二维位场在有源空间的解析延拓

位场的向下延拓对重、磁等位场资料的处理与解释具有重要意义,但现有的延拓方法在位场向下接近场源时会产生剧烈震荡,计算过程很不稳定,而且理论上都不能越过场源. 本文在复数域里定义了一个具有位场和几何双重特性的新函数PFGR,提出了一套新的延拓方法,在理论上实现了位场在包含场源的下半空间里的解析延拓,经过模型试算验证,表明该方法可以延拓越过场源,准确确定场源奇点,计算过程稳定,对测量中的随机噪声也具有较好的抗干扰能力.     

重力场向下延拓Milne法

重力场向下延拓能够突出局部和浅部的异常信息,分离叠加的异常特征.但是向下延拓通常具有过程不稳定、下延深度小、结果不准确等问题.针对向下延拓所存在的不足,本文利用重力场及其垂向一阶导数,基于辛普森（Simpson）求积公式,推导出重力场向下延拓米尔尼（Milne）公式.将本文向下延拓方法应用于模型数据,向下延拓模型结果及误差曲线表明,相对于向下延拓快速傅里叶变换（FFT）法和积分迭代法,向下延拓Milne法的深度更大,相对误差更小;相对模型值,向下延拓Milne法能够获得稳定且准确的结果.对加拿大乃查科（Nechako）盆地地区实测航空重力数据进行本文方法向下延拓验证,处理结果表明,相对于实测异常,本文方法向下延拓结果能够很好还原实测数据,并且在进一步向下延拓中反映原始异常的趋势,增强局部和细小异常信息.

     

正则化等效层重力向下延拓方法

近年来,利用时移微重力技术进行储层开发监测受到国内外学者广泛关注.时移微重力观测数据存在信噪比低,信号弱的问题,难以实现储层内物质运移的定量解释.为压制数据噪声,增强有效弱信号,本文研究了利用Tikhonov正则化方法反演等效层（源）,并由等效源实现重力场向下延拓的方法;在此基础上,本文推导了波数域正则化等效源向下延拓算子.针对向下延拓场幅值衰减问题,提出了正则化等效源迭代补偿算法.通过模拟数据实验研究了不同深度正则化等效源滤波算子及向下延拓算子的波数响应;与波数域Tikhonov正则化向下延拓方法相比,正则化等效源向下延拓方法的延拓精度更高、更稳定.最后,将基于迭代补偿的正则化等效源向下延拓技术应用于实测时移微重力数据证实了该方法能够有效增强局部异常,实现时移微重力数据大深度稳定向下延拓.

     

利用余弦变换计算重力异常的向上延拓

利用余弦变换计算重力异常的向上延拓是一种新方法.根据余弦变换的基本性质,推导了二度、三度体异常向上延拓余弦变换谱理论公式,采用离散余弦变换实现了该法的数值计算;研究了无限长水平圆柱体的补偿因子中主频段的特性,给出了二度体的线性补偿方式;补偿后的理论模型异常向上延拓具有较高的计算精度,除边部几个数据因数据的离散和有限截断使误差较大外（最大误差为6.23%）,其余数据的误差均在1%以内,理论值和计算值曲线基本重合.这说明,与Fourier变换相比,离散余弦变换在数值计算中,受非周期性深度因子的影响小,补偿方式易于选择,其计算方法优于Fourier变换.     

约束等效源稳定向下延拓方法研究

在等效源向下延拓方法的理论基础上,研究提出加入观测平面以下空间实测数据作为约束的等效源约束向下延拓法,用于二维位场数据向下延拓.与传统的向下延拓方法和等效源法延拓相比,等效源约束向下延拓法抗噪声性强,能延拓出由于延拓深度过大而衰减至难以探测的高频信号,使延拓结果更接近真实值.理论重力模型数据的延拓结果显示该方法有效,延拓结果优于传统波数域迭代法和等效源法.利用等效源约束延拓法对我国某海域水面实测重力值进行向下延拓并与水下实测值进行对比,结果表明该方法延拓结果最接近实测值.本文方法为我国深水油气近海底重磁高精度探测研究提供一定的技术支撑.

     

Optimum expression for computation of the gravity field of a polyhedral body with linearly increasing density

The formula for the computation of the gravity field of a polyhedral body whose density is linearly dependent on some coordinate is derived and transformed into the optimum form for numerical calculation.     

Shoreline change at an infinite jetty for wave time series

Future shoreline changes on a sandy beach with a structure such as a jetty or groin can be estimated when wave time series is known (i.e. sequence of wave height, period, and direction). This paper presents an extension of an existing solution (Pelnard-Considere, 1956) for the linearized partial differential equation for shoreline change at an infinite jetty where waves are time varying and when the angle of the shoreline is small with respect to the waves breaking at the shoreline. The novel solution provided in this paper allows the previous constant wave condition solution to be extended to the case where wave properties (i.e. wave direction, wave height, and wave period) are time varying. Example usage of the method presented shows that shorelines may be of different final plan form shape for time varying wave conditions even though the sediment transport along adjacent beaches is not spatially varying (i.e. spatially constant) from time step to time step. Although this difference in shape may have been known previously using numerical models, it could not be proved analytically. Reversals of wave height, period, and direction time series are shown to provide different final shoreline shapes even though the time series consists of the same waves although in different ordered time. The solution provided will allow one line numerical shoreline models to be tested using an analytic solution.     

