Size Scaling of Cross Correlation Between Multiple Variables

Reservoir models have large uncertainty because of spatial variability and limited sample data. The ultimate aim is to use simultaneously all available data sources to reduce uncertainty and provide reliable reservoir models for resource assessment and flow simulation. Seismic impedance or some other attribute provides a key source of data for reservoir modeling. These seismic data are at a coarser scale than the hard well data and it not an exact measurement of facies proportions or porosity. A requirement for data integration is the cross-covariance between the well and seismic data.The size-scaling behavior of the cross correlation for different measurement scales was nvestigated. The size-scaling relationship is derived theoretically and validated by numerical studies (including an example with real data). The limit properties of the cross-correlation coefficient when the averaging volume becomes large is shown. After some averaging volume, the volume-dependent cross-correlation coefficient reaches a limit value. This plateau value is controlled mainly by the large-scale behavior of the cross and direct variograms.The cross correlation can increase or decrease with volume support depending on the relative importance of long- and short-scale covariance structures. If the direct and cross variograms are proportional, there is no change in the cross correlation as the averaging volume changes. Our study shows that the volume-dependent cross-correlation coefficient is sensitive to the shape of the cross variogram and differences between the direct variograms of the well data and seismic data.     

Crossover from Nonlinearity Controlled to Heterogeneity Controlled Mixing in Two-Phase Porous Media Flows

We use high resolution Monte Carlo simulations to study the dispersive mixing in two-phase, immiscible, porous media flow that results from the interaction of the nonlinearities in the flow equations with geologic heterogeneity. Our numerical experiments show that distinct dispersive regimes occur depending on the relative strength of nonlinearity and heterogeneity. In particular, for a given degree of multiscale heterogeneity, controlled by the Hurst exponent which characterizes the underlying stochastic model for the heterogeneity, linear and nonlinear flows are essentially identical in their degree of dispersion, if the heterogeneity is strong enough. As the heterogeneity weakens, the dispersion rates cross over from those of linear heterogeneous flows to those typical of nonlinear homogeneous flows.     

等比例尺放大法实现遥感图像精确定位

介绍一种卫星遥感图像定位方法——等比例尺放大法,该方法可以实现遥感图像的精确定位,满足遥感产品制作与服务的需要。此外,还具体介绍了如何利用VC语言实现等比例尺放大法图像定位。     

Runoff Scaling in Large Rivers of the World

Runoff and precipitation scaling with respect to drainage area is analyzed for large river basins of the world, those with mean annual runoff in excess of 10 k³/yr. The usefulness of the specific runoff (runoff per unit drainage area, m/yr) to categorize runoff scaling laws across the complete spectrum of climatic and hydrologic conditions is evaluated. It is found that (1) runoff scales with drainage are in those river basins with specific runoff in excess of 0.15 m/yr (r² = 0.88); (2) runoff scaling with drainage area shows remarkably high statistical correlation (r²= 0.97) in river basins with specific runoff equal to or larger than 1.0 m/yr; (3) runoff does not Inc.rease with Inc.reasing drainage area in river basins with specific runoff below 0.15 m/yr, where no discernible statistical association was found between runoff and drainage area; and (4) precipitation depth (m/yr) is inversely proportional to drainage area raised to a fractional exponent in river basins with specific runoff in excess of 0.15 m/yr.     

基于三对象多维标度法及其应用

本文提供了基于三对象（样品或变量）的多维标度法。计算方案是通过一维标度求法（数量化理论Ⅳ的扩展）和多维标度求法把原始问题降至为标准特征值—特征向量问题来解决，该方法的主要目的是提取更多信息、简化数据结构并重新标度研究对象于新的低维空间，以便能通过二维“因子轴”来直接检验，它适合于定性和定量数据。编写计算程序进行标度分析，在内蒙古赤峰某金矿进行矿产预测应用效果良好。     

A Simple Parameterisation for Flux Footprint Predictions

Flux footprint functions estimate the location and relative importance of passive scalar sources influencing flux measurements at a given receptor height. These footprint estimates strongly vary in size, depending on receptor height, atmospheric stability, and surface roughness. Reliable footprint calculations from, e.g., Lagrangian stochastic models or large-eddy simulations are computationally expensive and cannot readily be computed for long-term observational programs. To facilitate more accessible footprint estimates, a scaling procedure is introduced for flux footprint functions over a range of stratifications from convective to stable, and receptor heights ranging from near the surface to the middle of the boundary layer. It is shown that, when applying this scaling procedure, footprint estimates collapse to an ensemble of similar curves. A simple parameterisation for the scaled footprint estimates is presented. This parameterisation accounts for the influence of the roughness length on the footprint and allows for a quick but precise algebraic footprint estimation.     

A New Model for Quantifying Anisotropic Scale Invariance and for Decomposition of Mixing Patterns

A new power–law function has been derived to represent the relationship between area of the set consisting of wave numbers with spectral energy density above S (A(>S)) on the two-dimensional frequency plane and S. The power–law relation holds if the field concerned possessing isotropic scale invariance or generalized scaling invariance involves rotational and ratio-scale changing transforms. The equation is valid for dealing with common exploration geophysical and geochemical fields encountered in mineral exploration and environmental assessment. This power–law function not only provides a new model for characterizing anisotropic scaling invariance for generalized scaling field, for example, estimating the power exponent of power spectrum of generalized scale invariance measure in frequency domain, but also forms a theoretical base for the S–A filtering technique developed for decomposing a mixing field into components on the basis of distinct scaling properties in the frequency domain. It is demonstrated that the method has potential to become a general technique for image processing and pattern recognition.     

Effects of Young's modulus on fault displacement

Elastic crack models predict a linear relationship between displacement (u) and rupture (trace) length (L) during slip in a fault zone. Attempts to find universal-scaling laws for L/u, however, have generally failed. Here I propose that these attempts have failed because they do not take into account the changes in the mechanical properties, in particular Young's modulus (stiffness), of the fault zone as it evolves. I propose that Young's modulus affects fault displacement both spatially and temporally: spatially when the trace of a fault at a given time dissects host rocks of different stiffnesses, and temporally when the stiffness of the fault zone itself changes. During the evolution of an active fault zone, the effective Young's modulus of its damage zone and fault core normally decreases, and so does the L/u ratio of the fault. By contrast, during inactive periods sealing and healing of the damage zone and core may increase the stiffness, hence the L/u ratio in subsequent slips. This model predicts that not only will the scaling of L/u within a given fault population vary in space and time, but also that of individual faults. To cite this article: A. Gudmundsson, C. R. Geoscience 336 (2004).     

Émergence de la complexité dans un modèle simple de comportement mécanique des roches

We propose a mechanical model for the behaviour of rocks based on progressive damage at the elementary scale and elastic interaction. It allows us to simulate several experimental observations: mechanical behaviour ranging from brittle to ductile, fractal structure of the damage, power-law distribution of the damage avalanches. These macroscopic properties are not incorporated at the elementary scale, but are the results of the interaction between elements. This emerging complexity permits us to consider the strain rock process as a complex system characterized by non-linear dynamics. To cite this article: D. Amitrano, C. R. Geoscience 336 (2004).