Using Kolmogorov-Smirnov Statistics to Compare Geostrophic Velocities Measured by the Jason, TOPEX, and Poseidon Altimeters

The Kolmogorov-Smirnov (K-S) test is used to compare probability density functions (PDFs) of geostrophic velocities measured by the TOPEX, Poseidon, and Jason altimeters. Velocity PDFs are computed in 2.5° by 2.5° boxes for regions equatorward of 60° latitude. Although velocities measured by the TOPEX and Jason altimeters can differ, on the basis of the K-S test the velocities are statistically equivalent during the ∼200 day period when the satellites followed the same orbit. Full records from TOPEX, Poseidon, and Jason show less agreement, which can be attributed to temporal variability in ocean surface velocities and differing levels of measurement noise.     

Hydraulic conductivity in frozen soils

An apparatus has been developed for investigation of hydraulic conductivity of frozen soils. The test procedure is isothermal and involves the passage of water from one reservoir into the frozen sample and out of the frozen sample into a second reservoir. The water in the reservoirs remains unfrozen because it contains dissolved lactose. The concentration of lactose is such that, initially, the water in the reservoirs is in thermodynamic equilibrium with the water in the soil. On application of pressure to one reservoir a known hydraulic gradient is established and flow takes place. Flow is shown to vary linearly with hydraulic gradient. The hydraulic conductivity coefficient depends on soil type and temperature and is related to the unfrozen water content. At temperatures within a few tenths of 0°C the coefficient apparently ranges from 10^?5 to 10^?9 cm sec^?1, and decreases only slowly below about ?0·5°C. Soils known to be susceptible to frost heave are shown to have significant hydraulic conductivities well below 0°C.     

Characteristic behavior and order relations for indicator variograms

Heuristic models for indicator variograms and their parameters (practical nugget effect and range) are proposed for a bivariate normal distribution with spherical correlogram. These models can be used conveniently as a preliminary check for bivariate normality. In the general non-Gaussian case, indicator variogram models for multiple threshold values must verify a certain number of order relations (inequalities) established directly from the properties of a general bivariate cumulative distribution function. An interesting, little-known maximum hole effect for indicator correlation is pointed out.     

超定边值问题的样条解法

正在进行和即将进行的大量GPS＋Levelling测量使得大地水准面也成为直接观测量，因此经典的Molodensky天文重力准已经不能适应这一情况。为了从更广泛的意义上更好地利用各类观测值，本文使用样条函数作为基函数，讨论了局部地区超定边值问题的样条解法。     

Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

A general solution of Biot's field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed.     

Positive definiteness is not enough

Geostatisticians know that the mathematical functions chosen to represent spatial covariances and variograms must have the appropriate type of positive definiteness, but they may not realize that there are restrictions on the types of covariances and variograms that are compatible with particular distributions. This paper gives some examples showing that (1) the spherical model is not compatible with the multivariate lognormal distribution if the coefficient of variation is 2.0 or more (even in 1-D), and (2) the Gaussian covariance and several other models are not compatible with indicator random functions. As these examples concern quite different types of random functions, it is clear that there is a general problem of compatibility between spatial covariance models (or variograms) and a specified multivariate distribution. The problem arises with all distributions except the multivariate normal, and not just the two cited here. The need for a general theorem giving the necessary and sufficient conditions for a covariance or a variogram to be compatible with a particular distribution is stressed.     

Simulation of geological surfaces using fractals

Methods suggested in the past for simulated ore concentration or pollution concentration over an area of interest, subject to the condition that the simulated surface is passing through specifying points, are based on the assumption of normality. A new method is introduced here which is a generalization of the subdivision method used in fractals. This method is based on the construction of a fractal plane-to-line functionf(x, y, R, e, u), where(x, y) is in[a, b]×[c, d], R is the autocorrelation function,e is the resolution limit, andu is a random real function on [–1, 1]. The simulation using fractals escapes from any distribution assumptions of the data. The given network of points is connected to form quadrilaterals; each one of the quadrilaterals is split based on ways which are extensions of the well-known subdivision method. The quadrilaterals continue to split and grow until resolution obtained in bothx andy directions is smaller than a prespecified resolution. If thex coordinate of theith quadrilateral is in[a _i ,b _i ] and they coordinate is in[c _i ,d _i ], the growth of this quadrilateral is a function of(b _i –a _i ) and(d _i –c _i ); the quadrilateral could grow toward the positive or negativez axis with equal probability forming four new quadrilaterals having a common vertex.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

碱性体系t-BAMBP萃取微量铷及热力学函数研究

通过对4-叔丁基-2-(α-甲苄基)苯酚(t-BAMBP)萃取微量铷的性能的研究,详细考察了稀释剂、碱度和温度对萃取的影响。实验结果表明,在260#溶剂油体系中,铷的分配比较之在环己烷体系和四氯化碳体系高;强碱性环境和低温条件有利于铷的萃取。同时通过斜率法和饱和法确定了萃合物组成为RORb·ROH,并研究了萃取过程的热焓、吉布斯自由能及熵变等基础热力学性质,结果表明该萃取反应为放热反应,萃取过程熵减。