航空矢量重力测量确定区域地球重力场的理论与方法

发布时间：2018-04-21 12:36

本文选题：航空矢量重力测量 + 大地水准面　；参考：《武汉大学》2014年博士论文

【摘要】：地球重力场研究是大地测量学的核心任务之一。随着全球导航定位技术的发展,航空重力测量已成为高效测定中高频地球重力场信息的主要手段。航空重力测量与地面重力测量、海洋重力测量、卫星重力测量技术相互补充,形成了空天地一体化的地球重力场观测系统。在地面重力测量难以到达的困难区域开展航空重力测量,可以有效填补重力空白区域,有利于改善重力场数据的精度和分辨率及精化局部地球重力场和区域大地水准面,国家经济建设、军事和国防建设、地球物理学、海洋学、地球动力学、资源勘探等相关地球科学领域也将从中收益。以美国、加拿大、丹麦为首的发达国家率先开展了航空重力测量研究,并进行了大量的飞行实验,我国也在2002年成功研制了自己的航空重力测量系统CHAGS。众多研究结果表明,航空标量重力测量数据在5～10km的分辨率尺度上能够达到1～3mGal的精度,这也意味着航空标量重力测量技术已进入成熟阶段。航空矢量重力测量技术不仅能获取航空标量重力测量观测值(即重力矢量的垂直分量),也能测得重力矢量的水平分量,是目前大地测量领域的研究热点之一。迄今为止国内还没有航空矢量重力测量系统,在航空矢量重力测量数据处理方面也尚处于起步阶段。在此背景下,本文研究利用航空矢量重力测量数据确定区域地球重力场的理论与方法,研制航空矢量重力测量数据处理软件包,对我国航空矢量重力测量技术的发展具有重要的科学意义与应用价值。本文的主要工作及贡献如下： (1) Stokes积分、Hotine积分以及Possion积分都由近区贡献和远区贡献两部分组成,计算远区贡献的关键在于求解积分核函数的截断系数。基于截断系数的通用表达式,本文给出了截断系数的变步长高斯积分数值解法。因Stokes截断系数和Hotine标准核截断系数存在递推算法,通过比较递推法与变步长高斯积分法的计算结果,验证了变步长高斯积分法的有效性。 (2)在Jekeli(1979)和李叶才(1989)的基础上,给出了Hotine改化核(级数展开式从2阶开始)截断系数的递推公式。通过比较变步长高斯积分法和递推法的有效性,验证本文给出的递推公式的正确性。 (3)基于窗函数法和切比雪夫逼近法设计了两类适用于航空矢量重力测量的有限冲激响应(FIR)低通数字滤波器。先采用模拟的高度数据验证了滤波器性能,然后对实测静态GPS数据进行了低通滤波处理,并在数据处理中详细分析了滤波器的相位延迟和数据截短等影响。结果表明：(a)在相同的设计指标下,依照切比雪夫逼近法所设计的滤波器比采用窗函数法设计的滤波器具有更好的低通滤波效果；(b)对于静态GPS测量数据,依照切比雪夫逼近法所设计的滤波器能以±1-2mgal的精度确定垂直加速度,以优于±1mGal的精度确定水平加速度。 (4)研究了航空矢量重力测量数据的归算方法,包括采用径向改正方法将航线高度处的重力观测值归算到平均飞行高度面上、采用两步交叉点平差法来进行测线系统误差的补偿、选用加权平均法和Shepard曲面拟合法对观测值作格网化处理。针对扰动重力水平分量,采用模拟算例验证了本文提出的平均高度面归算方法,结果表明参考场的阶次是影响水平分量归算精度的主要因素,且高阶次部分对归算精度的影响较低阶次部分要大。针对扰动重力垂直分量,依据本文提出的归算方案对美国大地测量局(NGS)发布的航空标量重力实测数据块EN01进行了数据处理,给出了6200m(大地高)高度处2°×3°的范围内5’×5’的规则格网重力扰动数据。相对于该区域的EGM2008格网重力扰动参考值,加权平均法和Shepard曲面拟合法输出结果的精度分别为±1.59mGal和±1.36mGal. (5)从第二类Helmert凝集法的基本原理出发,研究了基于牛顿积分的解析核与级数展开核的地形归算方法,并推导了地形对重力矢量水平分量的带限直接影响改正公式。基于级数展开核的地形归算公式可调节积分核函数的起始阶数和最大阶数,无需经过低通滤波即可获得与航空重力信号频谱范围一致的地形影响改正值。采用3"×3"SRTM地形高程数据的数值计算结果表明：基于级数展开核计算的带限直接地形影响和间接地形影响与基于解析牛顿核计算并经过低通滤波处理后得到的带限直接地形影响和间接影响吻合较好,二者计算的重力矢量各分量的直接地形影响差值的RMS在2.5mGal以内,大地水准面间接地形影响差值的RMS在3cm以内,基于级数展开核的带限地形影响计算公式可用于航空矢量重力测量数据的地形归算。 (6)针对航空矢量重力测量的垂直分量,在频域内研究了逆Possion积分法、解析延拓法和迭代法等三种向下延拓算法,并采用上述三种方法将模拟生成的垂直分量向下延拓到大地水准面上。计算结果表明,逆Possion积分结合Wiener滤波的向下延拓方法在可靠性和稳定性方面明显优于解析延拓和迭代法。 (7)针对低信噪比的水平分量,提出了基于频域输入输出理论的向下延拓方法。分析了白噪声的标准差分别为1.5mGal和6mGal时单输入单输出系统(即逆Possion积分结合Wiener滤波的快速算法)和双输入单输出系统对水平分量的向下延拓效果。研究结果表明：当水平分量的精度较高时,二者均能实现水平分量的稳定向下延拓；当水平分量的精度较低时,单输入单输出法的向下延拓效果较差,而双输入单输出法能实现水平分量的稳定向下延拓。 (8)研究了利用航空矢量重力测量观测值的水平分量确定大地水准面的剖面积分法。利用EGM2008生成2km、3km、4km、5km飞行高度处的模拟水平分量,并加入高斯白噪声。当白噪声的标准差为6mGal时,采用剖面积分法所得相对大地水准面的精度在分米级,在某些极值点上误差最大可达40cm；当白噪声的标准差为1.5mGal时,采用剖面积分法所得相对大地水准面的精度分别为3.31cm、4.79cm、5.16cm、5.64cm。剖面积分的结果说明,当水平分量的噪声水平较低时,采用剖面积分法能确定高精度的相对大地水准面。 (9)研究了利用航空矢量重力测量观测值的垂直分量确定绝对大地水准面的一步解法。利用EGM2008生成2km、3km、4km、5km飞行高度处的模拟垂直分量,加入标准差为1.5mGal的高斯白噪声,采用一步法所得绝对大地水准面的精度分别为5.08cm、5.64cm、6.23cm、6.54cm。 (10)在联合航空重力矢量三分量求解大地水准面方面,本文采用频域输入输出法融合水平分量和垂直分量,数据融合后的输出为空中垂直分量,再采用一步法来确定大地水准面。分析了垂直分量的噪声水平为1.5mGal,水平分量的噪声水平分别为1.5mGal、3mGal、6mGal时,由H=2km、3km、4km、5km航线高度处的三分量联合确定大地水准面的精度。实验结果表明：(a)当水平分量的噪声水平明显高于垂直分量的噪声水平时,并不能改善大地水准面的精度：(b)当水平分量具有与垂直分量一致的精度水平时,由各航线高度处的重力矢量确定的绝对大地水准面的精度分别为4.32cm、4.90cm、5.41cm、5.88cm,较单独采用垂直分量时有所提高。
[Abstract]:The study of the earth gravity field is one of the core tasks of geodesy. With the development of global navigation and positioning technology, aeronautical gravimetry has become the main means to efficiently determine the information of the middle and high frequency earth gravity field. An integrated earth gravity field observation system. Aeronautical gravity measurement in difficult areas of difficult ground gravity measurement can effectively fill gravity blank areas, improve the accuracy and resolution of gravity field data, improve local gravity field and regional geoid, national economic construction, military and national defense construction. Geophysics, oceanography, geodynamics, resource exploration and other related fields of earth sciences will also benefit from it.
