本文選題：球諧函數(shù)　切入點(diǎn)：重力場模型　出處：《東華理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：地球重力場模型是指地球引力位按球諧函數(shù)展開的一組位系數(shù)的集合,是對地球重力場的擬合或逼近。將重力場用球諧函數(shù)展開,對擾動函數(shù)施以簡單的線性運(yùn)算即可簡單快速的導(dǎo)出重力異常、大地水準(zhǔn)面差距和垂線偏差等具有重要應(yīng)用價(jià)值的重力場元。因此,本文主要針對如何利用球諧函數(shù)快速準(zhǔn)確的計(jì)算重力場元展開研究。主要的研究內(nèi)容和成果如下:(1)計(jì)算球諧函數(shù)的一個(gè)關(guān)鍵問題是快速準(zhǔn)確地遞推締合勒讓德函數(shù)。從計(jì)算精度和計(jì)算速度兩個(gè)方面探討了四種常用締合勒讓德函數(shù)的適用性,實(shí)驗(yàn)表明,當(dāng)階數(shù)超高時(shí),標(biāo)準(zhǔn)向前列和標(biāo)準(zhǔn)向前行的計(jì)算速度最快,但計(jì)算精度最差,跨階次計(jì)算速度略快于beliokv,兩者精度相當(dāng)。通過插入比例因等方法改善遞推過程不穩(wěn)定的現(xiàn)象,但增加了運(yùn)算次數(shù),犧牲了計(jì)算速度。綜合實(shí)驗(yàn)得到跨階次遞推算法更適宜作為超高階締合勒讓德函數(shù)的遞推算法。(2)利用球諧函數(shù)導(dǎo)出重力異常、大地水準(zhǔn)面差距和垂線偏差等有重要應(yīng)用的重力場元。通過三角函數(shù)的快速計(jì)算、先經(jīng)行緯度循環(huán)再進(jìn)行經(jīng)度循環(huán)以及簡化數(shù)組索引下標(biāo)等方法提高計(jì)算速度,并通過實(shí)驗(yàn)驗(yàn)證了程序的正確性。結(jié)合Horner求和算法改善級數(shù)求和狀況,并進(jìn)一步提高計(jì)算效能。(3)以大地水準(zhǔn)面精化為例,提出用QR矩陣分解法避免求解參數(shù)過程中的求逆過程,分析了光滑因子對多面函數(shù)的轉(zhuǎn)換精度的影響�；谥亓瞿Ｐ捅容^分析了四種擬合模型的優(yōu)劣以及采用最優(yōu)的擬合算法分析不同重力場模型對轉(zhuǎn)換精度的影響。綜合實(shí)驗(yàn)得到采用二次曲面法更適用于大地水準(zhǔn)面精化的擬合,并且超高階的重力場模型在小工程區(qū)域內(nèi)的區(qū)別不大。(4)根據(jù)上述的研究成果,使用ASP.NET(Csharp)編程語言實(shí)現(xiàn)了締合勒讓德的穩(wěn)定性分析、重力場元的計(jì)算、重力場元的二維可視化以及高程轉(zhuǎn)換等功能,采用webGL實(shí)現(xiàn)重力場元的三維可視化,設(shè)計(jì)開發(fā)了一個(gè)重力場計(jì)算平臺。
[Abstract]:The gravity field model of the earth refers to the set of potential coefficients of the earth's gravitational potential expanded according to the spherical harmonic function, which is the fitting or approximation of the earth's gravity field. The gravity field is expanded with the spherical harmonic function. The gravitational field elements with important application value such as gravity anomaly, geoid difference and vertical deviation can be derived by simple linear operation on perturbation function. This paper mainly focuses on how to use spherical harmonic function to calculate gravitational field element quickly and accurately. The main research contents and results are as follows: 1) A key problem in the calculation of spherical harmonic function is the fast and accurate recursion association Legendre function. The applicability of four commonly used associative Legendre functions is discussed in terms of accuracy and speed. The experimental results show that when the order is high, the calculation speed of the standard moving forward to the front and the standard is the fastest, but the calculation accuracy is the worst. The calculation speed of cross-order is slightly faster than that of beliokv.The accuracy of the two methods is similar. The instability of the recursive process is improved by means of inserting proportional factors, but the number of operations is increased. At the expense of computational speed, it is found that the cross-order recursive algorithm is more suitable as a recursive algorithm for super-high order associating Legendre function.) the spherical harmonic function is used to derive gravity anomalies. The difference of geoid and the deviation of vertical line and other important applied gravity field elements. Through the fast calculation of trigonometric function, the longitude cycle is carried out first and then the longitude cycle is carried out, and the calculation speed is improved by simplifying the array index subscript, etc. The correctness of the program is verified by experiments. Combining with the Horner summation algorithm to improve the summation of series, and to further improve the computational efficiency, taking geoid refinement as an example, the QR matrix decomposition method is proposed to avoid the inverse process in the process of solving parameters. The influence of smoothing factor on the conversion accuracy of multi-plane function is analyzed. Based on the gravity field model, the advantages and disadvantages of the four fitting models are compared and the influence of different gravity field models on the conversion accuracy is analyzed by using the optimal fitting algorithm. Comprehensive experiments show that Quadric surface method is more suitable for geoid refinement. And the super high order gravity field model in the small engineering area is not different. (4) according to the above research results, the stability analysis of associating Legendre and the calculation of gravity field element are realized by using ASP. Net Csharp) programming language. The two-dimensional visualization and elevation conversion of gravity field elements are realized by using webGL. A gravity field computing platform is designed and developed.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P223.0

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