Observational and Critical State Physics Descriptions of Long-Range Flow Structures
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Using Fracture Seismic methods to map fluid-conducting fracture zones makes it important to understand fracture connectivity over distances greater 10–20 m in the Earth’s upper crust. The principles required for this understanding are developed here from the observations that (1) the spatial variations in crustal porosity are commonly associated with spatial variations in the magnitude of the natural logarithm of crustal permeability, and (2) many parameters, including permeability have a scale-invariant power law distribution in the crust. The first observation means that crustal permeability has a lognormal distribution that can be described as κ ≈ κ 0 exp ( α ( φ − φ 0 ) ) , where α is the ratio of the standard deviation of ln permeability from its mean to the standard deviation of porosity from its mean. The scale invariance of permeability indicates that αϕο = 3 to 4 and that the natural log of permeability has a 1/k pink noise spatial distribution. Combined, these conclusions mean that channelized flow in the upper crust is expected as the distance traversed by flow increases. Locating the most permeable channels using Seismic Fracture methods, while filling in the less permeable parts of the modeled volume with the correct pink noise spatial distribution of permeability, will produce much more realistic models of subsurface flow.Keywords:
Log-normal distribution
Tortuosity
Channelized
Based on the soil sample of the Linyi county and GS+ software,the spatial variation characteristics of the soil nutrients were studied.The geographical statistical method was carried on the analysis to spatial variation of the soil organic matters and macroelements.Result indicated that the soil organic matters and total nitrogen had small variation degree,the rapidly available potassium taking the second place,the available phosphorus showing the biggest variation,they all belonged to the medium variation;The spatial variation of the soil organic matter,total nitrogen and rapidly available potassium mainly caused by the area factor,and the spatial distribution manifests for the medium spatial relativity.The spatial variation of the available phosphorus fiercely caused by the stochastic factor,and spatial distribution manifests for the weak spatial relativity.
Variation (astronomy)
Soil nutrients
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Geostatistics combining with GIS was applied to analyze the spatial variability and spatial distribution of soil nutrients in Gaomi at county scale,including 9 soil nutrients of SOM,AN(alkaline hydrolyzing nitrogen),TN,available K,available P,Mn,Cu,Zn and B.The results showed that the variation coefficient of soil nutrients followed the order of P Zn K Cu B Mn AN TN SOM.P had the highest variation coefficient of 48.80%,while SOM had the lowest of 21.76%.The semivariograms of soil nutrients were best described by exponential model,except for that of Mn,which was best fitted by liner model.K,Cu and Zn had significant spatial self-correlation,and other nutrients had medium spatial self-correlation.The spatial self-correlation degree ordered as K Cu Zn B TN AN B SOM P Mn.The spatial correlation range of B was the highest of 28716 meters,and that of available Cu was the lowest of 1410 meters.Mn and B showed an obvious regularity in spatial distribution,with the content of Mn increased gradually from north to south,while content of B decreased gradually from north to south in the study area.SOM,TN and alkali-hydrolysable nitrogen showed a similar spatial pattern,Cu and Zn had no significant geographical trends,and the high value areas of K and P spatial distributed sporadically.This study revealed the spatial distribution of soil nutrients in Gaomi,which had a positive significance for precision agriculture and sustainable use of land resource.
Geostatistics
Soil test
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Spatial variability of soil bulk density for various layers was measured and analyzed by using traditional statistics and geo-statistics,which was performed in characteristic field in the Yellow River Delta.The results indicate that soil samples for all layers showed compaction trend to some extent,and the variation in bulk density for all layers was rather weak.Soil bulk density all exhibited moderate spatial autocorrelation resulting from compound impact of structural and stochastic factors.Fractal dimension proved that bulk density for all layers showed weak spatial dependency,and the variability of claypan in depth and distribution was the crucial reason of resulting in the spatial heterogeneity of bulk density.The spatial distribution maps interpolated by Kriging interpolation showed that spatial distribution of salinity was closely related to soil texture,and bulk density for all layers exhibited the similarity in spatial distribution in a certain range.The further correlation analysis indicate that soil bulk density for all layers was significantly correlated with each other.The spatial distribution maps of bulk density,which were obtained through the study on spatial variability,can serve as a scientific basis for the regional management,harness and amelioration of moderate-and-low-yield farmlands and obstacle soils in the Yellow River Delta.
Spatial Dependence
Geostatistics
Semivariance
Variogram
Soil texture
Spatial heterogeneity
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