磁异常梯度数据向下延拓算法研究

发布时间：2018-07-10 16:54

本文选题：磁异常梯度 + 向下延拓　；参考：《哈尔滨工程大学》2014年硕士论文

【摘要】：地磁辅助导航系统因其全天候、全地域、高隐蔽性等优点,已经成为惯性辅助导航系统中不可或缺的一部分。水下地磁辅助导航系统是基于水下地磁匹配原理进行导航定位的,其定位精度与水下地磁数据库的精度有着直接的关系。位场延拓技术是构建水下地磁数据库的有效手段。本文选取所含地磁信息更多的磁异常梯度数据作为研究对象,围绕高精度、高效率等需求展开,重点研究了磁异常梯度数据向下延拓技术。由于位场向下延拓的不稳定性,使得国内外许多学者致力于寻求各种不同算法以解决这方面的问题。基于积分迭代的各种改进算法不仅有效地解决了位场大距离向下延拓的不稳定性问题,而且在保证大距离向下延拓的前提下,使数据处理的精度和速度都得到了大幅度的提升。本文简要介绍了地磁场要素及其基本构成,通过对磁异常总强度的介绍,引出了本文的研究对象——磁异常梯度。推导了磁异常梯度数据在空间域和频率域上的位场延拓表达式,为后续的算法研究提供理论依据。通过对磁异常梯度延拓因子的变化分析,指出传统的傅里叶变换方法在向下延拓过程中是不稳定的。传统的频率域向下延拓迭代法是一种基于傅里叶变换的迭代法,在其进行数据迭代运算之前,需要利用傅里叶变换将空间域中的数据转换到频率域上,目的是减少计算量,提高计算速度。本文以提高计算速度为目的,通过研究发现Hartley变换保证了变换前后的信号熵和能量不变,而且作为一种实数域内的变换,Hartley变换省去了傅里叶变换中虚数部分的运算,计算速度比傅里叶变换提高了很多。在研究了向下延拓迭代法后,本文利用Hartley变换代替傅里叶变换,提出了基于Hartley变换的向下延拓迭代法。最后应用理论模型仿真与实测数据对基于傅里叶变换的向下延拓迭代法和基于Hartley变换的向下延拓迭代法进行了对比试验,结果表明基于Hartley变换的迭代法在保证向下延拓精度的同时可以将计算时间大幅缩小。针对基于Hartley变换的迭代法在抑制噪声方面所表现出的不足,本文结合正则化理论,研究了磁异常梯度向下延拓正则化算法。论文首先介绍了经典的Tikhonov正则化理论以及一些常用的正则化参数选取方法;通过正则化分析,定义了一种向下延拓正则化算子,该算子能够保证向下延拓计算结果连续依赖于观测数据,利用曲率函数配合L-曲线法选择了最优正则化参数;通过被添加噪声的磁异常梯度数据对正则化算法进行了验证,结果表明磁异常梯度向下延拓正则化算法对噪声拥有更强的抑制能力,表现出了很好的自适应性;文章最后对两种算法的适用范围进行了讨论。最后,为了满足实际研究的需要,结合Matlab和VC++各自的特点,采用两者混合编程的方式,设计了一个简单的可用于实验室内研究的向下延拓软件。该软件可以通过对数据文件的加载,在输入向下延拓深度并点击对应的算法按钮后,自动绘制出延拓深度位置处的磁异常梯度数据等值线图。
[Abstract]:The geomagnetic auxiliary navigation system has become an integral part of the inertial navigation system because of its all-weather, whole region and high concealment. The underwater magnetic auxiliary navigation system is based on the principle of underwater geomagnetic matching, and its positioning accuracy has a direct relationship with the accuracy of underwater geomagnetic database. The extension technology is an effective means to construct underwater geomagnetic database. In this paper, more magnetic anomaly gradient data of geomagnetic information are selected as the research object, and the downward continuation technology of magnetic anomaly gradient data is focused on the high precision and high efficiency. A variety of different algorithms are sought to solve this problem. A variety of improved algorithms based on integral iteration not only effectively solve the instability problem of the large distance downward continuation of the bit field, but also make the accuracy and speed of data processing greatly improved on the premise of ensuring the large distance downward extension. In this paper, the elements of the geomagnetic field and its basic composition are introduced. By introducing the total intensity of magnetic anomalies, the object of this paper, magnetic anomaly gradient, is derived. The expression of the potential field extension of the magnetic anomaly gradient data in the spatial and frequency domains is derived, which provides a theoretical basis for the study of the subsequent algorithms. It is pointed out that the traditional Fourier transform method is unstable in the downward continuation process. The traditional frequency domain downward continuation iteration method is an iterative method based on Fourier transform. The Fourier transform is used to convert the data from the space domain to the frequency domain before the data iteration is performed. The purpose is to reduce the calculation. In order to improve the calculation speed, in order to improve the calculation speed, this paper finds that the Hartley transform ensures the entropy and energy of the signal before and after the transformation, and as a real domain transformation, the Hartley transform saves the operation of the imaginary part of the Fu Liye transform, and the calculation speed is much higher than that of the Fu Liye transform. After studying the downward continuation method, this paper uses the Hartley transform instead of Fu Liye transform, and proposes a downward continuation iterative method based on Hartley transformation. Finally, the theoretical model simulation and the measured data are used to compare the downward continuation iterative method based on the Fu Liye transformation and the downward continuation iterative method based on the Hartley transformation. It is shown that the iterative method based on Hartley transform can reduce the calculation time greatly while ensuring the downward continuation accuracy. In this paper, in this paper, the regularization algorithm for the downward continuation of magnetic anomaly gradient is studied in view of the deficiency of the iterative method based on Hartley transformation in reducing the noise. This paper first introduces the classical Ti. Khonov regularization theory and some commonly used regularized parameter selection methods; through regularization analysis, a downward continuation regularization operator is defined. The operator can ensure that the result of downward continuation depends on the observation data continuously. The optimal regularization parameter is selected by the curvature function combined with the L- curve method; by adding noise, the operator can choose the optimal regularization parameter. The magnetic anomaly gradient data is verified by the regularization algorithm. The results show that the magnetic anomaly gradient downward continuation regularization algorithm has a stronger suppression ability and shows good adaptability. Finally, the scope of application of the two algorithms is discussed. Finally, in order to meet the needs of the actual research, Matlab and VC++ are combined. A simple downward continuation software, which can be used in laboratory research, is designed by using the two mixed programming methods. The software can automatically draw the magnetic anomaly gradient data line at the depth position of the extension by loading the data file, and after the input downward extension depth and clicking the corresponding algorithm button. Figure.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN96

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