本文選題：航空矢量重力測量 + 大地水準(zhǔn)面　； 參考：《武漢大學(xué)》2014年博士論文

【摘要】：地球重力場研究是大地測量學(xué)的核心任務(wù)之一。隨著全球?qū)Ш蕉ㄎ患夹g(shù)的發(fā)展,航空重力測量已成為高效測定中高頻地球重力場信息的主要手段。航空重力測量與地面重力測量、海洋重力測量、衛(wèi)星重力測量技術(shù)相互補(bǔ)充,形成了空天地一體化的地球重力場觀測系統(tǒng)。在地面重力測量難以到達(dá)的困難區(qū)域開展航空重力測量,可以有效填補(bǔ)重力空白區(qū)域,有利于改善重力場數(shù)據(jù)的精度和分辨率及精化局部地球重力場和區(qū)域大地水準(zhǔn)面,國家經(jīng)濟(jì)建設(shè)、軍事和國防建設(shè)、地球物理學(xué)、海洋學(xué)、地球動力學(xué)、資源勘探等相關(guān)地球科學(xué)領(lǐng)域也將從中收益。 以美國、加拿大、丹麥為首的發(fā)達(dá)國家率先開展了航空重力測量研究,并進(jìn)行了大量的飛行實(shí)驗(yàn),我國也在2002年成功研制了自己的航空重力測量系統(tǒng)CHAGS。眾多研究結(jié)果表明,航空標(biāo)量重力測量數(shù)據(jù)在5～10km的分辨率尺度上能夠達(dá)到1～3mGal的精度,這也意味著航空標(biāo)量重力測量技術(shù)已進(jìn)入成熟階段。航空矢量重力測量技術(shù)不僅能獲取航空標(biāo)量重力測量觀測值(即重力矢量的垂直分量),也能測得重力矢量的水平分量,是目前大地測量領(lǐng)域的研究熱點(diǎn)之一。迄今為止國內(nèi)還沒有航空矢量重力測量系統(tǒng),在航空矢量重力測量數(shù)據(jù)處理方面也尚處于起步階段。在此背景下,本文研究利用航空矢量重力測量數(shù)據(jù)確定區(qū)域地球重力場的理論與方法,研制航空矢量重力測量數(shù)據(jù)處理軟件包,對我國航空矢量重力測量技術(shù)的發(fā)展具有重要的科學(xué)意義與應(yīng)用價(jià)值。 本文的主要工作及貢獻(xiàn)如下： (1) Stokes積分、Hotine積分以及Possion積分都由近區(qū)貢獻(xiàn)和遠(yuǎn)區(qū)貢獻(xiàn)兩部分組成,計(jì)算遠(yuǎn)區(qū)貢獻(xiàn)的關(guān)鍵在于求解積分核函數(shù)的截?cái)嘞禂?shù)�；诮�?cái)嘞禂?shù)的通用表達(dá)式,本文給出了截?cái)嘞禂?shù)的變步長高斯積分?jǐn)?shù)值解法。因Stokes截?cái)嘞禂?shù)和Hotine標(biāo)準(zhǔn)核截?cái)嘞禂?shù)存在遞推算法,通過比較遞推法與變步長高斯積分法的計(jì)算結(jié)果,驗(yàn)證了變步長高斯積分法的有效性。 (2)在Jekeli(1979)和李葉才(1989)的基礎(chǔ)上,給出了Hotine改化核(級數(shù)展開式從2階開始)截?cái)嘞禂?shù)的遞推公式。通過比較變步長高斯積分法和遞推法的有效性,驗(yàn)證本文給出的遞推公式的正確性。 (3)基于窗函數(shù)法和切比雪夫逼近法設(shè)計(jì)了兩類適用于航空矢量重力測量的有限沖激響應(yīng)(FIR)低通數(shù)字濾波器。先采用模擬的高度數(shù)據(jù)驗(yàn)證了濾波器性能,然后對實(shí)測靜態(tài)GPS數(shù)據(jù)進(jìn)行了低通濾波處理,并在數(shù)據(jù)處理中詳細(xì)分析了濾波器的相位延遲和數(shù)據(jù)截短等影響。結(jié)果表明：(a)在相同的設(shè)計(jì)指標(biāo)下,依照切比雪夫逼近法所設(shè)計(jì)的濾波器比采用窗函數(shù)法設(shè)計(jì)的濾波器具有更好的低通濾波效果；(b)對于靜態(tài)GPS測量數(shù)據(jù),依照切比雪夫逼近法所設(shè)計(jì)的濾波器能以±1-2mgal的精度確定垂直加速度,以優(yōu)于±1mGal的精度確定水平加速度。 (4)研究了航空矢量重力測量數(shù)據(jù)的歸算方法,包括采用徑向改正方法將航線高度處的重力觀測值歸算到平均飛行高度面上、采用兩步交叉點(diǎn)平差法來進(jìn)行測線系統(tǒng)誤差的補(bǔ)償、選用加權(quán)平均法和Shepard曲面擬合法對觀測值作格網(wǎng)化處理。針對擾動重力水平分量,采用模擬算例驗(yàn)證了本文提出的平均高度面歸算方法,結(jié)果表明參考場的階次是影響水平分量歸算精度的主要因素,且高階次部分對歸算精度的影響較低階次部分要大。針對擾動重力垂直分量,依據(jù)本文提出的歸算方案對美國大地測量局(NGS)發(fā)布的航空標(biāo)量重力實(shí)測數(shù)據(jù)塊EN01進(jìn)行了數(shù)據(jù)處理,給出了6200m(大地高)高度處2°×3°的范圍內(nèi)5’×5’的規(guī)則格網(wǎng)重力擾動數(shù)據(jù)。