Two modified algorithms to transform Cartesian to geodetic coordinates on a triaxial ellipsoid

The paper presents modified Lin and Wang??s (1995) and Hedgley??s (1976) algorithms to tackle the problem of transforming Cartesian to geodetic coordinates on a triaxial ellipsoid. Originally, the methods were developed for an ellipsoid of revolution but due to their universality, they may be adapted to the more complicated problem stated on a triaxial ellipsoid what is in fact done in this work. Two modified methods are compared to the vector method recently introduced by Feltens. The modified methods turn out to be more accurate and faster than the algorithm presented by Feltens.     

Lame surfaces as a generalisation of the triaxial ellipsoid

In modern geodesy the triaxial ellipsoid as a generalisation of the ellipsoid of revolution has a significant position in studying the figure of the Earth. Lame surfaces represent a generalisation of the triaxial ellipsoid. The following paragraphs are devoted to curvatures of the Lame surfaces.     

Closed formulae for transformation of the cartesian coordinate system into a system of geodetic coordinates

Summary Relations for the direct transformation of the Cartesian coordinate system into a system of geodetic coordinates.

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u ¶rt;u , , z ¶rt;uu , , h.

     

The rotated Cartesian coordinate method to remove the axial singularity of cylindrical coordinates in finite‐difference schemes for elastic and viscoelastic waves

When modelling the propagation of 3D non‐axisymmetric elastic and viscoelastic waves in cylindrical coordinates using the finite‐difference time‐domain method, a mathematical singularity occurs due to the presence of terms in the elastic and viscoelastic wave equations. For many years, this issue has been impeding the accurate numerical solution near the axis. In this work, we propose a simple but effective method for the treatment of this numerical singularity problem. By rotating the Cartesian coordinate system around the z‐axis in cylindrical coordinates, the numerical singularity problems in both 2D and 3D cylindrical coordinates can be removed. This algorithm has three advantages over the conventional treatment techniques: (i) the excitation source can be directly loaded at , (ii) the central difference scheme with second‐order accuracy is maintained, and (iii) the stability condition at the axis is consistent with the finite‐difference time‐domain in Cartesian coordinates. This method is verified by several 3D numerical examples. Results show that the rotating the Cartesian coordinate method is accurate and stable at the singularity axis. The improved finite‐difference time‐domain algorithm is also applied to sonic logging simulations in non‐axisymmetric formations and sources.     

An optimized finite difference method based on a polar coordinate system for regional-scale irregular topography

The finite difference method (FDM) is an important numerical approach for simulating the propagation of seismic waves, and some FDMs can be used to study the impact of the Earth’s curvature and topography over large distances. To efficiently model the effects of the Earth’s irregular topography on the propagation of seismic waves, here we optimize a previously proposed grid mesh method and develop a novel two-dimensional boundary-conforming FDM based on a curvilinear polar coordinate system. This method efficiently simulates the propagation of seismic waves in an arc-shaped model with large variations in surface topography. Our method was benchmarked against other reported methods using several global-scale models. The consistency of the results confirms the validity of our proposed optimization strategy. Furthermore, our findings indicate that the proposed optimization strategy improves computational efficiency.     

Calculation of the amplitudes of elastic waves in anisotropic media in Cartesian or ray-centred coordinates

Studia Geophysica et Geodaetica - We derive various expressions for the amplitude of the ray-theory approximation of elastic waves in heterogeneous anisotropic media, and show their mutual...     

On the application of the coupled finite-infinite element method to geodetic boundary-value problem

Our aim is to introduce the Coupled Finite-Infinite Element Method (CFIEM) as a new alternative approach to the Earth’s gravity field modelling. We show that if the computational domain is large enough in radial direction, one can obtain the qualitatively and quantitatively comparable solution to the solution by the Finite Element Method (FEM). We study the influence of the size of the computational domain on the final CFIEM solution as well as the successive refinement of the discretization and its convergence to the exact solution. As an input data we use the synthetic boundary conditions computed from a Synthetic Earth Gravity Model (SEGM) and we test the CFIEM solution by the data generated directly from SEGM and the solution by the FEM.     

The determination of the regional part of the vertical gradient anomaly by a geodetic method

Summary The significance of the vertical gradients of gravity is great in geophysics and also in geodesy. In geophysics the observed vertical gradients can give valuable information about mass distributions close to the surface of the earth and in geodesy they may be used in determining the shape of the equipotential surfaces. The observed vertical gradients are very sensitive to masses close to the surface of the earth and they change very rapidly. Therefore, they should not be used for purposes such as the reduction of the observed gravity to the sea level. The normal vertical gradients are not the best either for this purpose because they are much too uniform on the surface of the earth. The best values for practical purposes are probably the regional vertical gradients.This paper presents a method to determine the regional vertical gradient anomalies in large areas from geodetic observations which, added to the normal part, will give the regional vertical gradients.     

基于卡方分布函数的辐射带电子蝴蝶状投掷角分布的优化判别方法

受不同物理过程影响,辐射带电子呈现多种投掷角分布类型,其中蝴蝶状分布尤为引人关注,其特征为通量在90°投掷角附近有极小值、在较低投掷角处达到峰值.现有研究普遍通过对几个特定投掷角间的通量比值进行限定来识别蝴蝶状分布,然而,该方法所挑选的电子分布并不一定符合蝴蝶状分布特征,这为准确研究电子蝴蝶状分布的现象学规律及其背后物理机制带来了一定困难.针对该问题,本文建立了一个基于卡方分布函数的判别模型,通过比较电子观测通量剖面与模型模拟的理想蝴蝶状分布剖面的相似性来判别电子蝴蝶状分布.使用范艾伦卫星上REPT仪器提供的L-shell > 3空间区域内两组不同投掷角分辨率的电子通量数据对该判别方法进行验证,结果表明该方法能明显提升判别效果,分别使基于17个投掷角和36个投掷角的电子通量数据判别蝴蝶状分布的误判率下降12.6%和27.5%.本文的分析结果证实了提高投掷角精度有利于准确确定辐射带电子的投掷角分布类型,发展的模型方法也对深入开展地球与行星磁层中电子蝴蝶状分布的统计学研究具有重要价值.

