重力和重力梯度数据联合反演方法研究

发布时间：2018-07-10 01:14

本文选题：重力和重力梯度联合反演 + 重力和重力梯度数据分析　；参考：《吉林大学》2016年博士论文

【摘要】：重力数据的处理和解释一直是地球物理数据处理和解释中的重要组成部分。近年来,随着全张量重力梯度测量系统(FTG)的发展及应用,重力梯度数据的地位也越来越重要。从理论上说,重力数据是重力位在垂直方向上的偏导数,重力梯度数据则是重力位在各方向的二次求导。在求导计算过程中,低频信号被压制,高频信号被增强。所以,在频率域比较重力数据和重力梯度数据,结果表明,重力数据包含较多的低频信息,重力梯度数据则包含较多的高频信息。因此,将重力和重力梯度数据联合,可以实现信息的互补,有效的降低反演中的多解性。基于这一点,本文针对重力和重力梯度数据联合反演的问题展开讨论。首先,对重力和重力梯度数据进行量化比较分析。通过重力梯度数据在频率域的表达式,推导重力梯度各分量之间的关系,发现在重力梯度各分量中,zzg分量包含的信息更多;随后,通过对比不同深度模型的zg分量和zzg分量的振幅谱,分析zg分量和zzg分量随深度的变化;分别对zg和zzg分量进行反演计算,结果表明,zg反演结果在深部的分辨率较高,zzg反演在浅部具有较高的分辨率。我们通过再加权反演的方法将深度加权函数结合到稳定函数部分,在仅考虑深度加权,不加任何其他约束条件的情况下,分别对重力场和重力梯度数据各分量进行反演计算,依据各分量的反演结果,对各分量在反演计算中的表现有了一个直观的印象,对各分量所包含信息的特点进行对比。随后,我们针对重力和重力梯度联合反演问题深入讨论。与单一分量反演相比,多分量联合反演需要消耗更多的计算时间和内存。首先,在反演计算开始前,我们需要计算并存储各分量的灵敏度矩阵。因为分量种类的增加,存储和计算灵敏度矩阵所消耗的内存空间和计算时间也增加。因此,我们提出了一种快速计算灵敏度矩阵的方法,能够有效的减少计算时间,并基于此提出了一种存储灵敏度矩阵的策略。之后,我们对反演过程中深度加权函数的选择展开了讨论。我们列举了几种深度加权函数,针对其在重力和重力梯度反演中的表现进行了对比,最后选择了基于异常体深度信息的加权函数。这种深度加权函数依据异常体的埋深设置权值,与数据类型无关,因而适用于重力和重力梯度数据联合反演。我们给出了再加权光滑反演的计算流程及相应的公式推导。基于再加权的光滑反演,我们对深度加权函数对异常体埋深信息准确性的要求进行了讨论,发现在埋深信息与实际信息存在一定差异时,采用这种深度加权函数,仍能获得合理的反演结果。之后,我们将其应用到反演计算中,并将这种加权函数在反演中的表现与基于灵敏度矩阵的深度加权函数进行对比。结果表明,基于异常体深度信息的加权函数,因为将深度信息结合到了反演计算中,有效的提高了反演结果的分辨率。接下来,针对稳定函数的选择开展了研究,并对本文所采用的优化算法展开了讨论。针对不同的地质体,需要选择不同的稳定函数。本文中,我们主要针对具有陡峭边界的地质体,因此选择了最小梯度支撑函数作为构成联合反演正则化方程的稳定函数。本文中,我们主要采用非线性共轭梯度算法,这是一种适合解决大规模反演问题的算法。这种算法在三维电磁反演中有着广泛的应用,在重力和重力梯度反演中的应用则较少。通过模型试验,我们将非线性共轭梯度算法与BFGS拟牛顿法进行对比,发现与BFGS拟牛顿法相比,虽然非线性共轭梯度算法收敛速度较慢,但是其消耗的时间更短,对内存的要求更低。为了将密度约束结合到反演计算中,同时,确保不会对反演过程的稳定性造成影响,我们采用了不等式约束条件。我们建立了由多个不同异常体组成的模型,对重力梯度分量组合反演进行对比和讨论。结果表明,多分量组合能够有效的提高反演结果的分辨率,但是,当数据量达到一定程度后,虽然数据能够更好的拟合,反演结果收敛程度更好,但是,反演结果与理论模型的一致性降低,这就需要额外的信息来约束反演过程。综合考虑反演结果和反演效率,我们给出了反演结果和反演效率最佳的分量组合。随后,我们基于同一模型对重力和重力梯度联合反演进行了对比和讨论。结果表明:加入重力数据后,得到的联合反演的结果与重力梯度分量组合反演结果大体一致;对于其中的某些异常体,加入重力数据后,其反演结果的分辨率得到了提升。针对具有不同埋深的异常体,我们将空间梯度加权函数应用到了反演计算中。这一函数的应用,使得我们能够将前次的反演结果中的有效信息作为先验信息结合到下次的反演计算中。通过模型试验,我们发现,采用这种方法,反演结果的分辨率得到了提升。最后,我们将本文中的方法应用到了在美国路易斯安娜州的文顿盐丘测得的实际数据。利用重力和重力梯度数据进行三维反演计算,进而依据反演结果推断盐盖的分布。通过对不同分量组合反演结果对比,我们发现zg|xyg|xzg|yyg|yzg|zzg反演结果最好。我们给出了反演结果的三维分布图,与该地区已有的研究成果对比,可以得出,我们的反演结果是合理的。
[Abstract]:The processing and interpretation of gravity data has always been an important part of geophysical data processing and interpretation. In recent years, with the development and application of the full tensor gravity gradient measurement system (FTG), the status of gravity gradient data is becoming more and more important. In theory, gravity data is the partial derivative of gravity position in the vertical direction and the gravity gradient. The data is the two derivation of the gravity position in all directions. In the course of the calculation, the low frequency signal is suppressed and the high frequency signal is enhanced. Therefore, the gravity data and the gravity gradient data are compared in the frequency domain. The results show that the gravity data contains more low frequency information and the gravity gradient data contains more high frequency information. Therefore, gravity and the gravity data are included in the gravity data. The combination of gravity gradient data can achieve complementary information and effectively reduce the multiple solvability in the inversion. Based on this, this paper discusses the problem of joint inversion of gravity and gravity gradient data. First, the gravity and gravity gradient data are quantified and compared. The gravity gradient data in the frequency domain expression, deduce the weight of gravity and gravity gradient data. It is found that the zzg component contains more information in each component of the gravity gradient, and then, by comparing the ZG component and the amplitude spectrum of the zzg component of the different depth models, the ZG component and the zzg component are analyzed with the depth, and the ZG and zzg components are back calculated respectively. The results show that the ZG inversion results are in the deep part. The resolution is high, and the zzg inversion has a high resolution in the shallow part. We combine the depth weighted function with the stable function part by the method of the re weighted inversion. In the case of only considering the depth weighting and without any other constraints, we invert the gravity field and the gravity gradient data respectively, according to each component. The inversion results have an intuitive impression on the performance of each component in the inversion calculation, and compare the characteristics of the information contained in each component. Then, we discuss the joint inversion problem of gravity and gravity gradient. Compared with the single component inversion, the Multicomponent Joint back performance needs to consume more time and memory. First, Before the inversion is started, we need to calculate and store the sensitivity matrix of each component. Because of the increase of the component, the memory space and calculation time consumed by the storage and calculation sensitivity