Abstract: |
In general, the edge effect refers to the influences of boundaries of the simulation area (volume) on the characteristics being simulated, whether it is an image (or pattern) or the statistics of variables. The effect is widely reported in the point process literature (Cressie 1993, Stoyan et al. 1995, Diggle 2003) because of its significant influence on the point pattern generated, but not so in geostatistics as the main focus is on the second order statistics, in particular, the variogram, which are less directly connected to the effects. Although edge effects are usually ignored in geostatistical simulations, they can have a significant effect on simulations outputs, especially for situations in which the variogram range is relatively large compared to the size of the simulation area (volume). The effect is generally acknowledged (e.g., Journel and Kyriakidis , 2004, Deutsch and Journel, 1998) but has never been properly investigated. Failure to account properly for edge effects can bias simulations by generating values with shorter ranges of correlation. In the work presented in this paper, we investigate edge effects in detail for sequential Gaussian and indicator simulations and derive the critical threshold at which an edge effect becomes significant. Edge correction techniques, such as guard areas, are also investigated to mitigate the effect.
References Cressie, N.A. (1993), Statistics for spatial data, John Wiley & Sons. Deutsch, C. V. and Journel, A. G. (1998), GSLIB, geostatistical software library and user?s guide (2nd ed.), Oxford University Press. Diggle, P. (2003), Statistical analysis of spatial point patterns (second edition). London, Edward Arnold. Journel, A. G. and Kyriakidis, P. C. (2004), Evaluation of mineral reserves, a simulation approach, Oxford University Press. Stoyan, D., Kendall, W. and Mecke, J. (1995) Stochastic geometry and its applications (2nd ed.), John Wiley & Sons. |
