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1.
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering.  相似文献   

2.
Kriging with strings of data   总被引：1，自引：0，他引：1  
The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r(n) is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r(n),and presents a number of examples.  相似文献   

3.
The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r(n) is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r(n),and presents a number of examples.  相似文献   

4.
Strain analysis of the Baraitha conglomerate is attempted by direct measurements on extracted pebbles and by micrometric analysis. The overall deformation is of flattening type, with thek value lower by more than half in the matrix than in the pebbles. The viscosity contrast between pebbles and matrix (μ i/μm) is in the ratio of 2:1 and the bulk deformation appears to be strongly controlled by Ci (concentration of pebbles expressed as percentage). The total shortening (≃35%) in the Baraitha conglomerate is comparable with the shortening accomplished in the folding of the overlying Bijawar Group volcanosedimentary sequence. The bulk strain axesX t, Yt andZ t, as determined from the analysis of the deformed conglomerate, are unsymmetrically oriented with reference to folds formed by oblique flexural-slip with neitherX t norY tcoincident with the fold hinges. The lack of transection of folds by cleavage again suggests flattening deformation. The extension in theY tdirection is greater in the matrix than in the pebbles.  相似文献   

5.
The thermo-elastic behavior of a natural epidote [Ca1.925 Fe0.745Al2.265Ti0.004Si3.037O12(OH)] has been investigated up to 1,200 K (at 0.0001 GPa) and 10 GPa (at 298 K) by means of in situ synchrotron powder diffraction. No phase transition has been observed within the temperature and pressure range investigated. P–V data fitted with a third-order Birch–Murnaghan equation of state (BM-EoS) give V 0 = 458.8(1)Å3, K T0 = 111(3) GPa, and K′ = 7.6(7). The confidence ellipse from the variance–covariance matrix of K T0 and K′ from the least-square procedure is strongly elongated with negative slope. The evolution of the “Eulerian finite strain” vs “normalized stress” yields Fe(0) = 114(1) GPa as intercept values, and the slope of the regression line gives K′ = 7.0(4). The evolution of the lattice parameters with pressure is slightly anisotropic. The elastic parameters calculated with a linearized BM-EoS are: a 0 = 8.8877(7) Å, K T0(a) = 117(2) GPa, and K′(a) = 3.7(4) for the a-axis; b 0 = 5.6271(7) Å, K T0(b) = 126(3) GPa, and K′(b) = 12(1) for the b-axis; and c 0 = 10.1527(7) Å, K T0(c) = 90(1) GPa, and K’(c) = 8.1(4) for the c-axis [K T0(a):K T0(b):K T0(c) = 1.30:1.40:1]. The β angle decreases with pressure, βP(°) = βP0 −0.0286(9)P +0.00134(9)P 2 (P in GPa). The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α0 + α1 T −1/2. The refined parameters for epidote are: α0 = 5.1(2) × 10−5 K−1 and α1 = −5.1(6) × 10−4 K1/2 for the unit-cell volume, α0(a) = 1.21(7) × 10−5 K−1 and α1(a) = −1.2(2) × 10−4 K1/2 for the a-axis, α0(b) = 1.88(7) × 10−5 K−1 and α1(b) = −1.7(2) × 10−4 K1/2 for the b-axis, and α0(c) = 2.14(9) × 10−5 K−1 and α1(c) = −2.0(2) × 10−4 K1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α0(a): α0(b): α0(c) = 1 : 1.55 : 1.77. The β angle increases continuously with T, with βT(°) = βT0 + 2.5(1) × 10−4 T + 1.3(7) × 10−8 T 2. A comparison between the thermo-elastic parameters of epidote and clinozoisite is carried out.  相似文献   

6.
The paper proposes a simple, accurate, precise, and rapid method for determining the high atomic number (Z) major-element, tantalum (Z = 73), in the rare mineral, columbite [(Fe,Mn) (Nb,Ta)2O6] — tantalite [(Fe,Mn) (Ta,Nb)2O6], by wavelength-dispersive x-ray fluorescence spectrometry (WDXRFS). The other major-element in columbite-tantalite is the lower atomic number niobium (Z = 41). The method uses the characteristic radiation, TaKα, and an LiF 420 analysing crystal, to overcome the problems associated with the serious x-ray spectral-line interference of the secondorder NbKα and NbKβ with the first-order TaLα1 and TaLβ1 respectively.  相似文献   

