基于三次样条插值的地面核磁共振反演方法研究

发布时间：2018-05-18 03:01

本文选题：地面核磁共振 + 核函数　；参考：《吉林大学》2017年硕士论文

【摘要】：地面核磁共振技术利用地下水中氢质子的自旋性质,通过在地面铺设探测线圈,对地下水进行直接的无损的探测,凭借其方法的高效性和对结果评估的准确性,该技术成为主要的现代地球物理找水方法。近年来,随着磁共振探测方法研究的不断深入,已经由一维探测向二维、三维探测发展。目前常用的二维磁共振探测通常采用阵列式线圈,在地面同一条测线上铺设一个发射线圈和多个接收线圈,接收线圈采用边对边或者半覆盖方式内嵌在发射线圈内部,然后利用多通道磁共振仪器同时进行探测。该方法可以对地下水进行二维探测成像,但是针对地下复杂含水构造仍然不能进行准确的探测,由于地面测点有限,其反演结果精度和成像平滑度都有待提高。若铺设多个探测线圈,可以提高结果精度,但是会增加探测工作量,降低工作效率。针对上述缺点,本文提出基于三次样条插值的地面核磁共振反演方法,该方法可以在提高反演精度和成像平滑度的同时,减少野外探测铺设线圈的工作量。本文首先对三维空间进行网格剖分,计算接收和发射线圈周围空间分布的磁场强度,计算正反演所需的核函数。建立地下含水体模型,正演计算得到E0-q曲线。然后对初始振幅E0进行三次样条插值计算,得到新的数据矩阵,再进行二维含水量反演成像,利用二分法搜索最优正则化因子,提高反演算法效率。最后,针对不同的地下含水体模型进行了正演仿真和反演计算,验证该方法的适用性。本文在进行正演时,提出利用三次样条插值方法对初始振幅E0进行插值计算,扩大数据矩阵,然后重新计算核函数使之与新的数据矩阵对应,通过对核函数进行SVD分解得到分辨率矩阵,对比插值前后的模型分辨率信息,验证基于三次样条插值的正演方法对浅层探测区域的高分辨能力。针对经过三次样条插值方法对各探测线圈的初始振幅0E进行插值后,数据矩阵和核函数矩阵扩大,导致反演计算量增大的问题,本文提出利用二分法搜索最优正则化因子?,不用计算每一个?对应的目标函数的值,可以大幅减少计算量,提高反演算法的效率。为了检验该方法得到的反演结果的精确度,本文进行了初始振幅插值结果和含水量反演结果的误差分析。在理想情况下,初始振幅插值结果均方根误差均小于7 n V,在加入20 n V噪声后,插值结果最大均方根误差为13.475 n V。在反演结果方面,基于三次样条插值的反演方法可以降低含水量反演结果整体均方根误差4个百分点。最后,使用该方法对长春市烧锅镇和安徽省黄山市阳台村的野外实测数据进行了反演解释,验证该方法的有效性。通过上述研究,本文得出基于三次样条插值的地面核磁共振反演方法能够在减少探测线圈数量的同时,提高反演精度和成像平滑度,实际运用中可以有效降低工作量,提高工作效率。此外,本文提出的方法运用在三维探测和数据解释方面更具实际意义,三维探测常用的测量模式是利用5个线圈在四个水平方向进行半覆盖形式铺设,在测量区域的对角线上移动测量,其探测线圈的增加数量是按平方形式增长,因此基于三次样条插值的反演方法可以大幅减少三维探测的线圈铺设工作量,并且得到平滑精确的地下水成像结果。
[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.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O482.532

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