The problem of the spatial variation of a spectral band ratio: a first order approach based on probability theory

Numerous efforts have been made to study how the spatial distribution of ground surface objects controls the image semivariogram. The present paper is centered on how the histograms and semivariograms of the individual bands x and y influence the spatial variation of a simple spectral ratio u = arctan(x/y). The image histogram of each separate band is described by a proper distribution. The exponential model is used to describe the semivariograms of x and y. Taking the first derivatives of the spectral ratio u for x and y and taking into account the mathematical behavior of the histograms of bands x and y, an approximate expression for the semivariogram γ _u of the spectral ratio is derived. This mathematical expression shows how the spatial variation of the spectral ratio depends on the standard deviations of the histograms, as well as the ranges of the semivariograms of x and y. Experimentation with multispectral images is then carried out and it shows that theoretical predictions agree, in qualitative terms, with real data. The results and conclusions of this paper may be useful in assessing the efficiency of various spectral band ratios and vegetation indices, which are often used in geological and environmental research (mapping of hydrothermal zones and land cover types).     

Two-dimensional analysis of shape-fabric using projections of digitized lines in a plane

A method of two-dimensional shape-fabric analysis is presented which is based on the projection of lines or ellipses on the x-axis. If a set of lines or ellipses displays a preferred orientation, the average length of projection of the lines or ellipses on the x-axis changes with direction in the x-y plane. The proposed method involves use of Fortran programs which evaluate the average length of projection of lines (e.g., outlines of ooides, pressure solution seams) while the fabric is rotated by small increments in a counterclockwise sense about the origin of the x - y plane. Data acquisition is by digitizing the lines on an enlarged photograph. The sets of x-y coordinates that are thus obtained serve as input for the programs. The basic equations of the method are explained and application to a sedimentary fabric is demonstrated.The proposed method is both fast and sensitive. It is especially useful if the particle outlines are closely spherical or if the fabric is only weakly developed. Yet, the method is not restricted to weak fabrics only. Also, if the fabric is due to deformation this method yields the axes of the two-dimensional strain ellipse.     

Fault displacement modelling using 3D vector fields

In history matching and sensitivity analysis, flexibility in the structural modelling is of great importance. The ability to easily generate multiple realizations of the model will have impact both on the updating workflow in history matching and uncertainty studies based on Monte Carlo simulations. The main contribution to fault modelling by the work presented in this paper is a new algorithm for calculating a 3D displacement field applicable to a wide range of faults due to a flexible representation. This gives the possibility to apply this field to change the displacement and thereby moving horizons and fault lines. The fault is modelled by a parametric format where the fault has a reference plane defined by a centre point, dip and strike angles. The fault itself is represented as a surface defined by a function z = f(x,y), where x, y and z are coordinates local to the reference plane, with the z-axis being normal to the plane. The displacement associated with the fault outside the fault surface is described by a 3D vector field. The displacement on the fault surface can be found by identifying the intersection lines between horizons and the fault surface (fault lines), and using kriging techniques to fill in values at all points on the surface. Away from the fault surface the displacement field is defined by a monotonic decreasing function which ensures zero displacement at a specified distance from the fault. An algorithm is developed where the displacement can be increased or decreased according to user-defined parameters. This means that the whole displacement field is changed and points on horizons around the fault can be moved accordingly by applying the modified displacement field on them. The interaction between several faults influencing the same points is taken care of by truncation rules and the ordering of the faults. The method is demonstrated on a realistic synthetic case based on a real reservoir.     

Rapid determination of lineament and joint densities

Lineament, joint and drainage density values are obtainable from the number of intersections between the mapped lines and a superimposed test grid or array, using the stereological equation where x is the density (length per area) and n′ is the number of intersections per unit length of the test array. Circular test grid must be used in order to eliminate the effect of preferred orientation on the n′-values.     

