共查询到19条相似文献，搜索用时 171 毫秒
1.
在应用快速Hartly变换(FHT)或快速Fourier变换(FFT)计算Stokes积分公式时,总是先将Stokes 公式化成卷积形式,然后用 FHT或 FFT完成卷积运算,从而避免了复杂费时的积分计算。但由于 Stokes公式不严格满足卷积定义,欲将其化成卷积形式必须作一些近似。这种近似虽能在一定精度范围满足要求,但对于高精度要求仍有不能允许的计算误差。本文建议采用球面坐标转换方法,能有效地消除无论是用 FHT或 FFT 计算Stokes 积分卷积化所带来的误差影响。 相似文献
2.
Vening—Meinesz公式的球面卷积形式 总被引：4，自引：0，他引：4
过去利用快速Fourier变换（FFT）或快速Hartley变换（FHT）技术计算垂线偏差是假设地球是一个平面。在此基础上导出的Vening-Meinesz公式平面卷积形式虽然在一定精度范围内可以满足要求，但会产生较大的近似误差。然而，Vening-Meinesz公式同样可以发展为由FHT技术计算的二维球面卷积公式。数值计算表明：在Δ(?)=10°，Δλ=13°（5′×5′平均重力异常）范围内，Vening-Meinesz球面卷积公式的计算结果与数值积分结果的均方差m_ξ=±0.03秒、m_η=±0.02秒，比平面卷积公式的计算结果与数值积分结果的均方差m_ξ=±0.14秒、m_η=±0.30秒有显著提高。 相似文献
3.
一种消除stokes积分卷积化近似误差影响的有效方法 总被引：1，自引：0，他引：1
在应用快速Ｈａｒｔｌｙ变换或快速Ｆｏｕｒｉｅｒ变换计算Ｓｔｏｋｅｓ积分公式时，总是先将Ｓｔｏｋｅｓ公式化成卷积形式，然后用ＦＨＴ或ＦＦＴ完成卷积运算，从而避免了复杂费时的积分计算。但由于Ｓｔｏｋｅｓ公式不严格满足卷积定义，欲将其化成卷积形式必须作一些近似。这种近虽能在一定精度范围满足要求，但对于高精度要求仍有不能允许的计算误差。本文建议采用球面坐标转换方法，能有效地消除无论是用ＦＨＴ或ＦＦＴ计算Ｓ 相似文献
4.
中国海域大地水准面和重力异常的确定 总被引：12，自引：1，他引：12
从莫洛金斯基(Molodensky)等1960年给出的由垂线偏差计算大地水准面空域积分公式出发,导出了其相应谱域1维严密卷积和2维球面及平面卷积公式。由Topex/Poseidon,ERS 1/2及Geosat/GM,ERM测高资料求解的垂线偏差计算了我国海域及其邻区大地水准面,其中计算格网为2.5′×2.5′。为了检核,将测高垂线偏差由逆维宁 迈尼兹(Vening Meinesz)公式反演重力异常,与海上船测重力值进行了外部检核;同时还利用司托克斯(Stokes)公式,由上述反演的重力异常计算大地水准面高,与莫洛金斯基公式直接解得的相应结果进行比较作为内部检核。前者的中误差为±9mGal(1Gal=1cm/s2),后者为±0.025m。本文在积分计算中充分应用了2维平面坐标形式和1维卷积严格公式,并做了比较和自校核。 相似文献
5.
联合TOPEX/Poseidon,ERS2和Geosat卫星测高资料确定中国近海重力异常 总被引：12，自引：3，他引：12
处理了 TOPEX/Poseidon(第 9周期至第 2 4 9周期 ) ,ERS2 (第 0周期至第 44周期 )和Geosat/GM(第 1周期至第 2 5周期 )以及 Geosat ERM(第 1周期至第 66周期 )卫星测高资料 ,求解了各自卫星任务的交叉点和垂线偏差 ,利用逆 Vening- Meinesz公式确定了 2 .5′×2 .5′中国近海海洋重力异常 ,并与我国南海船测重力异常作了比较 ,其精度为± 9.3m Gal( 1 Gal=1 cm/s2 )。本文同时导出了严密的 2维平面卷积公式 ,它与 1维严密卷积公式计算结果差值的标准差为± 0 .1 m Gal,而 2维球面公式为± 0 .5 m Gal 相似文献
6.
本文针对平面网角度平差未考虑各角度的相关性,理论有失其严密性,而方向平差理论严密,但是其法方程构造和解算通常较为复杂的特点,文中利用角度的相关信息构造的转换矩阵,推导了一组顾及相关性的平面网角度平差公式。顾及相关性的角度平差法与方向平差法结果一致,但其数学模型更为简单和易于计算机编程。 相似文献
7.
