Multifractal Simulation of GeochemicalMap Patterns

INTRODUCTIONThe mathematical modeling of geochemical data continuesto present an important challenge to earth scientists. Basically,the available data are 2-dimensional realizations of 3dimensional patterns, which are the results of one or more genetic processes that usually are poorly understood. It may bedifficult to project from the observations into the rock mass. Inthis paper, multifractal modeling is advocated as a methodologyto characterize geochemical patterns. If a geochemical pa…     

The fractal properties of geochemical landscapes as an indicator of weathering and transport processes within the Eastern Alps

Variations in surface morphology and lithology provide an opportunity to study lithologic and morphologic influences on the spatial pattern of stream-sediment geochemistry within two contrasting environments of the Eastern Alps (Hohe Tauern Range and Gurktaler Alpen Range). The fractal dimension, a measure of surface roughness over a variety of scales, is used to model the dissipation of erosive products due to climatic controlled denudation and fluvial mass transport. Based on a spatial correlation analysis, specific elemental concentrations are used as indicators for a dominant lithotype. Fractal geometry of these elements has been estimated by sequential Gaussian simulation of the area/perimeter relationship (Dal) and by the estimation of multifractal spectra. It is shown that within a 510–780 km² survey area the spatial variations of Al, Ga, Ni and Ca can be approximated by single fractals but for those of Ag and Sn multifractal models must be used. Fractal properties derived from simulated surfaces are explainable by the process controlling the spatial structure of the data. Climatic and tectonic parameters apparently influences Dal at large scales. At smaller scales rock-type variation exert an additional influence on Dal.     

Numerical simulation of ultrasonic waves in reservoir rocks with patchy saturation and fractal petrophysical properties

We simulate the propagation of ultrasonic waves in heterogeneous poroviscoelastic media saturated by immiscible fluids. Our model takes into account capillary forces and viscous and mass coupling effects between the fluid phases under variable saturation and pore fluid pressure. The numerical problem is solved in the space–frequency domain using a finite element procedure and the time–domain solution is obtained by a numerical Fourier transform. Heterogeneities due to fluid distribution and rock porosity–permeability are modeled as stochastic fractals, whose spectral densities reproduce saturation an petrophysical variations similar to those observed in reservoir rocks. The numerical experiments are performed at a central frequency of 500 kHz, and show clearly the effects of the different heterogeneities on the amplitudes of shear and compressional waves and the importance of wave mode conversions at the different interfaces.     

A chain causality model for oil and gas accumulation

The formation of oil and gas reservoirs is the result of infinitesimal amounts of hydrocarbons that accumulate in sedimentary basins through a process of chain reactions, which occur one step at a time. The reactions can be divided into a set of interrelated static factors, which can be divided into a subset of interrelated factors. The chain reactions define a genetic model that has a layered structure with the property of forward chaining. It is an attempt to portray the process of formation of oil and gas reservoirs. By using this model in petroleum exploration, potential pool-size distributions can be evaluated.     

Correlation analysis of large-scale structure using data from the SDSS DR5 LRG catalog

Correlation properties of the large-scale structure of the distribution of luminous red galaxies are evaluated using data from Data Release 5 of the Sloan Digital Sky Survey. The correlations on small scales are characterized by the distribution of distances to the nearest neighboring galaxy ω(r). The conditional number density Γ(r) indicates a power law correlation with an exponent γ = 1.0±0.1 over scales of [1, 30] Mpc/h in redshift space. For larger scales of [30, 200] Mpc/h, a transition from a power law to a flat segment is observed. However, the presence of a flat segment in the estimated conditional density is only a necessary, but not sufficient, condition for homogeneity of a given sample. In particular, the flat segment may be caused by the presence of superlarge structures (such as have been discovered in the most recent ultra-deep COSMOS survey) which lead to a systematic shift in the estimated conditional number density. The behavior of the reduced two-point correlation function) ξ(r) is also discussed for scales of [1, 200] Mpc/h. Over small scales, where ξ(r) >> 1, the slopes of the reduced correlation function and the conditional number density are the same. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 393–408 (August 2008).     

Arctic sea ice distribution in summer based on aerial photos

1Introduction TheArcticOceanisoneoftheimportantcold sourcesontheearth,whichaffectsglobalclimateand oceancirculationseriously.Itsinteractionwithglobal climatesystemisrepresentedbyseaice,whichisthe mainfeatureonthesurfaceoftheArcticOcean(Aa- gaard,etal.,1989).Firstly,seaiceplaysapivotalrole intheheatandmassbalanceonthesurfaceoftheArc- ticOcean.Seaicenotonlyobstructstheheatexchange betweenatmosphereandocean,butalsoreflectsthe mostofthelocalsolarradiationbacktotheatmo- spherebecauseofitshighalb…     

Stochastic computational modelling of highly heterogeneous poroelastic media with long‐range correlations

The compaction of highly heterogeneous poroelastic reservoirs with the geology characterized by long‐range correlations displaying fractal character is investigated within the framework of the stochastic computational modelling. The influence of reservoir heterogeneity upon the magnitude of the stresses induced in the porous matrix during fluid withdrawal and rock consolidation is analysed by performing ensemble averages over realizations of a log‐normally distributed stationary random hydraulic conductivity field. Considering the statistical distribution of this parameter characterized by a coefficient of variation governing the magnitude of heterogeneity and a correlation function which decays with a power‐law scaling behaviour we show that the combination of these two effects result in an increase in the magnitude of effective stresses of the rock during reservoir depletion. Further, within the framework of a perturbation analysis we show that the randomness in the hydraulic conductivity gives rise to non‐linear corrections in the upscaled poroelastic equations. These corrections are illustrated by a self‐consistent recursive hierarchy of solutions of the stochastic poroelastic equations parametrized by a scale parameter representing the fluctuating log‐conductivity standard deviation. A classical example of land subsidence caused by fluid extraction of a weak reservoir is numerically simulated by performing Monte Carlo simulations in conjunction with finite elements discretizations of the poroelastic equations associated with an ensemble of geologies. Numerical results illustrate the effects of the spatial variability and fractal character of the permeability distribution upon the evolution of the Mohr–Coulomb function of the rock. Copyright © 2004 John Wiley & Sons, Ltd.