhì)大學(xué)(北京)》2017年碩士論文

【摘要】：頻率域航空電磁測(cè)量(AEM)能夠在地面電法不能到達(dá)的偏遠(yuǎn)地區(qū)獲得大量的電磁數(shù)據(jù)。典型的航空電磁測(cè)量每隔幾米一個(gè)采樣點(diǎn),故可能包含上萬(wàn)個(gè)采樣點(diǎn),甚至更多。這些大規(guī)模數(shù)據(jù)的定量計(jì)算是十分耗時(shí),并極具挑戰(zhàn)性。正演是反演的基礎(chǔ),因此快速而精確的正演數(shù)值模擬計(jì)算是反演取得良好成果的關(guān)鍵。積分方程(IE)法作為數(shù)值模擬中的一種有效的方法,因?yàn)槠渲粚?duì)異常體區(qū)域進(jìn)行剖分,故具有計(jì)算速度快的優(yōu)勢(shì)。然而,積分方程技術(shù)的主要困難在于線性方程矩陣的大小,如果線性方程矩陣過大,則將需要消耗大量的內(nèi)存,計(jì)算時(shí)間也增大很多。積分方程技術(shù)的這一限制在反演問題中變得更加嚴(yán)重,因?yàn)榉囱輹r(shí)對(duì)于不同的迭代模型參數(shù)需要多次正演計(jì)算。為了解決這個(gè)問題,一些近似的解法被引進(jìn)全積分解中。國(guó)外學(xué)者Zhdanov和Fang (1996a,1997)開發(fā)出了基于電反射系數(shù)的準(zhǔn)線性近似算法(QL近似)。在這種近似的方法中異常區(qū)域內(nèi)的異常電場(chǎng)通過一個(gè)電反射張量λ與背景場(chǎng)Eb成比例。通過求解一個(gè)基于散射電流的積分方程的最小值問題得到這個(gè)電反射張量λ。這種方法的優(yōu)點(diǎn)在于如果想要簡(jiǎn)化和加速計(jì)算,電反射張量能夠被假定為標(biāo)量或者對(duì)角張量來(lái)取代全張量。然而,QL近似的一個(gè)問題是其電反射張量λ需要在每一個(gè)新的激發(fā)源情況下重新計(jì)算一次。這就意味著這個(gè)近似方法不適合用于多源排列的反演方案里,尤其是這些數(shù)據(jù)的三維反演方法變得極度不切實(shí)際。為解決這個(gè)問題,Zhdanov等基于所謂的“局部”電反射張量又開發(fā)出了一種新的準(zhǔn)線性近似(QL)方法,該方法具有源獨(dú)立性。這種新的方法被稱作局部準(zhǔn)線性近似(LQL)方法,它結(jié)合了局部非線性近似(LN)和原始的準(zhǔn)線性近似(QL)方法的思想。本文就是將這種局部準(zhǔn)線性近似(LQL)的方法應(yīng)用到頻率域航空電磁法的合成數(shù)據(jù)反演中,反演結(jié)果顯示了在解決多源排列的頻率域航空電磁法中,這個(gè)方法是穩(wěn)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.
【學(xué)位授予單位】：中國(guó)地質(zhì)大學(xué)(北京)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P631.326

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