基于卷积神经网络的高光谱图像分类是当前的研究热点,先后发展了空洞卷积、可形变卷积等先进模型。然而,现有可形变卷积只在空间维偏移,忽略了高光谱图像光谱之间的差异信息。为此,本文将可形变卷积从空间维扩展到光谱维,设计了光谱可形变卷积,提出了光谱可形变卷积网络SDCNN（Spectral Deformable Convolutional Neural Network）。首先,利用全连接层学习光谱可形变卷积的偏移量,采用线性差值对图像光谱维进行特征校准;其次,采用多层1×1卷积进行光谱维特征聚合;最后,使用三维卷积层提取光谱?空间联合特征。不同于空间可形变卷积,光谱可形变卷积只在光谱维上进行偏移,可以为不同类别选择更合适的特征波段,提升模型的判别性。在国际通用测试数据Indian Pines、University of Pavia以及University of Houston上进行了实验,结果表明：本文提出的SDCNN方法优于其他深度学习方法,在相同样本条件下取得了更高的分类精度,总体精度达到了98.86%（Indian Pines,10%/类）、99.81%（University of Pavia,5%/类）以及97.41%（University of Houston,50个/类）,验证了该方法的有效性。 相似文献
8.
李建成 《武汉大学学报(信息科学版)》2003,28(6):655-657
基于修改的Poisson积分 ,首先给出了球面扰动位向上延拓的积分表达式。在此基础上 ,由微分原理得出了球外部空间Neumann逆问题的解式 ,利用物理大地测量学的基本微分方程 ,导出了球外部空间的逆Stokes公式 ,并对这两类积分公式的核函数进行了讨论 相似文献
9.
10.
针对井下某些巷道地磁空间变化平缓,地磁匹配概率低的问题,构建了井下巷道地磁卷积增强算子（convolution enhancement algorithms, CEA）,进行地磁匹配前的目标区域和匹配向量的卷积增强预处理,去除数据噪声和增强识别特征。以Laplace、高通滤波（High Pass）、索伯尔滤波（Sobel）图像卷积算子为基础,通过列向量特征的锐化处理,建立了井下巷道地磁卷积增强的Laplace、High Pass和Sobel卷积算子模板。选取某金矿4个巷道的地磁数据,开展了CEA算子卷积前后的均方差算法地磁匹配定位的仿真试验。试验结果表明,CEA算子卷积可以增强匹配序列和地磁图的地磁空间特征,降低了匹配数据中的噪声影响。在数据CEA卷积前后的地磁统计特征对比中发现,Laplace算子不仅保持了原有地磁图变化特征,还增大了数据空间变化的差异度,降低了相关性,效果明显。特别是600 nT的高噪声干扰匹配试验中,Laplace算子卷积能够降低噪声对地磁定位扰动影响,有效提高了地磁匹配定位的概率和精度,具有较强的鲁棒性,适合作为井下巷道地磁匹配的数据预处理模型。 相似文献
11.
A formula for computing the gravity disturbance from the second radial derivative of the disturbing potential 总被引：6，自引：0，他引：6
J. Li 《Journal of Geodesy》2002,76(4):226-231
A formula for computing the gravity disturbance and gravity anomaly from the second radial derivative of the disturbing potential
is derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified
Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted
to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the
corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation.
Received: 27 December 2000 / Accepted: 3 September 2001 相似文献
12.
1 ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆａｓｔＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍ (ＦＦＴ)ｔｅｃｈｎｉｑｕｅｉｓａｖｅｒｙｐｏｗｅｒｆｕｌｔｏｏｌｆｏｒｔｈｅｅｆｆｉｃｉｅｎｔｅｖａｌｕａｔｉｏｎｏｆｇｒａｖｉｔｙｆｉｅｌｄｃｏｎｖｏｌｕｔｉｏｎｉｎｔｅｇｒａｌｓ.Ｔｈａｎｋｓｔｏｔｈｅｇｏｏｄｃｏｍｐｕｔａｔｉｏｎｅｆｆｉｃｉｅｎｃｙ ,ｔｈｅＦＦＴｔｅｃｈｎｉｑｕｅ ,ｉｎｔｈｅｍｉｄ＿1 980ｓ ,ｂｅｇａｎｔｏｆｉｎｄｗｉｄｅｓｐｒｅａｄｕｓｅｉｎｇｅｏｉｄｄｅｔｅｒｍｉｎａｔｉｏｎ ,ｗｈｅｎｃｏｍｐａｒ… 相似文献
13.