A thermodynamic model of Fe–Cr spinels

A new thermodynamic model for multi-component spinel solid solutions has been developed which takes into account thermodynamic consequences of cation mixing in spinel sublattices. It has been applied to the evaluation of thermodynamic functions of cation mixing and thermodynamic properties of Fe₃O₄–FeCr₂O₄ spinels using intracrystalline cation distribution in magnetite, lattice parameters and activity-composition relations of magnetite–chromite solid solutions. According to the model, cation distribution in binary spinels, (Fe_1-x²⁺ Fe_x³⁺)[Fe_x²⁺Fe_2-2y-x³⁺Cr_2y]O₄, and their thermodynamic properties depend strongly on Fe²⁺–Cr³⁺ cation mixing. Mixing of Fe²⁺–Fe³⁺ and Fe³⁺–Cr³⁺ can be accepted as ideal. If Fe²⁺, Fe³⁺ and Cr are denoted as 1, 3 and 4 respectively, the equation of cation distribution is –RT ln(x²/((1–x)(2–2y–x)))= G₁₃^* + (1–2x)W₁₃+y(W₁₄–W₁₃–W₃₄) where G₁₃^* is the difference between the Gibbs energy of inverse and normal magnetite, W_ij is a Margules parameter of cation mixing and G₁₃^*, J/mol =–23,000+13.4 T, W₁₄=36 kJ/mol, W₁₃=W₃₄=0. The positive nonconfigurational Gibbs energy of mixing is the main reason for changing activity–composition relations with temperature. According to the model, the solvus in Fe₃O₄–FeCr₂O₄ spinel has a critical temperature close to 500°C, which is consistent with mineralogical data.     

Smoothing and interpolation by kriging and with splines

Let scalar measurements at distinct points x₁, , x_n be y₁, , y_n.We may look for a smooth function f(x)that goes through or near the points (x_i, y_i).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem.     

On the Ergodicity Hypothesis in Heterogeneous Formations

Application of the ergodicity hypothesis to the stochastic subsurface hydrology has been checked by investigating the hydraulic conductivity field. The relative variance of the spatial average of conductivity, which is denoted as R, and the error index E.I. = , were employed to justify the uncertainties and errors of using the ergodicity hypothesis. Six factors influence R: autocorrelation function; variance of logconductivity; spatial correlation scales of logconductivity; domain sizes; anisotropy; and dimensionality of the problem. Closed-form analytical solutions of R for the linear autocorrelation function were derived and the numerical integration of R for the exponential autocorrelation function for one-, two-, and three-dimensional problems calculated. It is easy to fulfill the ergodicity hypothesis under these conditions: weak heterogeneity and large ratio of domain size vs. correlation length (L/I). The uncertainties and errors of using this hypothesis increase rapidly when the variances of logconductivity increase and/or the ratios of L/I decrease. The ergodicity hypothesis has less error when applied to a problem with higher dimensionality.     

Multiscale remote-sensing retrieval in the evapotranspiration of Haloxylon ammodendron in the Gurbantunggut desert, China

Transpiration, an essential component of surface evapotranspiration, is particularly important in the research of surface evapotranspiration in arid areas. The paper explores the spectral information of the arid vegetal evapotranspiration from a semi-empirical perspective by the measured data and the up-scaling method. The paper inverted the transpiration of Haloxylon ammodendron at the canopy, pixel and regional scales in the southern edge of the Gurbantunggut desert in Xinjiang, China. The results are as follows: at the canopy scale, the optimal exponential model of the sap flow rate based on the hyperspectrum is y = 0.0015e^3.8922x , R ² = 0.806. At the pixel scale, there was a good linear relationship between the sap flow and the SR index, with a relationship of y = ?1197.38x ³ + 1048.43x ² ? 305.47x + 455.15, R ² = 0.845. At the regional scale, based on the optimal exponential model and the EO-1 Hyperion remote-sensing data, the transpiration of the study area was inverted. Comparing the results of the SEBAL and SEBS models, the errors of the simulation results were 7.78 and 8.80 %. The paper made full use of the knowledge flow at different scales, bridging the scale difference in canopy and remote-sensing images to avoid the information bottleneck in the up-scaling. However, there are many constraints in the data acquirement, the efficiency of the models, the endmembers determination, the temporal–spatial up-scaling, and the accuracy assessment, which would be improved in future studies.     

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.     

遥感与GIS技术支持下的湖北省生态环境综合分析

在遥感与地理信息系统技术支持下，应用主成分分析法对湖北省全省生态环境质量状况进行了综合评价，得出了湖北省全省生态环境质量状况分级图。在定义生态环境背景指数和土地资源利用程度指数的基础上，通过生成生态环境背景图和土地利用程度图，分析了生态环境背景与土地利用程度的关系，通过相关分析证明土地资源利用程度与生态环境背景有着明显的相关关系，生态环境的好坏决定了土地资源利用程度的高低。同时，对湖北省生态环境演变机制及其驱动因子进行了一些探讨。     