The developed countries, headed by the United States, Canada and Denmark, took the lead in the research of Aeronautical gravimetry, and carried out a large number of flight experiments. In 2002, our country also successfully developed its own aeronautical gravity measurement system CHAGS.. The results show that the aeronautical scalar gravity measurement data can reach 1 to 3m in the resolution scale of 5 to 10km. The precision of Gal, which also means that the aeronautical scalar gravity measurement technology has entered the mature stage. The aeronautical Vector Gravimetry is not only able to obtain the observational values of the aeronautical scalar gravity measurement (i.e. the vertical component of the gravity vector), but also can measure the horizontal component of the gravity vector. It is one of the hot spots in the field of large surveying at present. There is no air Vector Gravimetry system, and it is still in the initial stage in the data processing of Aeronautical Vector Gravimetry. In this context, this paper studies the theory and method of determining the regional gravity field by using the airborne vector gravimetry data, and develops the software package for the aeronautical vector gravity measurement data processing, and the vector gravity of our country. The development of measurement technology has important scientific significance and application value.
The main work and contribution of this article are as follows:
(1) the Stokes integral, the Hotine integral and the Possion integral are all composed of two parts of the near area contribution and the far zone contribution. The key to the calculation of the contribution of the far zone is to solve the truncation coefficient of the integral kernel function. Based on the general expression of the truncation coefficient, this paper gives the variable step length Gauss integral numerical solution of the truncation coefficient. Because of the truncation coefficient and Hotine, the truncation coefficient and the Hotine of the truncation coefficient are given in this paper. The recursive algorithm is used to calculate the standard nuclear truncation coefficient. The validity of variable step Gauss integral method is verified by comparing the results of recursive method and variable step Gauss integral method.
(2) on the basis of Jekeli (1979) and Li Yecai (1989), the recurrence formula of the truncation coefficient of the Hotine modified nucleus (series expansion from the beginning of the 2 order) is given. The validity of the recursion formula given in this paper is verified by comparing the validity of the variable step length method and the recurrence method.
(3) based on the window function method and Chebyshev approximation method, two kinds of limited impulse response (FIR) low pass digital filters are designed for aeronautical Vector Gravimetry. First, the performance of the filter is verified by the simulated height data. Then the measured static GPS data are processed with low pass filter, and the filter is analyzed in detail in the data processing. The effect of phase delay and data truncation. The results show: (a) under the same design index, the filter designed by the Chebyshev approximation method has better low pass filtering effect than the filter designed by the window function method; (b) for static GPS measurement data, the filter designed according to the Shen Chebyshev approximation method can be + 1-2 The accuracy of MgAl is determined by vertical acceleration, which is better than the accuracy of + 1mGal to determine horizontal acceleration.
(4) the calculation method of Airborne Vector Gravimetry data is studied, including the use of radial correction method to calculate the gravity observation value at the height of the flight route to the average flight height surface. The method of two step intersection adjustment is used to compensate the error of the line system, and the weighted mean method and the Shepard surface fitting method are used to make the observation value as the grid. In view of the horizontal component of the disturbed gravity, a simulation example is used to verify the average height surface reduction method proposed in this paper. The results show that the order of the reference field is the main factor affecting the precision of the horizontal component, and the higher order part has a larger influence on the accuracy of the return than the lower order part. The proposed algorithm deals with the data processing of the aeronautical scalar gravity measured data block EN01 issued by the United States geodetic Bureau of geodetic survey (NGS), and gives the regular grid gravity disturbance data of 5 '* 5' in the range of 2 * * 3 degrees at the height of the earth (high earth height). Relative to the gravity disturbance reference value of the EGM2008 lattice in this region, the weighted mean method and the Shepard curve are given. The accuracy of the output method is 1.59mGal and + 1.36mGal. respectively.
