發(fā)布時間：2018-05-18 03:01

  本文選題：地面核磁共振 + 核函數(shù)��； 參考：《吉林大學(xué)》2017年碩士論文

【摘要】：地面核磁共振技術(shù)利用地下水中氫質(zhì)子的自旋性質(zhì),通過在地面鋪設(shè)探測線圈,對地下水進行直接的無損的探測,憑借其方法的高效性和對結(jié)果評估的準確性,該技術(shù)成為主要的現(xiàn)代地球物理找水方法。近年來,隨著磁共振探測方法研究的不斷深入,已經(jīng)由一維探測向二維、三維探測發(fā)展。目前常用的二維磁共振探測通常采用陣列式線圈,在地面同一條測線上鋪設(shè)一個發(fā)射線圈和多個接收線圈,接收線圈采用邊對邊或者半覆蓋方式內(nèi)嵌在發(fā)射線圈內(nèi)部,然后利用多通道磁共振儀器同時進行探測。該方法可以對地下水進行二維探測成像,但是針對地下復(fù)雜含水構(gòu)造仍然不能進行準確的探測,由于地面測點有限,其反演結(jié)果精度和成像平滑度都有待提高。若鋪設(shè)多個探測線圈,可以提高結(jié)果精度,但是會增加探測工作量,降低工作效率。針對上述缺點,本文提出基于三次樣條插值的地面核磁共振反演方法,該方法可以在提高反演精度和成像平滑度的同時,減少野外探測鋪設(shè)線圈的工作量。本文首先對三維空間進行網(wǎng)格剖分,計算接收和發(fā)射線圈周圍空間分布的磁場強度,計算正反演所需的核函數(shù)。建立地下含水體模型,正演計算得到E0-q曲線。然后對初始振幅E0進行三次樣條插值計算,得到新的數(shù)據(jù)矩陣,再進行二維含水量反演成像,利用二分法搜索最優(yōu)正則化因子,提高反演算法效率。最后,針對不同的地下含水體模型進行了正演仿真和反演計算,驗證該方法的適用性。本文在進行正演時,提出利用三次樣條插值方法對初始振幅E0進行插值計算,擴大數(shù)據(jù)矩陣,然后重新計算核函數(shù)使之與新的數(shù)據(jù)矩陣對應(yīng),通過對核函數(shù)進行SVD分解得到分辨率矩陣,對比插值前后的模型分辨率信息,驗證基于三次樣條插值的正演方法對淺層探測區(qū)域的高分辨能力。針對經(jīng)過三次樣條插值方法對各探測線圈的初始振幅0E進行插值后,數(shù)據(jù)矩陣和核函數(shù)矩陣擴大,導(dǎo)致反演計算量增大的問題,本文提出利用二分法搜索最優(yōu)正則化因子?,不用計算每一個?對應(yīng)的目標(biāo)函數(shù)的值,可以大幅減少計算量,提高反演算法的效率。為了檢驗該方法得到的反演結(jié)果的精確度,本文進行了初始振幅插值結(jié)果和含水量反演結(jié)果的誤差分析。在理想情況下,初始振幅插值結(jié)果均方根誤差均小于7 n V,在加入20 n V噪聲后,插值結(jié)果最大均方根誤差為13.475 n V。在反演結(jié)果方面,基于三次樣條插值的反演方法可以降低含水量反演結(jié)果整體均方根誤差4個百分點。最后,使用該方法對長春市燒鍋鎮(zhèn)和安徽省黃山市陽臺村的野外實測數(shù)據(jù)進行了反演解釋,驗證該方法的有效性。通過上述研究,本文得出基于三次樣條插值的地面核磁共振反演方法能夠在減少探測線圈數(shù)量的同時,提高反演精度和成像平滑度,實際運用中可以有效降低工作量,提高工作效率。此外,本文提出的方法運用在三維探測和數(shù)據(jù)解釋方面更具實際意義,三維探測常用的測量模式是利用5個線圈在四個水平方向進行半覆蓋形式鋪設(shè),在測量區(qū)域的對角線上移動測量,其探測線圈的增加數(shù)量是按平方形式增長,因此基于三次樣條插值的反演方法可以大幅減少三維探測的線圈鋪設(shè)工作量,并且得到平滑精確的地下水成像結(jié)果。
[Abstract]:Ground magnetic resonance (NMR) technology uses the spin properties of hydrogen protons in ground water. By laying detection coils on the ground, the ground water is detected directly and nondestructive. By virtue of its efficiency and accuracy of evaluation, the technology is the main modern geophysical method for finding water. In recent years, with the method of magnetic resonance detection At present, the commonly used two-dimensional magnetic resonance detection usually uses array coil, laying a transmitting coil and multiple receiving coils on the same line on the ground, the receiving coil is embedded inside the launching coil by the side to side or half cover mode, and then uses more. The method can detect and imaging groundwater at the same time. This method can detect and imaging groundwater in two dimensions, but it can still not be detected accurately for the complex underground water bearing structure. Because of the limited ground measurement point, the accuracy of the inversion results and the imaging smoothness are still to be improved. If a number of detection coils are laid, the accuracy of the results can be improved. In view of the above shortcomings, this paper proposes a ground magnetic resonance inversion method based on three spline interpolation. This method can reduce the workload of field detection and lay coils while improving the accuracy of inversion and the smoothness of imaging. The magnetic field intensity around the space around the coil is collected and the kernel function required for the positive and negative performance is calculated. The underground water body