7.
This paper describes a natural-gradient field tracer test to characterise solute-transport properties in a sand and gravel aquifer in the Hebei Province, northern China. Some laboratory-scale column tests on aquifer material and a local-scale field borehole-dilution test have been conducted previously, but the field test reported herein represents the only large-scale tracer test in the aquifer, which is the sole water supply to the city of Shi Jiazhuang and which is threatened by urban pollution. The aim of the study was to quantify the transport behaviour of nonreactive pollutants in this aquifer. Little quantitative data are available concerning its solute-transport properties; thus, the results of the tracer test are significant and critical for understanding pollutant transport and fate. The in-situ tracer test was carried out in the aquifer using a slug injection of the geochemically conservative, radioactive iodine tracer 131I. The longitudinal (α L ) and transverse (α T ) hydrodynamic dispersivities for solute transport in the field are 1.72 and 0.0013 m, respectively. The ratio of longitudinal dispersivity α L and the flow length at the field scale is 1:10. The ratio between α L and α T from the in-situ test (~1,300:1) demonstrates a dominant longitudinal dispersion in this fluvial sand and gravel aquifer. The tracer test further indicates a relatively short transit time for the aquifer (linear velocities ~13 m/d) under natural-gradient conditions. Electronic Publication  相似文献   

8.
Isobaric volume measurements for MgO were carried out at 2.6, 5.4, and 8.2 GPa in the temperature range 300–1073 K using a DIA-type, large-volume apparatus in conjunction with synchrotron X-ray powder diffraction. Linear fit of the thermal expansion data over the experimental pressure range yields the pressure derivative, (∂α/∂P) T , of −1.04(8) × 10−6 GPa−1 K−1 and the mean zero-pressure thermal expansion α0, T  = 4.09(6) × 10−5 K−1. The α0, T value is in good agreement with results of Suzuki (1975) and Utsumi et al. (1998) over the same temperature range, whereas (∂α/∂P) T is determined for the first time on MgO by direct measurements. The cross-derivative (∂α2/∂P∂T) cannot be resolved because of large uncertainties associated with the temperature derivative of α at all pressures. The temperature derivative of the bulk modulus, (∂K T/∂T) P , of −0.025(3) GPa K−1, obtained from the measured (∂α/∂P) T value, is in accord with previous findings. Received: 2 April 1999 / Revised, accepted: 22 June 1999  相似文献   

9.
This paper presents an approach to solve the kriging problem, defined in terms of projections, by using Gram-Schmidt orthogonalization. The Gram-Schmidt orthogonalization allows us to find an optimal approximationY* in then-dimensional subspaceH n of any vectorY element of a Hilbert spaceH. This approach requiresO(n 3) multiplication operations to obtain an orthogonal basis, andO(n 2) multiplications needed to calculate kriging solution for a given point.  相似文献   

10.
The unit cell parameters, extracted from Rietveld analysis of neutron powder diffraction data collected between 4.2 K and 320 K, have been used to calculate the temperature evolution of the thermal expansion tensor for gypsum for 50 ≤ T ≤ 320 K. At 300 K the magnitudes of the principal axes are α 11  = 1.2(6) × 10−6 K−1, α 22  = 36.82(1) × 10−6 K−1 and α 33  = 25.1(5) × 10−6 K−1. The maximum axis, α 22 , is parallel to b, and using Institution of Radio Engineers (IRE) convention for the tensor orthonormal basis, the axes α 11 and α 33 have directions equal to (−0.979, 0, 0.201) and (0.201, 0, 0.979) respectively. The orientation and temperature dependent behaviour of the thermal expansion tensor is related to the crystal structure in the I2/a setting. Received 12 February 1998 / Revised, accepted 19 October 1998  相似文献   