matrix also increase. Therefore, we propose a square method to quickly calculate the sensitivity matrix, which can effectively reduce the calculation time and based on this method. A strategy of storage sensitivity matrix is proposed. After that, we discuss the selection of depth weighted functions in the inversion process. We enumerate several depth weighted functions, compare their performance in gravity and gravity gradient inversion, and finally choose the weighted function based on the depth information of abnormal body. The weighted function is based on the depth of the buried depth of the abnormal body, which is independent of the data type, so it is applicable to the joint inversion of gravity and gravity gradient data. We give the calculation process of the reweighted smooth inversion and the derivation of the corresponding formula. It is found that when there is a certain difference between the buried depth information and the actual information, a reasonable inversion result can still be obtained by using this depth weighted function. After that, we apply it to the inversion calculation and compare the performance of this weighted function with the depth weighted function based on the sensitivity matrix. The weighted function based on the depth information of the abnormal body is based on the combination of the depth information into the inversion calculation, which effectively improves the resolution of the inversion results. Next, the selection of the stable function is studied, and the optimization algorithms used in this paper are discussed. Different stability functions need to be selected for different geological bodies. In this paper, we mainly aim at a geological body with steep boundary, so we choose the minimum gradient support function as a stable function to form a joint inversion regularization equation. In this paper, we mainly use the nonlinear conjugate gradient algorithm, which is a suitable algorithm for solving large-scale inversion problems. This algorithm is in three-dimensional electromagnetic inverse. It has a wide range of applications and less applications in gravity and gravity gradient inversion. Through the model test, we compare the nonlinear conjugate gradient algorithm with the BFGS quasi Newton method, and find that compared with the BFGS quasi Newton method, the nonlinear conjugate gradient algorithm has a slower convergence rate, but its consumption time is shorter and the memory needs to be improved. In order to combine the density constraints into the inversion calculation and to ensure that the stability of the inversion process will not be affected, we have adopted the inequality constraints. We have established a model composed of several different abnormal bodies, and compared and discussed the combination inversion of the gravity gradient component. The results show that the multicomponent combination can be used. It can improve the resolution of the inversion results, but when the amount of data is reached to a certain degree, although the data can be better fitted, the convergence of the inversion results is better, but the consistency of the inversion results and the theoretical model is reduced. This requires additional information to restrain the inversion process. We give a comprehensive consideration of the inversion results and the efficiency of inversion. We give a comprehensive consideration of the inversion results and the efficiency of inversion. Then, we compare and discuss the joint inversion of gravity and gravity gradient based on the same model. The results show that the results of joint inversion obtained from the gravity data are in general agreement with the results of the combined inversion of gravity gradient components. After the gravity data, the resolution of the inversion results has been improved. For the abnormal body with different buried depth, we apply the spatial gradient weighting function to the inversion calculation. The application of this function enables us to combine the effective information in the previous inversion results as the first test information to the next inversion calculation. In the model test, we found that the resolution of the inversion results has been improved by this method. Finally, we applied the method in this paper to the actual data measured in the Lewis Anna salt dunes in the United States. The gravity and gravity gradient data were used to calculate the three-dimensional inversion, and then the distribution of the salt cover was deduced from the inversion results. By comparing the inversion results of different component combinations, we find that the zg|xyg|xzg|yyg|yzg|zzg inversion results are the best. We have given the three-dimensional distribution map of the inversion results, and compared with the existing research results in this area, we can conclude that our inversion results are reasonable.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P631.1

【参考文献】