model is established and the E0-q curve is obtained by forward calculation. Then the initial amplitude E0 is calculated by three spline interpolation, and the new data matrix is obtained, then the two-dimensional water content inversion imaging is carried out, and the optimal regularization cause is searched by the dichotomous method. In the end, the applicability of the method is verified by the forward simulation and inversion of the different underground water models. In this paper, the three spline interpolation method is used to interpolate the initial amplitude E0, and the number matrix is expanded, then the kernel function is recalculated and the new number is recalculated. According to the matrix corresponding, the resolution matrix is obtained by SVD decomposition of the kernel function, and the resolution information of the model before and after the interpolation is compared, and the high resolution ability of the forward method based on the three spline interpolation is verified. The data matrix is interpolated for the initial amplitude 0E of the detection coils by the three spline interpolation method. And the expansion of the kernel function matrix leads to the increase of the inverse calculation. In this paper, a dichotomy is proposed to search the optimal regularization factor. Without calculating the value of the corresponding target function, the calculation can be reduced greatly and the efficiency of the inversion algorithm can be improved. In order to test the accuracy of the inversion results obtained by this method, this paper has carried out the beginning of this paper. In the ideal case, the root error of the initial amplitude interpolation is less than 7 n V. After adding 20 N V noise, the maximum mean square root error of the interpolation result is 13.475 n V. in the inversion result, and the inversion method based on the three spline interpolation can reduce the water content inversion knot. The total root mean square error is 4 percentage points. Finally, the field data of Changchun burning pot town and Huangshan City balcony village in Anhui province are retrieved to verify the validity of the method. Through the above study, the ground nuclear magnetic resonance inversion method based on the three spline interpolation can reduce the detection coil. At the same time, in order to improve the accuracy of inversion and the smoothness of imaging, the actual application can effectively reduce the workload and improve the working efficiency. In addition, the method proposed in this paper is more practical in the aspects of three-dimensional detection and data interpretation, and the commonly used measurement mode of three-dimensional detection is to use 5 coils in four horizontal directions to half cover the form. Laying, moving measurements on the diagonal of the measuring area, the increase in the number of detection coils increases according to the square form, so the inversion method based on the three spline interpolation can greatly reduce the workload of the coil laying of the three dimensional detection and get a smooth and accurate result of the groundwater imaging.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O482.532

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