Spatial continuity measures for probabilistic and deterministic geostatistics

Geostatistics has traditionally used a probabilistic framework, one in which expected values or ensemble averages are of primary importance. The less familiar deterministic framework views geostatistical problems in terms of spatial integrals. This paper outlines the two frameworks and examines the issue of which spatial continuity measure, the covarianceC (h) or the variogram (h), is appropriate for each framework. AlthoughC (h) and (h) were defined originally in terms of spatial integrals, the convenience of probabilistic notation made the expected value definitions more common. These now classical expected value definitions entail a linear relationship betweenC (h) and (h); the spatial integral definitions do not. In a probabilistic framework, where available sample information is extrapolated to domains other than the one which was sampled, the expected value definitions are appropriate; furthermore, within a probabilistic framework, reasons exist for preferring the variogram to the covariance function. In a deterministic framework, where available sample information is interpolated within the same domain, the spatial integral definitions are appropriate and no reasons are known for preferring the variogram. A case study on a Wiener-Levy process demonstrates differences between the two frameworks and shows that, for most estimation problems, the deterministic viewpoint is more appropriate. Several case studies on real data sets reveal that the sample covariance function reflects the character of spatial continuity better than the sample variogram. From both theoretical and practical considerations, clearly for most geostatistical problems, direct estimation of the covariance is better than the traditional variogram approach.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.     

利用共线方程对空间实验室影象进行数字几何纠正

本文论述了利用共线方程对空间实验室影象实施数字几何纠正的理论依据、数据准备、外方位元素解求过程中参量的确定及锚点纠正法的可行性和纠正精度,提出了纠正过程中几个必须注意的环节,以提高精度,缩短机时。同时还介绍了自编软件包的组成。     

两层大地中三维体的激发极化与电阻率响应的积分方程模拟

用散射、叠加方法推导出两层大地的并矢格林函数。使用这些函数,含三维异常体的二层大地的边值问题转变为积分方程。使用矩量法,可解此积分方程。 使用偶极-偶极装置计算了激发极化和电阻率响应的几个数值结果,并对这一算法作了几方面检验。     

并矢格林函数等效源法在钻孔电磁波法中的应用

针对双孔电波法的实际情况,研究无限有耗媒质中,在半波偶极天线激励下,存在导电异常体的散射问题。理论上是根据等效源定理在散射体内引入等效电流,利用并失格林函数建立电场的积分方程并将其化为矩阵方程。在数值计算中,精心设计计算机程序,为提高计算精度,采取小圆柱体作为剖分单元。从物理角度对积分方程奇异点做巧妙的处理。经多次试算,结果令人满意。从而证明本文提出的理论和计算方法的有效性和适用性。     

计算横向非均匀介质体波理论地震图的Maslov渐近法

本文运用Maslov渐近理论编写的二维横向非均匀介质中的理论地震图程序,与其它类型算法作了精确对比,结果表明,在层状介质模型中,本程序的结果无论振幅还是波形对比都与反射率法基本相同。对于二维横向非均匀模型,在射线理论的非奇点处,本算法与射线方法基本一致,在射线理论的奇异点处,Maslov方法消除了射线理论所固有奇点,提高了计算精度。     

有限元素法全倾角波动方程偏移

本文试图从两个方面提高波动方程偏移的效果:1.使用全方向波动方程进行偏移,使之适用于任意倾角界面的反射;2.使用有限元素法提高微分方程数值解法的精度。     

A new ultrasonic interferometer for the determination of equation of state parameters of sub-millimeter single crystals

A new giga-Hertz ultrasonic interferometer has been developed, based on ultrasonic microscopy technology. The interferometer operates from 0.3 GHz to 1.5 GHz. The high frequency and associated small wavelengths together with the large bandwidth make it possible to measure travel times in samples with thicknesses of several microns and allow for unprecedented accuracy in bond corrections. An absolute accuracy of 1 part in 10⁵ in travel time measurements is achievable in single crystals (thickness of 200 microns) or glasses of interest to the earth sciences. The high precision travel time data, combining with sample length measurements using a laser interferometer built in our laboratory, yield very high precision ultrasonic velocities.The interferometer is intended for use in conjunction with a newly developed 4 GPa gas piston cylinder apparatus (Getting andSpetzler, 1993) for equation of state measurements under simultaneous pressure and temperature. A separate correction for the bond will be made for each datum at every point in temperature pressure space.     

潜水一维非稳态运动的解析理论及应用

讨论了潜水一维非稳态运动Boussinesq方程的对称性,并采用Lie群变换,就某些边界条件求出了其解析解,以便与线性化近似理论作比较;在此基础上,分析了Boussinesq方程线性化所引起的误差问题,并得到了特定条件下严格的零误差线性化方法。最后,通过算例的分析对比,提出了在线性化时应该遵循的一些原则。     

Stochastic Models of Quasigeostrophic Turbulence

Atmospheric and oceanic eddies are believed to be manifestations of quasigeostrophic turbulence — turbulence that occurs in rapidly rotating, vertically stratified fluid systems. The heat, momentum, and water transport by these eddies constitute a significant component of the climate balance, without which climate change cannot be understood. A major, unsolved problem is whether the turbulent eddy fluxes can be parameterized in terms of the large-scale, background flow. In the past, stochastic models have been used quite extensively to investigate quasigeostrophic turbulence in the case in which the eddy statistics are isotropic and homogeneous. Unfortunately, these models ignore the background shear which is absolutely essential to maintaining the eddies in the presence of dissipation. Recent attempts to extend stochastic models to shear flows have shown significant skill in predicting the structure of the eddy fluxes in arbitrary, three-dimensionally varying flows. This paper provides an accessible introduction to these models. The topics reviewed include quasigeostrophic turbulence and two-dimensional turbulence, non-modal andoptimal perturbations, mathematical theory of stochastic models, stochastic model simulations with realistic background states, and recent closure theories. A list of unsolved problems concludes this review.