There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals, i.e., the planar 2D convolution, the spherical 2D convolution and the spherical 1D convolution. The largest drawback of both the planar and the spherical 2D FFT methods is that, due to the approximations in the kernel function, only inexact results can be achieved. Apparently, the reason is the meridian convergence at higher latitudes. As the meridians converge, the ??,?λ blocks do not form a rectangular grid, as is assumed in 2D FFT methods. It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function, but also causes an approximation error during the implementation of 2D FFT in computer. In order to meet the increasing need for precise determination of the vertica deflections, this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections. After having made a detailed comparison between the planar and the spherical 2D FFT formulae, we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method. And then, a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper. A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT. The second part of this paper is to discuss the influences of the spherical harmonic reference field, the limited capsize, and the singular integral on the computation of the vertical deflections. The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro-observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters. 相似文献
14.
This work is an investigation of three methods for regional geoid computation: Stokes’s formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223–232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes’s formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes’s formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level. 相似文献
15.
Solving the geodetic boundary-value problem (GBVP) for the precise determination of the geoid requires proper use of the fundamental equation of physical geodesy as the boundary condition given on the geoid. The Stokes formula and kernel are the result of spherical approximation of this fundamental equation, which is a violation of the proper relation between the observed quantity (gravity anomaly) and the sought function (geoid). The violation is interpreted here as the improper formulation of the boundary condition, which implies the spherical Stokes kernel to be in error compared with the proper kernel of integral transformation. To remedy this error, two correction kernels to the Stokes kernel were derived: the first in both closed and spectral forms and the second only in spectral form. Contributions from the first correction kernel to the geoid across the globe were [−0.867 m, +1.002 m] in the low-frequency domain implied by the GRIM4-S4 purely satellite-derived geopotential model. It is a few centimeters, on average, in the high-frequency domain with some exceptions of a few meters in places of high topographical relief and sizable geological features in accordance with the EGM96 combined geopotential model. The contributions from the second correction kernel to the geoid are [−0.259 m, +0.217 m] and [−0.024 m, +0.023 m] in the low- and high-frequency domains, respectively. 相似文献
16.
Lars E. Sjöberg 《Journal of Geodesy》2006,79(12):675-681
The application of Stokes’s formula to determine the geoid height requires that topographic and atmospheric masses be mathematically removed prior to Stokes integration. This corresponds to the applications of the direct topographic and atmospheric effects. For a proper geoid determination, the external masses must then be restored, yielding the indirect effects. Assuming an ellipsoidal layering of the atmosphere with 15% increase in its density towards the poles, the direct atmospheric effect on the geoid height is estimated to be −5.51 m plus a second-degree zonal harmonic term with an amplitude of 1.1 cm. The indirect effect is +5.50 m and the total geoid correction thus varies between −1.2 cm at the equator to 1.9 cm at the poles. Finally, the correction needed to the atmospheric effect if Stokes’s formula is used in a spherical approximation, rather than an ellipsoidal approximation, of the Earth varies between 0.3 cm and 4.0 cm at the equator and pole, respectively. 相似文献
17.
On the ellipsoidal correction to the spherical Stokes solution of the gravimetric geoid 总被引：2，自引：0，他引：2
The solutions of four ellipsoidal approximations for the gravimetric geoid are reviewed: those of Molodenskii et al., Moritz, Martinec and Grafarend, and Fei and Sideris. The numerical results from synthetic tests indicate that Martinec and Grafarends solution is the most accurate, while the other three solutions contain an approximation error which is characterized by the first-degree surface spherical harmonic. Furthermore, the first 20 degrees of the geopotential harmonic series contribute approximately 90% of the ellipsoidal correction. The determination of a geoid model from the generalized Stokes scheme can accurately account for the ellipsoidal effect to overcome the first-degree surface spherical harmonic error regardless of the solution used. 相似文献
18.
A method is presented with which to verify that the computer software used to compute a gravimetric geoid is capable of producing
the correct results, assuming accurate input data. The Stokes, gravimetric terrain correction and indirect effect formulae
are integrated analytically after applying a transformation to surface spherical coordinates centred on each computation point.
These analytical results can be compared with those from geoid computation software using constant gravity data in order to
verify its integrity. Results of tests conducted with geoid computation software are presented which illustrate the need for
integration weighting factors, especially for those compartments close to the computation point.
Received: 6 February 1996 / Accepted: 19 April 1997 相似文献
19.
Prior to Stokes integration, the gravitational effect of atmospheric masses must be removed from the gravity anomaly g. One theory for the atmospheric gravity effect on the geoid is the well-known International Association of Geodesy approach in connection with Stokes integral formula. Another strategy is the use of a spherical harmonic representation of the topography, i.e. the use of a global topography computed from a set of spherical harmonics. The latter strategy is improved to account for local information. A new formula is derived by combining the local contribution of the atmospheric effect computed from a detailed digital terrain model and the global contribution computed from a spherical harmonic model of the topography. The new formula is tested over Iran and the results are compared with corresponding results from the old formula which only uses the global information. The results show significant differences. The differences between the two formulas reach 17 cm in a test area in Iran. 相似文献