基于向上延拓的航空重力向下解析延拓解

位场向下与向上延拓之间存在固有的内在联系,向上延拓解算具有稳定可靠的优良特性,本文据此提出了借助向上延拓信息实现航空重力向下延拓稳定解算的两种方法,分别建立了点对点向下解析延拓模型和最小二乘向下解析延拓模型.其核心思想是,依据泰勒级数展开模型,将位场向下延拓解算过程转换为向上延拓计算和垂向偏导数解算两个步骤,通过第一步的处理有效抑制数据观测噪声对解算结果的干扰,通过第二步的处理成功实现向下延拓反问题的稳定解算,较好地解决了向下延拓解算固有的不适定性问题.分析研究了两种解析延拓模型的计算精度及适用条件,利用超高阶位模型EGM2008建立的模拟标准场数据对两种模型解算结果的合理性和有效性进行了数值验证,证明本文新方法实用易行,具有较高的应用价值.

     

Numerical behaviour of the downward continuation of gravity anomalies

The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the Poisson integral using point, single mean, and doubly averaged kernel are examined. Correct evaluation of the integral in its innermost zone is a challenging task. To avoid instabilities, an analytical planar approximation is used in the innermost integration zone. In addition it is shown that the single mean mode has the minimum discretization error. Downward continuation of point and mean anomalies by singly and doubly averaged kernel are the same mean anomalies on the geoid.     

Improved daily GRACE gravity field solutions using a Kalman smoother

Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure.The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations.From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.     

A study of the upward continuation of gravity data from a plane surface

Summary A summation method of upward continuation of gravity data has been considered under the assumption that observations are available at regular intervals. The upward continued value has been obtained as the sum of products of individual gravity values and corresponding theoretical coefficients. Besides the usual parameter involving horizontal and vertical distances, the theoretical coefficients have been generalized to be dependent also on i) the order of a low order polynomial assumed to represent the gravity variation around a grid point and ii) the weights assigned to the gravity values at the nearest four grid points used for least-squares determination of the polynomial. Since the observations in practical cases are available over a finite area only, the effect of truncation of the area of the integration has also been discussed separately. The method has been programmed and tested on a three-dimensional model, whose true gravity effects were computed at various levels over a finite area. Upward continued values have been computed under various assumptions about the gravity field in the outside region. Comparisons of these results with the true values indicate that the truncation effect becomes increasingly important for larger values of the ratio of elevation to grid separation and/or when the gravity field is not a local one. It has also been found that the greater is the above ratio, the less important is the effect of weights on the theoretical coefficients and practically vanishes(<10 ^–4 ) when the ratio is greater than5.0.     

Coupled hydrodynamic response of concrete gravity dams using finite and infinite elements

This paper presents the application of the finite element method for analysing the two-dimensional response of reservoir-dam systems subjected to horizontal ground motion. The interaction between the dam and the reservoir as well as the compressibility of water has been taken into account. The complete system has been considered to be composed of two substructures, namely the reservoir and the dam. To take into account the large extent of the reservoir, it has been idealized using specially developed infinite elements coupled with standard finite elements while the dam is represented using finite elements alone. Structural damping of the dam and radiation damping in the fluid phase have been accounted for in the analysis. It is concluded that the effect of radiation damping is considerable at high frequencies of excitation. The coupled response of the system is significantly large at and near the fundamental natural frequency of the system in comparison to the uncoupled responses. The method is computationally quite economical, capable of taking into account the arbitrary geometry of the system and is recommended for practical application. Further applications and extensions of the approach to three dimensional analyses are possible.     

Analytical power series solutions to the two-dimensional advection–dispersion equation with distance-dependent dispersivities

As is frequently cited, dispersivity increases with solute travel distance in the subsurface. This behaviour has been attributed to the inherent spatial variation of the pore water velocity in geological porous media. Analytically solving the advection–dispersion equation with distance-dependent dispersivity is extremely difficult because the governing equation coefficients are dependent upon the distance variable. This study presents an analytical technique to solve a two-dimensional (2D) advection–dispersion equation with linear distance-dependent longitudinal and transverse dispersivities for describing solute transport in a uniform flow field. The analytical approach is developed by applying the extended power series method coupled with the Laplace and finite Fourier cosine transforms. The developed solution is then compared to the corresponding numerical solution to assess its accuracy and robustness. The results demonstrate that the breakthrough curves at different spatial locations obtained from the power series solution show good agreement with those obtained from the numerical solution. However, owing to the limited numerical operation for large values of the power series functions, the developed analytical solution can only be numerically evaluated when the values of longitudinal dispersivity/distance ratio e_L exceed 0·075. Moreover, breakthrough curves obtained from the distance-dependent solution are compared with those from the constant dispersivity solution to investigate the relationship between the transport parameters. Our numerical experiments demonstrate that a previously derived relationship is invalid for large e_L values. The analytical power series solution derived in this study is efficient and can be a useful tool for future studies in the field of 2D and distance-dependent dispersive transport. Copyright © 2008 John Wiley & Sons, Ltd.     

