Rayleigh scattering: Volterra equation for the matrix source function

Multiple Rayleigh scattering is examined in a semi-infinite atmosphere with uniformly distributed primary sources of partially polarized radiation. The resulting linear polarization is described by a 2×2 matrix transfer equation. A matrix generalization of Rybicki's two point Q-integral is obtained for this case. It is shown that the Volterra equation for the matrix source function for this problem is a particular case of our Q integral. Applying the Laplace transform to it yields the matrix form of the Ambartsumyan-Chandrasekhar H-equation. The Volterra equation for Sobolev's matrix resolvent function is another simple consequence of this equation. Translated from Astrofizika, Vol. 52, No. 2, pp. 301–310 (May 2009).     

基于缓变地形的远程海啸传播模拟的改进

在Sung(2002)所提出方案的基础上,考虑了非线性的作用,使得浅水差分方程组的数值解可以近似代替精度较高但却难以计算的Boussinesq方程的理论解,通过实验将新方案与Sung(2002)所提方案进行了比较,表明新方案适用于地形变化的情况。     

二维波动方程速度的正则化-同伦-测井约束反演

针对二维波动方程反问题,将大范围收敛的同伦方法引入速度参数的反演过程中,并将其与求解不适定问题的Tikhonov正则化有机结合,提出了一种新的、特别适用于非线性的、不适定的、多极值的地震勘探反演问题的反演策略：正则化－同伦方法. 为了充分利用测井资料和地震资料的互补特征,进一步提高反演分辨率并压制噪声,设计了正则化-同伦－测井约束联合反演方法. 大量数值试验结果表明了这两种方法的有效性.     

A novel RANSAC approach to robustly solve the 3D similarity transformation problem

A novel RANSAC robust estimation technique is presented as an effiecient method for solving the seven-parameter datum transformation problem in the presence of outliers. RANSAC method, which is frequently employed in geodesy, has two sensitive features: (i) the user adjusts some parameters of the algorithm, making it subjective and a rather difficult procedure, and (ii) in its shell, a nonlinear system of equation should be solved repeatedly. In this contribution, we suggest an automatic adjustment strategy for the most important parameter, ‘the threshold value’, based on the ‘early stopping’ principle of the machine-learning technology. Instead of using iterative numerical methods, we propose the use of an algebraic polynomial system developed via a dual-quaternion technique and solved by a non-iterative homotophy method, thereby reducing the computation time considerably. The novelty of the proposed approach lies in three major contributions: (i) the provision for automatically finding the proper error limit parameter for RANSAC method, which has until now been a trial-and-error technique; (ii) employing the algebraic polynomial form of the dual-quaternion solution in the RANSAC shell, thereby accelerating the repeatedly requested solution process; and (iii) avoiding iterations via a heuristic approach of the scaling parameter. To illustrate the proposed method, the transformation parameters of the Western Australian Geodetic Datum (AGD 84) to Geocentric Datum Australia (GDA 94) are computed.     

Numerical investigation of oscillations induced by submerged sliding masses within a harbor of constant slope

Oscillations within a rectangular harbor of constant slope induced by submerged sliding masses are investigated numerically based on Boussinesq-type equations and results are used to reveal the characteristics of the generated oscillations. The numerical result of each transverse eigenfrequency is very close to the theoretical prediction and the spatial structure of each mode of the oscillations may also be well captured by the existing analytical solutions based on shallow water equations. The investigation shows that relatively small-scale sliding masses whose width is small compared with the harbor width may induce obvious transverse oscillations. The predominant transverse components are those with small mode numbers when the solid slides start moving from the backwall. In comparing the oscillations induced by the slides of constant velocity and those accelerated by gravity force with bottom friction, it is observed that the movements accelerated by gravity force may facilitate the development of very low transverse oscillation modes while those with constant velocity may also be in favor of the higher ones. The augmentation of the sliding velocity along the constant slope may shift the amplitudes of the oscillation components to smaller values, which corresponds to the physical understandings of the waves generated by underwater sliding masses or landslides. While the sliding masses may not act on an isolated point of the bottom but follow a certain trajectory along the harbor, the transverse oscillations induced by them are sensitive to their position of departure in both the cross-harbor direction and the offshore direction. Longitudinal oscillations may be induced by relatively large sliding masses of harbor width on a constant slope within the harbor. Although the longitudinal oscillations may not reach a steady state without forcing terms at the entrance of the harbor, some patterns of several low-mode ones occur and wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions. It is revealed that the longitudinal oscillations are also sensitive to the moving velocity and initial location of the sliding masses.     