11.
Laboratory tracer experiments were conducted to investigate longitudinal dispersivity (α x ) as well as the transversal (α y ) and vertical (α z ) dispersivities in homogeneous 3–5 mm sandy aquifer. The experiments were carried out in a channel 12-m long, 1.35-m wide and 0.60-m high which was built in the Hydraulics Laboratory of Civil Engineering Department in Dokuz Eylul University. NaCl was used as a tracer and conductivity values were measured at 220 measurement points. Mass Transport 3 Dimensional (Zheng and Wang in SERDP-99-1, US Army Engineer Research and Development Center, Vicksburg, MS, 1999; MT3DMS code) which is a three-dimensional solute transport simulation model incorporating finite differences solution option was used to solve the three-dimensional advective–dispersive transport equation. The estimated dispersivity values were modified until an acceptable compatibility between the observed and calculated concentrations at measurement points was reached. The best match was obtained for α x  = 12 cm, α y /α x  = 0.2 and α z /α x  = 0.05. These values are compatible with those encountered in the literature.  相似文献   

12.
The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T 0|−n , where T is temperature and T 0 is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K 1 = (C 11 +C 12 +C 13)/3 and K 3 = (C 33 +2C 13)/3 decrease rapidly toward the transition, whereas, shear moduli C 44, C S1 = (C 11 +C 33 -2C 13)/4 and C S3 = (C 11 -C 12)/2 = C 66 decrease only slightly. The shear modulus C S3 = C 66 increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.  相似文献   

13.
The thermoelastic behavior of a natural clintonite-1M [with composition: Ca1.01(Mg2.29Al0.59Fe0.12)Σ3.00(Si1.20Al2.80)Σ4.00O10(OH)2] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V 0 = 457.1(2) ?3, K T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K T0(a) = 0.0023(1) GPa−1; β(b) = 1/3K T0(b) = 0.0018(1) GPa−1; β(c) = 1/K T0(c) = 0.0072(3) GPa−1]. The β-angle increases in response to the applied P, with: βP = β0 + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α0 + α1 T −1/2. The refined parameters for clintonite are as follows: α0 = 2.78(4) 10−5°C−1 and α1 = −4.4(6) 10−5°C1/2 for the unit-cell volume; α0(a) = 1.01(2) 10−5°C−1 and α1(a) = −1.8(3) 10−5°C1/2 for the a-axis; α0(b) = 1.07(1) 10−5°C−1 and α1(b) = −2.3(2) 10−5°C1/2 for the b-axis; and α0(c) = 0.64(2) 10−5°C−1 and α1(c) = −7.3(30) 10−6°C1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.  相似文献   

14.
Ab initio total energy calculations based on a new optimized oxygen psuedopotential have been used to study the structures and relative energies of α-quartz, a partly (OH)4 substituted version of the α-quartz structure, and interstitial water molecules in α-quartz. Hydrogen bonds formed from two hydroxyl groups of the (OH)4 defects in the substituted α-quartz structure promote a stable structure for the defect α-quartz at low temperature. Comparable ab initio calculation of the energy of the interstitial water molecule in the quartz structure indicates that, energetically, the (OH)4 defect is likely to be strongly favoured as a mode for the incorporation of water. Ab initio stress calculations confirm that the (OH)4 defect in quartz has a large associated stress field which is likely to lead to segregation of these defects on supersaturation in wet quartz. The calculations indicate that segregation should occur in the plane (10 0) of the α-quartz structure.  相似文献   

15.
This short note establishes the equivalence between trend surface analysis with polynomials of orderk and IRF-k (intrinsic random function of orderk) kriging with a nugget effect covariance model.  相似文献   