基于GRACE卫星重力数据确定地球重力场模型WHU-GM-05

基于卫星轨道运动的能量积分方程,可导出利用卫星跟踪卫星数据求解地球重力场的实用公式.本文在Jekeli给出的公式基础上导出了基于能量守恒方程利用两颗低-低卫星跟踪的扰动位差求解重力位系数的严密关系式.基于两颗GRACE卫星的观测数据,采用本文导出的严密能量积分方法求解得到120阶的GRACE地球重力场模型,命名为WHU-GM-05;将WHU-GM-05模型与国际上同类重力场模型EIGEN-GRACE系列和GGM02S分别在阶方差和大地水准面高等方面作了比较,并与美国和中国的部分地区GPS水准观测值进行了精度分析.结果表明基于本文推导的严密双星能量守恒方程得到的WHU-GM-05重力场模型精度与国际上同类重力场模型的精度相当.     

航线上重力基准构建的单点延拓方法

本文利用联合低阶重力位模型和地形数据的单点延拓方法将地面重力观测数据延拓到空中,构建了航线上重力基准,实现了两套航空重力观测数据的质量评价,实验结果表明:(1)单点延拓方法完全可以应用于航空重力观测数据的外部精度检核,效果良好,性价比高;(2)相比仅采用重力位模型或地形数据进行单点延拓计算,联合重力位模型和地形数据的延拓计算对航空重力观测数据的评估结果更加可靠;(3)联合低阶重力位模型和地形数据的单点延拓方法计算速度快、效率高.本文研究方法,也可适用于新研航空重力仪的标度因数、零偏等参数的在线标定.     

位场曲化平积分方程的迭代解

提出了位场曲化平的新方法.给定观测曲面S上的位场、S对下方水平面P的相对高程,确定P上的位场.利用由P向上延拓到S的积分式,建立这两个面上位场及相对高程三者所满足的方程,它是第一类Fredholm积分方程.用Fourier逆变换式把这一空间域积分式化为波数域积分式,再由指数函数的Taylor展开进一步化为级数式.积分方程的解采用逐次逼近法迭代计算,即用S上的位场观测值作为P上位场的初始迭代值,用导出的级数式求得S上的位场计算值、由S上的位场观测值与计算值之差校正P上的位场,多次迭代,直到满足迭代终止准则.我们还给出该积分方程的波数域迭代计算方法.模型算例表明,重力异常曲化平的均方差和磁异常曲化平的均方差分别为0.0008mGal和0.0019 nT,在主频为2.26 GHz的笔记本电脑运行,2048×2048数据量,计算时间是975 s.野外磁场实际资料处理也证实这种方法的有效性.     

利用微分进化法确定海洋磁场向下延拓中的最优参数

位场的解析延拓是实现不同高度海洋地磁场相互转换的主要途径,是构建海洋三维磁空间背景场模型的关键技术.针对位场向下延拓迭代法中最优正则化参数及最佳迭代次数难以确定问题,尝试引入微分进化法,以正则化参数及迭代次数为种群变量,以延拓结果的熵值为目标函数,以目标函数最小化为搜索准则,实现两种参数的并行全局寻优.采用实测数据对微分进化法在几种常用的迭代法中最优正则化参数及最佳迭代次数的确定进行了分析,与传统L-曲线准则确定的最优正则化参数及多次试验确定的最佳迭代次数进行对比,结果表明：微分进化法确定的最优参数能使三种迭代法取得最佳迭代效果,延拓结果与真实地磁场最为接近,并且该法计算稳定、自适应强,建议在海洋磁场数据向下延拓中应用.

     

The parameters of an infinite homogeneous elliptical cylinder determined from its gravity effects

Summary The Fourier transform of the vertical component of the attraction of a homogeneous horizontal infinite elliptical cylinder is computed. By comparing this function with the Fourier transform of the vertical component, determined experimentally, it is possible to determine the mass of the cylinder per unit length, as well as the position of the centre and of both the foci of the ellipse representing the cross-section of the cylinder.Decicated to Academician Alois Zátopek on His 65th Birthday     

重力辅助惯性导航中的重力场多尺度特性研究

重力辅助惯性导航是真正的无源导航,它已成为21世纪无源导航定位技术的主要研究方向之一.本文在进行了一般性的尺度概念及多尺度系统理论概述之后,结合重力场的固有特性,分别从重力场的模型尺度特性、空间尺度特性以及时间尺度特性详细介绍了地球重力场固有的多尺度特性.另外,根据重力辅助惯性导航系统中重力场数据的作用,从利用重力场实...