Trends spatial variations

The micropore volume varied from -0.15 to -0.35 cmVg. No clear trend was observed with respect to the spatial variation. Data for the BET surface area are shown in Fig. 14. The surface area varied from -300 to -900 mVg, again with no clear dependence upon spatial location withm the monolith. The surface area and pore volume varied by a factor -3 withm the monolith, which had a volume of -1900 cm. In contrast, the steam activated monolith exhibited similar imcropore structure variability, but in a sample with less than one fiftieth of the volume. Pore size, pore volume and surface area data are given in Table 2 for four large monoliths activated via Oj chemisorption. The data in Table 2 are mean values from samples cored from each end of the monolith. A comparison of the data m Table 1 and 2 indicates that at bum-offs -10% comparable pore volumes and surface areas are developed for both steam activation and Oj chemisorption activation, although the process time is substantially longer in the latter case. 

A second finding in the study of dikes exposed at Hess Deep concerns the spatial variation in their compositions (Stewart et al., 2002). Dikes were sampled over an area encompassing 25 km of an east-west flowhne, representing —3.7 X 10 yr of crustal accretion at the EPR. Indices of fractionation (MgO), and incompatible element ratios (La/Sm, Nb/Ti) show no systematic trends along flowline. Rather, over short (<4m) and long (—25 km) distances. 

The variability of biocides in indoor air and house dust is high. This variability is caused, on the one hand, by the conditions under which the sample were taken but, on the other hand, there are spatial variations within homes and the concentrations of biocides in an indoor environment are influenced by cultural and climatic factors. Furthermore concentrations may vary with season and temperature and there are trends downwards or upwards with respect to discontinued use or an increase in appUcation. 

The conceptual idea of geostatistics is that spatial variation of any variable Z can be expressed as the sum of three major components (Equation 15.1) (i) a structural component, having a constant mean or trend that is spatially dependent, (ii) a random, but spatially correlated component, and (iii) spatially uncorrelated random noise or residual term (Webster and Oliver, 2001) ... 

In common, geological variables are not stationary, which means that the mean value and variance vary in space (Gorelick, 1996). By determining the trend within the data it is possible to take into account this spatial variation of the mean and variance. A trend analysis divides conditional (measured) data in two components the regional trend and the deviation from the trend. An example of a method for trend analysis is polynominal regression. The theory of trend analysis is described by Davis (1986). 

A summary statistic for these spatial concentrations with respect to time or space. For example, how often this limit may be exceeded (say, 5% of the time) or to establish there is no spatial trend. This might be a trivial step in cases of no temporal variation or true spatial heterogeneity. 

All trace elements. All results obtained for trace elements are represented in Figure 4.5.9. Ideally the statistical analysis should take into account the effects of spatial location and time of sampling in order to analyze the total observed variation. However, spatial and temporal effects are not independent since it was not possible to collect all of the samples at the various locations simultaneously. It is clear that no significant variation was observed between sampling sites for some elements (e.g. Al, Cr, Cu) whereas trends can be observed for others (e.g. Fe, Mn, B). Concentrations of most trace elements were very low and this precluded any interpretation of results or any assessment of trends, and the statistical analysis focused on the same three trace elements (B, Sc and Zn) as those studied in the analysis of sampling uncertainty (see Uncertainty from sampling, above, pp. 311-316). 

The spatial distribution of these mineral constituents was assessed by contouring and by trend surface analysis. One problem that must be addressed in a study such as this, is whether the density of data points is sufficient to justify the description of trends across the basin, or is local variability in the constituents too great. Application of trend surface analysis permitted a statistical assessment of basinal trends, and indicated the extent of local variation. In this paper, contour maps are presented to show important basinal trends trend surface analysis indicated that these trends were statistically significant. Details of the trend surface technique and complete data are described in Rimmer (12). 

To test the significance of the calculated initial mechanical apertures, a constant initial aperture of 77 pm was used and the simulations repeated. The results produced different results to those for the calculated hydraulic apertures but the trend was similar (Table 3). Thus, the initial mechanical apertures emerge to have an impact on the resulting hydraulic apertures but, for the results presented, the significance appears to be less than the impact of the variation of the mechanical properties. From these results the importance of the mechanical properties and their spatial distribution in the rock mass to the estimation of hydraulic aperture appears to be strong. 

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