An adaptive grid technique for minimizing heterogeneity of cells or elements

Geostatistical techniques allow simulation of properties such as porosity or conductivity on a fine scale. Typically, porous media flow modeling is performed at a coarser scale. Upscaling properties from the fine scale to the coarser scale introduces potential errors which are constrained by the degree of homogeneity of the cell or element. Adaptive grid techniques can be used to minimize the heterogeneity in the individual cells or elements, thus minimizing potential upscaling errors. A geostatistical adaptive grid (GAG) algorithm based on local minimization of heterogeneity is introduced. Local minimization allows greater control over the type of distortion permitted. Comparisons are made with a general elastic grid adjustment (GEGA) algorithm based on global minimization of heterogeneity. Several sample problems are used to test and demonstrate the two approaches.     

A distributed water-heat coupled model for mountainous watershed of an inland river basin in Northwest China (III) using the outputs from Mesoscale model version 5

The distributed water-heat coupled (DWHC) model is calibrated, with the help of the Mesoscale model version 5 (MM5), by calculating the daily precipitation, the daily average air temperature at the 2.0 m heights and the daily potential evaporation in Heihe mountainous watershed area and its vicinity (96.786°∼102.284°E, 37.328°∼40.601°N, 17 × 10⁴ km²), from February 11 to June 30, 2003. The MM5 model periodically ran every 10 days in 3 km × 3 km grid resolution with an integral time step of 3 s. In the MM5 model, many scheme or options are consulted or adopted, such as the Grell scheme cumulus parameterization method, the Dudhia option, the cloud-radiation scheme, MRF PBL option and the modified Oregon State University Land-surface model (OSULSM). According to the projection transform methods, the MM5 outputs are interpolated to the 1 km × 1 km grid in Alberts projection by using triangle-based cubic interpolation (Cubic) and nearest neighbor interpolation (Nearest) methods, with which the DWHC model shares the same method. The result shows that, when the Nearest method is used, the Nash-Sutcliffe equation value of the daily average runoff is 0.79, the balance error is −0.79% and the goodness of fit R ² value is 0.81. Meanwhile, when the Cubic method is used, the Nash-Sutcliffe equation value, the balance error and the R ² value are 0.79, −0.65% and 0.80, respectively. Though the runoff simulation result is not favorable, it is still better than that using measured data at the meteorological and hydrological stations; the latter has a Nash-Sutcliffe equation value of 0.61. The MM5-DWHC model results also show that runoff mainly occurs on land surfaces and from shallow soil layers. According to model calibration results, certain outputs of MM5 are singular to some extent and the DWHC model is very sensitive to the initial values.     

Magnetic phase diagrams of Mg-, Fe-, (Cu + Ti)- and Cu-substituted braunite Mn<Superscript>2+</Superscript>Mn<Subscript>6</Subscript><Superscript>3+</Superscript>SiO<Subscript>12</Subscript>

 The magnetic behavior of the Jahn-Teller structure braunite, (Mn²⁺ _1−yM _y )(Mn³⁺ _{6− x} M_x)SiO₁₂, is strongly influenced by the incorporation of elements substituting manganese. Magnetic properties of well-defined synthetic samples were investigated in dependence on the composition. The final results are presented in magnetic phase diagrams. To derive the necessary data, ac susceptibility and magnetization of braunites with the substitutional elements M = Mg, Fe, (Cu+Ti) and Cu were measured. Whereas the antiferromagnetic ordering temperature, T _N , of pure braunite is hardly affected by the substitution of nonmagnetic Mg, it is rapidly suppressed by the substitution of magnetic atoms at the Mn positions. Typically for a concentration (x, y) ≥ 0.7 of the substituted elements, a spin glass phase occurs in the magnetic phase diagrams. Additionally, for the braunite system with Fe³⁺ substitutions, we observe in the concentration range 0.2 < x< 0.7 a double transition from the paramagnetic state, first to the antiferromagnetic state, followed by a transition to a spin glass state at lower temperatures. The unusual change of the magnetic properties with magnetic substitution at the Mn positions is attributed to the peculiar antiferromagnetic structure of braunite, which has been resolved recently. Received: 19 April 2001 / Accepted: 6 September 2001     

Experimental determination of three-dimensional dispersivities in homogeneous porous medium

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.     

