發(fā)布時(shí)間：2018-07-29 21:06

【摘要】：高密度電阻率法是一種重要的淺層地球物理方法,其應(yīng)用十分廣泛,特別是在水文、工程、環(huán)境地質(zhì)調(diào)查等方面的應(yīng)用越來越深入。為了提高精度和效率,并使其取得更好的應(yīng)用效果,高效的電阻率反演技術(shù)是必不可少的。因此,有必要對電阻率反演技術(shù)進(jìn)行更多的研究和討論。本文采用有限單元法實(shí)現(xiàn)了2.5D高密度電阻率正演研究,并基于Tikhonov正則化反演思想構(gòu)建反演目標(biāo)函數(shù),實(shí)現(xiàn)了不同反演最優(yōu)化方法和不同穩(wěn)定因子的2.5D高密度電阻率反演研究。首先,從2.5D高密度電阻率滿足的微分方程及邊界條件出發(fā),推導(dǎo)了關(guān)于電位的變分問題,采用三角單元網(wǎng)格剖分技術(shù),推導(dǎo)了線性插值單元剛度矩陣的表達(dá)式,同時(shí)對剛度矩陣采用高效的變寬帶存儲方式及結(jié)合線性方程組的直接求解技術(shù),最終實(shí)現(xiàn)了2.5D高密度電阻率的正演計(jì)算。通過設(shè)置水平層狀介質(zhì)及垂直接觸帶的模型驗(yàn)證了算法的正確性。其次,針對高密度電阻率反演問題,本文構(gòu)建了高密度電阻率反演正則化目標(biāo)函數(shù),采用了電極互換原理實(shí)現(xiàn)了偏導(dǎo)數(shù)矩陣的快速計(jì)算,對不同反演最優(yōu)化方法的收斂性進(jìn)行研究,詳細(xì)分析了反演結(jié)果。研究了不同的穩(wěn)定因子并進(jìn)行了大量試算,詳細(xì)分析了穩(wěn)定因子對反演結(jié)果的影響及采用改進(jìn)的L-curve正則化因子自動選擇算法等技術(shù)提高了反演解的穩(wěn)定性。通過研究最優(yōu)化算法發(fā)現(xiàn),共軛梯度法反演效果穩(wěn)定,收斂速度適中,高斯牛頓法反演效果理想,收斂速度快,擬牛頓法與高斯牛頓法收斂速度相當(dāng),最速下降法效果最差。穩(wěn)定因子的主要功能是對模型解的空間進(jìn)行限制,以減少多解性,求得穩(wěn)定解。通過對穩(wěn)定因子的研究可知,在高斯牛頓法的反演中,最小范數(shù)穩(wěn)定因子和最大平滑穩(wěn)定因子反演得到的異常模型邊界是光滑漸變的;而最小梯度支持穩(wěn)定因子具有更好的識別陡變異常體邊界的能力,有利于實(shí)現(xiàn)陡變邊界反演。
[Abstract]:High density resistivity method is an important shallow geophysical method, and its application is very extensive, especially in hydrology, engineering, environmental geological survey and so on. In order to improve the accuracy and efficiency, and achieve better application effect, high efficiency resistivity inversion technology is essential. Therefore, it is necessary to do more research and discussion on resistivity inversion technology. In this paper, the forward modeling of 2.5D high density resistivity is realized by finite element method, and the inversion objective function is constructed based on the idea of Tikhonov regularization inversion, and the 2.5D inversion of high density resistivity with different inversion optimization methods and different stability factors is realized. Firstly, based on the differential equation and boundary condition of 2.5D high density resistivity, the variational problem of potential is derived. The expression of linear interpolation element stiffness matrix is derived by using triangular element mesh generation technique. At the same time, the forward calculation of 2.5D high density resistivity is realized by using the efficient variable wideband storage method and the direct solution technique of linear equations for stiffness matrix. The correctness of the algorithm is verified by setting the model of horizontal layered medium and vertical contact band. Secondly, in order to solve the problem of high density resistivity inversion, the regularization objective function of high density resistivity inversion is constructed, and the fast calculation of partial derivative matrix is realized by using the principle of electrode exchange. The convergence of different inversion optimization methods is studied and the inversion results are analyzed in detail. The different stability factors are studied and a large number of experiments are carried out. The influence of the stability factors on the inversion results is analyzed in detail, and the stability of the inversion solution is improved by using the improved L-curve regularization factor automatic selection algorithm. By studying the optimization algorithm, it is found that the inversion effect of conjugate gradient method is stable, the convergence rate is moderate, the inversion effect of Gao Si Newton method is ideal and the convergence rate is fast, the convergence speed of quasi-Newton method is comparable to that of Gao Si Newton method, and the effect of steepest descent method is the worst. The main function of the stability factor is to limit the space of the model solution in order to reduce the multiplicity and obtain the stable solution. Through the study of the stability factor, we can know that in the inversion of Gao Si Newton method, the boundary of the abnormal model obtained by the inversion of the minimum norm stability factor and the maximum smooth stability factor is smooth and gradual. The minimum gradient support stability factor has a better ability to identify the boundary of the steeply variable anomaly, which is helpful for the inversion of the steeply variable boundary.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：P631.322

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本文編號：2154020