16.
The compressibility at room temperature and the thermal expansion at room pressure of two disordered crystals (space group C2/c) obtained by annealing a natural omphacite sample (space group P2/n) of composition close to Jd56Di44 and Jd55Di45, respectively, have been studied by single-crystal X-ray diffraction. Using a Birch–Murnaghan equation of state truncated at the third order [BM3-EoS], we have obtained the following coefficients: V 0 = 421.04(7) Å3, K T0 = 119(2) GPa, K′ = 5.7(6). A parameterized form of the BM3 EoS was used to determine the axial moduli of a, b and c. The anisotropy scheme is β c  ≤ β a  ≤ β b , with an anisotropy ratio 1.05:1.00:1.07. A fitting of the lattice variation as a function of temperature, allowing for linear dependency of the thermal expansion coefficient on the temperature, yielded αV(1bar,303K) = 2.64(2) × 10−5 K−1 and an axial thermal expansion anisotropy of α b  ≫ α a  > α c . Comparison of our results with available data on compressibility and thermal expansion shows that while a reasonable ideal behaviour can be proposed for the compressibility of clinopyroxenes in the jadeite–diopside binary join [K T0 as a function of Jd molar %: K T0 = 106(1) GPa + 0.28(2) × Jd(mol%)], the available data have not sufficient quality to extract the behaviour of thermal expansion for the same binary join in terms of composition.  相似文献   

17.
Covariance and variogram functions have been extensively studied in Euclidean space. In this article, we investigate the validity of commonly used covariance and variogram functions on the sphere. In particular, we show that the spherical and exponential models, as well as power variograms with 0<α≤1, are valid on the sphere. However, two Radon transforms of the exponential model, Cauchy model, the hole-effect model and power variograms with 1<α≤2 are not valid on the sphere. A table that summarizes the validity of commonly used covariance and variogram functions on the sphere is provided.  相似文献   

18.
Conditional Simulation of Random Fields by Successive Residuals   总被引：2，自引：0，他引：2  
This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.  相似文献   

19.
Based on gas chromatography and gas chromatography-mass spectrometry analyses, an amazing amount of hopanoids was detected in the peat deposits in the Dajiuhu National Wetland Park in central China. The hopanoids identified included hopanes (C27-C31 αβ, C27-C32 ββ, C29 βα), hopenes (hop-22(29)-ene, 22,29,30-trinorhop-17(21)-ene, hop-17(21)-ene, hop-13(18)-ene, etc.), hopanoic acids (C31-C34 ββ, C32-C33 βα, C32 αβ), hopanols (C32 ββ and αβ) and hopanone (22,29,30-trinorhop-21-one). C31 αβ-22R hopane was found to be the dominant hopanoid, more abundant than individual nalkanes derived from higher plants. These hopanoids, exclusive of some hopenes, are proposed to be primarily from bacteria. The dominant C31 αβ-22R hopane in young sediments, without any thermal maturation, might be formed through microbial epimerization under acidic conditions in the peatland as suggested before, or directly from aerobic bacteria. This finding highlights the importance of microbes in the formation of peatland as well as in the reconstruction of paleoenvironments.  相似文献   

20.
 Synchrotron excited X-ray photoelectron spectra (SXPS) of hexagonal pyrrhotite reveal three distinct Fe 3d-derived photopeaks within its outer valence band. The t 2gα band (majority spin) is centered at about 2.5 eV, the e g α band at about 1.0 eV and the t 2gβ (minority spin) contribution at about 0.25 eV. From these data the ligand field splitting energy is 1.5 (±0.2) eV and the majority spin pairing energy is 2.25 (±0.2) eV. These are the first such XPS measurements for this mineral. S 3p-derived bonding and non-bonding bands are identified, with the former centred at about 6.5 eV and the latter near 4.5 eV. The XPS results are remarkably consistent with SCF-Xα scattered wave molecular orbital calculations. Although the calculations and the collected spectra are consistent, they differ from a recent interpretation of the pyrrhotite valence band. An explanation for the discrepant results is provided. Auger resonant enhancement of Fe 3d photopeaks at 60 eV photon energy results in the t 2gα emission (at 2.5 eV) being strongly enhanced and broader than the t 2gβ emission (0.25 eV). The explanation of these observations requires the presence of weak Fe–Fe π and π* crystal (molecular) orbitals located near 2.5 eV, and separated by no more than about 0.5 eV. The π-bonded crystal orbitals are derived from weak mixing of adjacent Fe t 2g atomic orbitals along the c crystallographic axis. Received: 15 June 2000 / Accepted: 11 June 2001  相似文献   

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