     

水准椭球密度问题研究

本文总结了作者等最近十年来对地球重力学"水准椭球密度问题"进行研究的初步结果,首次提出了"密度水准椭球"概念,给出了从"匀质椭球"、"参数椭球"、"纬向密度椭球"、"似水准椭球"到"密度水准椭球"的研究路线,并对该问题的研究前景进行了讨论.     

球坐标系下三维大地电磁正演研究

大地电磁正演理论研究热点一直以来主要集中在如何提高计算效率和精度,但在剖面足够长、探测深度足够大的情况下,传统的笛卡尔坐标系数值模拟方式难以准确拟合地球曲率形态.本文研究了基于球坐标系的三维大地电磁正演,推导了交错网格有限差分三维正演公式,与一维解析解和三维标准模型测试对比,验证了正演算法的正确性.通过理论模型计算,对比分析球坐标和笛卡尔坐标系正演结果表明：球坐标系模拟更合理,避免了传统笛卡尔坐标拉伸投影所引入的误差,可代替目前的笛卡尔坐标模拟方法.基于球坐标和笛卡尔坐标系的三维大地电磁正演响应值随着频率变低差异越明显.球坐标和笛卡尔坐标计算结果差异度与频率、模型结构和电阻率有关.本文模型计算结果在数万秒周期处已出现接近10%的差异,对于较大尺度的长周期大地电磁,地球曲率的影响不能忽略.

     

Rock physics inversion based on an optimized MCMC method

Rock physics inversion is to use seismic elastic properties of underground strata for predicting reservoir petrophysical parameters.The Markov chain Monte Carlo...     

基于小波变换与小波包变换的降噪方法比较

在模拟地震记录信号中加入信噪比为17的高斯白噪声,然后分别采用小波降噪和小波包降噪方法,对含噪信号进行降噪处理。在不同降噪阈值下,比较降噪后信号的信噪比。结果表明:在同一降噪阈值下,小波包降噪后信号的信噪比高于小波降噪后信号的信噪比,而且采用wbmpen方法给定的阈值明显可以提高降噪后信号的信噪比。     

A practical method to transform frequency dependent impedance to time domain

In order to perform time history earthquake response analyses with consideration to both the dynamic soil–structure interaction and the non‐linear behaviour of the structure, it is important to transform the soil impedance in the frequency domain to the impulse response in the time domain. In this paper, a new transform method with high practicality is proposed. First, the formulation of the proposed transform method is described. Next, the validity of the method is examined using an example problem whose impulse response is analytically obtained. Then, the impedance of the rigid foundation on 2‐layered soil is transformed to the time domain, and the characteristics of the impulse response are investigated. Finally, time history earthquake response analyses of a structure on the soil using the obtained impulse response are carried out. The validity and the efficiency of the proposed method are confirmed through these investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

基于Curvelet变换的地震资料信噪分离技术

在地震资料中,噪声干扰严重影响了有效信号的提取,为此必须进行信噪分离处理.本文提出一种基于Curvelet变换和KL变换相结合的软硬阈值折衷处理方法.首先对地震数据进行Curvelet变换,然后对各尺度系数选取适当阈值压制噪声干扰,再利用KL变换提取数据中的相干有效信号,最后重构得到去噪后的记录.经合成记录和实际地震资料处理实验证明,该方法与小波变换法相比较,更能有效进行信噪分离,提高地震剖面信噪比和分辨率.     

The quasi-isotropic relative structure of a geodetic net and the procedure used to establish it

Summary The method of computing the quasi-isotropic relative structure (QIRS) of a geodetic net which maximizes the relative accuracy between a priori determined points of the net, the configuration of the net being taken into account, is described. The iteration procedure is used to establish this structure.

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nuam n aamu auumn mum naa uu¶rt;u mu, m nu¶rt;um au mum mmu ¶rt; ¶rt;au naau nm m uauu¶rt;u mu. nm umamu m¶rt; uu.

     

Stratigraphic coordinates: a coordinate system tailored to seismic interpretation

In certain seismic data processing and interpretation tasks such as spiking deconvolution, tuning analysis, impedance inversion, and spectral decomposition, it is commonly assumed that the vertical direction is normal to reflectors. This assumption is false in the case of dipping layers and may therefore lead to inaccurate results. To overcome this limitation, we propose a coordinate system in which geometry follows the shape of each reflector and the vertical direction corresponds to normal reflectivity. We call this coordinate system stratigraphic coordinates. We develop a constructive algorithm that transfers seismic images into the stratigraphic coordinate system. The algorithm consists of two steps. First, local slopes of seismic events are estimated by plane‐wave destruction; then structural information is spread along the estimated local slopes, and horizons are picked everywhere in the seismic volume by the predictive‐painting algorithm. These picked horizons represent level sets of the first axis of the stratigraphic coordinate system. Next, an upwind finite‐difference scheme is used to find the two other axes, which are perpendicular to the first axis, by solving the appropriate gradient equations. After seismic data are transformed into stratigraphic coordinates, seismic horizons should appear flat, and seismic traces should represent the direction normal to the reflectors. Immediate applications of the stratigraphic coordinate system are in seismic image flattening and spectral decomposition. Synthetic and real data examples demonstrate the effectiveness of stratigraphic coordinates.