相對于該區(qū)域的EGM2008格網(wǎng)重力擾動參考值,加權(quán)平均法和Shepard曲面擬合法輸出結(jié)果的精度分別為±1.59mGal和±1.36mGal. (5)從第二類Helmert凝集法的基本原理出發(fā),研究了基于牛頓積分的解析核與級數(shù)展開核的地形歸算方法,并推導(dǎo)了地形對重力矢量水平分量的帶限直接影響改正公式�；诩墧�(shù)展開核的地形歸算公式可調(diào)節(jié)積分核函數(shù)的起始階數(shù)和最大階數(shù),無需經(jīng)過低通濾波即可獲得與航空重力信號頻譜范圍一致的地形影響改正值。采用3"×3"SRTM地形高程數(shù)據(jù)的數(shù)值計(jì)算結(jié)果表明：基于級數(shù)展開核計(jì)算的帶限直接地形影響和間接地形影響與基于解析牛頓核計(jì)算并經(jīng)過低通濾波處理后得到的帶限直接地形影響和間接影響吻合較好,二者計(jì)算的重力矢量各分量的直接地形影響差值的RMS在2.5mGal以內(nèi),大地水準(zhǔn)面間接地形影響差值的RMS在3cm以內(nèi),基于級數(shù)展開核的帶限地形影響計(jì)算公式可用于航空矢量重力測量數(shù)據(jù)的地形歸算。 (6)針對航空矢量重力測量的垂直分量,在頻域內(nèi)研究了逆Possion積分法、解析延拓法和迭代法等三種向下延拓算法,并采用上述三種方法將模擬生成的垂直分量向下延拓到大地水準(zhǔn)面上。計(jì)算結(jié)果表明,逆Possion積分結(jié)合Wiener濾波的向下延拓方法在可靠性和穩(wěn)定性方面明顯優(yōu)于解析延拓和迭代法。 (7)針對低信噪比的水平分量,提出了基于頻域輸入輸出理論的向下延拓方法。分析了白噪聲的標(biāo)準(zhǔn)差分別為1.5mGal和6mGal時(shí)單輸入單輸出系統(tǒng)(即逆Possion積分結(jié)合Wiener濾波的快速算法)和雙輸入單輸出系統(tǒng)對水平分量的向下延拓效果。研究結(jié)果表明：當(dāng)水平分量的精度較高時(shí),二者均能實(shí)現(xiàn)水平分量的穩(wěn)定向下延拓；當(dāng)水平分量的精度較低時(shí),單輸入單輸出法的向下延拓效果較差,而雙輸入單輸出法能實(shí)現(xiàn)水平分量的穩(wěn)定向下延拓。 (8)研究了利用航空矢量重力測量觀測值的水平分量確定大地水準(zhǔn)面的剖面積分法。利用EGM2008生成2km、3km、4km、5km飛行高度處的模擬水平分量,并加入高斯白噪聲。當(dāng)白噪聲的標(biāo)準(zhǔn)差為6mGal時(shí),采用剖面積分法所得相對大地水準(zhǔn)面的精度在分米級,在某些極值點(diǎn)上誤差最大可達(dá)40cm；當(dāng)白噪聲的標(biāo)準(zhǔn)差為1.5mGal時(shí),采用剖面積分法所得相對大地水準(zhǔn)面的精度分別為3.31cm、4.79cm、5.16cm、5.64cm。剖面積分的結(jié)果說明,當(dāng)水平分量的噪聲水平較低時(shí),采用剖面積分法能確定高精度的相對大地水準(zhǔn)面。 (9)研究了利用航空矢量重力測量觀測值的垂直分量確定絕對大地水準(zhǔn)面的一步解法。利用EGM2008生成2km、3km、4km、5km飛行高度處的模擬垂直分量,加入標(biāo)準(zhǔn)差為1.5mGal的高斯白噪聲,采用一步法所得絕對大地水準(zhǔn)面的精度分別為5.08cm、5.64cm、6.23cm、6.54cm。 (10)在聯(lián)合航空重力矢量三分量求解大地水準(zhǔn)面方面,本文采用頻域輸入輸出法融合水平分量和垂直分量,數(shù)據(jù)融合后的輸出為空中垂直分量,再采用一步法來確定大地水準(zhǔn)面。分析了垂直分量的噪聲水平為1.5mGal,水平分量的噪聲水平分別為1.5mGal、3mGal、6mGal時(shí),由H=2km、3km、4km、5km航線高度處的三分量聯(lián)合確定大地水準(zhǔn)面的精度。實(shí)驗(yàn)結(jié)果表明：(a)當(dāng)水平分量的噪聲水平明顯高于垂直分量的噪聲水平時(shí),并不能改善大地水準(zhǔn)面的精度：(b)當(dāng)水平分量具有與垂直分量一致的精度水平時(shí),由各航線高度處的重力矢量確定的絕對大地水準(zhǔn)面的精度分別為4.32cm、4.90cm、5.41cm、5.88cm,較單獨(dú)采用垂直分量時(shí)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.

【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：P223.4

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