A new approach to simulating disorder in crystals

The technique of calculating lattice dissociation energies using static, minimum lattice energy, ionic models has been extended to allow for multiple occupancy of the ionic sites. A particular lattice site can have a fraction x of an ionic species A and a fraction y of an ionic species B, where the position of each can be relaxed separately along with the unit cell dimensions until an equilibrium is reached. Various degrees of long and short range order can be modelled. This technique has been applied to the mineral sillimanite, Al₂SiO₅, to calculate the effect on the lattice energy of (Al, Si) ordering over the tetrahedral sites. It is found using this method that (Al, Si) ordering with space group Pbmn stabilizes the material by 29.25 kcal/mol (Al^iv-O-Al^iv), with respect to the completely disordered material.     

Molecular dynamics study of pressure-induced transformation of quartz-type GeO2

We simulated quartz-type GeO₂ and investigated its high-pressure transformation using the molecular dynamics (MD) simulation method with a model potential. The calculated results under hydrostatic compression indicated that a pressure-induced amorphization of quartz-type GeO₂ originated from the mechanical instability of the quartz lattice as, in previous theoretical studies of SiO₂. Furthermore, quartz-type GeO₂ directly transformed to a rutile-like structure with only subtle displacements of ions under σ _{x y} imposed shear stressed decompression. This is the first reproduction of the quartz-to-rutile transformation. A possible pathway of this transition is proposed in this study. Received: 14 April 1999 / Revised, accepted: 11 August 1999     

Least-squares center-to-center and mean object ellipse fabric analysis

The subjectivity of ellipse fitting in many strain techniques has hindered the determination of fabric anisotropy and tectonic strain. However, many sets of x, y co-ordinates can be approximated as an ellipse using a least-squares algorithm to calculate a best-fit ellipse and associated average radial error. For instance, the two dimensional shape of many objects can be approximated as an ellipse by entering digitized co-ordinates of the object margin into the ellipse algorithm.The rim of maximum point density in a normalized Fry diagram is defined by normalized center-to-center distances between touching or nearly touching objects. The enhanced normalized Fry (ENFry) method automates ellipse fitting by entering center-to-center distances between these “touching” objects into the least-squares ellipse algorithm. For homogeneously deformed populations of 200 objects, the ENFry method gives an accurate and precise measure of whole-rock fabric anisotropy, particularly for low ellipticities. When matrix strain exceeds clast strain, manual ellipse fitting of normalized Fry plots gives more accurate matrix anisotropies.The mean object ellipse (MOE) method calculates the best-fit ellipse from the geometry of the objects. Three points from the margin of each object ellipse, centered at the origin and expanded or reduced to unit volume, are used to calculate the best-fit fabric ellipse. The MOE method is very precise for small data sets, making it a good method for mapping heterogenous object strain. However, least-squares calculations maximize the influence of distal and spurious ellipticities, causing the MOE method to overestimate the fabric ellipticity of most aggregates.     

试论区域重力测量远区地改的精度

在区域重力资料整理中,拟从1:5万地形图上读取1×1公里的高程网,建立全国地形图网结点高程数据库,用于计算区域重力远区地形改正值。但在山区能达到多大精度？这里为大家提供一份典型山区地形改正的试验资料,并据此谈些粗浅的看法,供同志们参考。     

Influence of sample and terrain unit on landslide susceptibility assessment at La Pobla de Lillet,Eastern Pyrenees,Spain

The reliability of susceptibility maps depends largely on the quality of the information used for its evaluation. This study seeks to analyze the influence of sample size and type on the results of discriminant analysis applied to shallow landslide susceptibility assessment. The study also assesses the role of the terrain unit in discriminant analysis. To this end, two databases based on fieldwork (slope unit) and GIS with 15- and 45-m grid cells (grid cell-based unit), were compared in the same zone at La Pobla de Lillet, Spanish Eastern Pyrenees. The results show that although there is no significant influence of the type of sample, it is necessary to use at least half of the individuals of the sample in order to obtain good results from discriminant analysis. It is the terrain unit that exerts the biggest influence on the result of susceptibility. Some morphometric parameters related to landslides were compared in the databases. The slope unit of the fieldwork database better reflects the land characteristics than the regular grid used by GIS. The values of the variables obtained by GIS procedures are smooth, obtaining mean errors for the slope angle variable of 19.5 and 33.5% for the grids of 15 and 45 m, respectively, in the study area. One-way and T tests demonstrate that the smoothness of the values exerts a decisive influence on the discriminant results. Kappa’s analysis shows that there is no significant equivalence between some of the categorical variables used in both databases. The use of these variables demand the application of clearly defined criteria. The cell size should match the dimensions of the phenomenon analyzed given the unsuitability of the grid of 45 m in this study.