(5) from the basic principle of the second kind of Helmert agglutination method, the terrain inversion method based on the analytic kernel and the series expansion kernel based on the Newton integral is studied, and the correction formula for the direct influence of the terrain on the horizontal component of the gravity vector is derived. The large order number, without the low pass filter, can obtain the correction value of the terrain influence which is consistent with the spectrum range of the airborne gravity signal. The numerical results using 3 "x 3" SRTM topographic elevation data show that the direct Terrain Influence and the indirect topographic influence based on the series expansion kernel calculation and the analysis based on the analytic Newton kernel and through the low pass filter The direct topography and indirect effects obtained by the wave treatment are in good agreement with the indirect effects. The RMS of the difference values of the direct topographic influence of each component of the gravity vector calculated by the two is within 2.5mGal, the RMS of the difference value of the geoid indirect topography is within 3cm, and the formula of the band limited terrain effect based on the series expansion kernel can be used for the vector gravity. The topographic calculation of the measured data.
(6) aiming at the vertical component of the Airborne Vector Gravimetry, three downward continuation algorithms, such as inverse Possion integral method, analytic continuation method and iterative method, are studied in the frequency domain, and the simulated vertical components are extended down to the geoid by the above three methods. The results show that the inverse Possion integral combined with the Wiener filter is downward. The continuation method is superior to analytical continuation and iteration methods in terms of reliability and stability.
(7) a downward continuation method based on the frequency domain input and output theory is proposed for the horizontal component of low signal to noise ratio, and the downward continuation effect of the standard deviation of the white noise is 1.5mGal and 6mGal, namely, the single input single output system (the inverse Possion integral combined with the Wiener filter) and the double input single output system for the horizontal component. The results show that, when the precision of the horizontal component is high, the two can achieve the steady downward continuation of the horizontal component. When the precision of the horizontal component is low, the downward continuation of the single input and single output method is poor, and the double input and single output method can achieve the stable downward continuation of the horizontal component.
(8) the sectional area division of the geoid is determined by the horizontal component of the aerial vector gravity measurement. The simulated horizontal component at the altitude of 2km, 3km, 4km and 5km is generated by EGM2008, and the Gauss white noise is added. When the standard deviation of the white noise is 6mGal, the precision of the relative geoid obtained by the sectional area division method is obtained. The maximum error in some extreme points can be up to 40cm. When the standard deviation of white noise is 1.5mGal, the precision of the relative geoid obtained by the sectional area method is 3.31cm, 4.79cm, 5.16cm and 5.64cm., respectively. The results show that when the horizontal component is low in noise level, the high precision can be determined by the section integral method. Relative geoid.
(9) a one-step method for determining the absolute geoid using the vertical component of the airborne vector gravity measurement is studied. Using EGM2008 to generate the simulated vertical components at the altitude of 2km, 3km, 4km and 5km, the Gauss white noise with a standard deviation of 1.5mGal is added, and the accuracy of the absolute geoid obtained by one step method is 5.08cm, 5.64cm, and 6, respectively. .23cm, 6.54cm.
(10) in the field of geoid, the frequency domain input and output method is used to fuse the horizontal and vertical components. The output of the data fusion is the vertical component in the air, and then the one step method is used to determine the geoid. The noise level of the vertical component is 1.5mGal and the horizontal component is noise level. At the time of 1.5mGal, 3mGal, and 6mGal, the accuracy of geoid is determined jointly by three components at the height of H=2km, 3km, 4km and 5km. The experimental results show that (a) when the horizontal component noise level is obviously higher than the noise level of the vertical component, the accuracy of the quasi surface of the earth water can not be improved: (b) when the horizontal component is with the vertical component, (b) The precision of the absolute geoid determined by the gravity vector at the height of each route is 4.32cm, 4.90cm, 5.41cm, and 5.88cm, respectively, when the vertical component is used separately.

【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：P223.4

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