Transformation of Lambert Conic Conformal Coordinates from a Global Datum to a Local Datum

A detailed gravimetric geoid around Japan has been computed on the basis of 30’ × 30’ block mean free‐air gravity anomalies and GSFC GEM‐8 geopotential coefficient set. The 30’ × 30’ block means were read from various gravity maps around Japan, and the block means have been compiled into the JHDGF‐1 gravity file. Since the gravity file is restricted around Japan (see Figure 1), additional gravity data are needed to perform the Stokes’ integration in the cap with radius ψ₀ = 20°. The 1° × 1° block gravity means have been used outside the JHDGF‐1 region. The remarkable features of the gravimetric geoid occur over the trench areas. The geoidal dents over the trenches amount to ‐20~ ‐25 m in comparison with the geoidal heights in the land areas of Japan. The mean error of the 30’ × 30’ detailed gravimetric geoid obtained is estimated to be around 1.4 m, and the relative undulation of the geoid between the distance of a few hundred kilometers may be more accurate.     

Combined Sea Surface Determination Based on Various Geometric and Dynamic Techniques

Abstract

The combined use of Global Positioning System (GPS) differential positioning as well as ERS‐1 altimeter data is considered in implementing geodetic vertical datums and their unification. The article describes concepts, techniques, practical realization, and associated questions and problems. Particular aspects in view of small sea surface perturbations in offshore areas in determining sea surface components (variable and steady state) are discussed. The combinations of tide gauge data with altimetry and (mainly) GPS positioning for geodetic purposes are discussed in detail. Special attention is devoted to the associated reference systems as well as to the combination of dynamic (level and nonlevel surfaces) with geometric quantities. The discussion is based on a specific ERS‐1 project supported by the National Science Foundation. Implications and practical impact of the project are outlined.     

远海航渡式水深测量水位改正方法研究

针对远海航渡式水深测量作业中的潮汐改正难题,基于全球潮汐场DTU10模型及GPS无验潮测深两种改正模式,通过潮汐场预报精度评估、验潮站实测数据比对分析以及GPS大地高计算潮汐值等多种手段,开展了大范围、长时段、单测线情况下水深测量水位改正研究,形成了一套适用性强的航渡水深测量水位改正方法与流程,为面向全球的海洋水深测量资料处理提供了潮汐、垂直基准和水位归算的方法和技术支持。     

GPS矿区地面近井网的建立实践与分析

结合GPS矿区地面近井网建立实例,阐述GPS在矿区地面近井网建立过程中的诸多问题,如等级确定、网型结构、分级构建、重点观测等,意在服务于矿山井下大型巷道贯通工程及后续工程的定向边的基准;通过该网的建立,获得了某矿山的地面与井下的长度和方向基准。该网已为某12km长的大型贯通工程应用,工程贯通平面方向误差为1．7cm,远小于工程贯通平面方向限差20cm。实践证明该做法具有积极的示范作用。     

基于Harris角点和SIFT特征的近景影像匹配

针对近景影像匹配过程中误匹配率较大的情况,本文提出了一种基于Harris和SIFT特征的近景影像匹配方法。该方法首先提取Harris角点和SIFT特征,运用灰度相关系数和BBF-KD树方法将Harris角点和SIFT特征完成双向一致性匹配;然后,利用基于RANSAC方法和P-H算法的相对定向得到内点集A与B,将内点集A、B合并生成Delaunay同名三角网;最后,在同名三角形约束下通过缩小Harris特征点阈值T得到新内点集,实时插入同名三角网中,直到生成足够数量的内点。实验所得内点数分别与合并加密匹配前以及其他方法相比都有显著增多,结果表明对于视角、尺度、旋转、光照及噪音等条件发生变化的不同影像,本文提出的近景影像匹配方法能提高匹配率及匹配可靠性。