Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Conditional simulation of diamond deposits Caers, J. (1), Gelders, J. (1), Rombouts, L. (2) & Vervoort, A. (1) 1. K.U.Leuven, Dep. Civil Engineering, Mining Research Unit. 2. Terraconsult B.V.B.A. A new methodology is presented for the conditional simulation of a spatial point process which is observed in nonadjacent cells, representing samples taken from a precious stone deposit (diamonds are the main source for application). It involves the statistical modelling of counting distributions, the construction of non-conditional simulation and the conditioning by a variant of the simulated annealing approach. The two dimensional spatial distribution of precious stones, like diamonds in alluvial and coastal deposits, shows a high degree of clustering. Usually, stones tend to gather in relatively small clusters or traps, made by potholes, gullies or small depressions in the rough bedrock. Therefore, when taking samples of such deposits, discrete distributions of the number of stones counted in each sample yield an extreme skewness. Most samples have no stones, whereas samples containing a few hundred stones are not uncommon. A method for fitting a new and general family of counting distributions based on the Neyman-Scott cluster model and the mixed Poisson process is presented, which can be used to model a varying degree of clustering. General recursion equations for the discrete probabilities of these distributions are derived. Application of this model to simulated data shows that information like cluster size, number of point events per cluster and number of clusters per measurement unit can easily be extracted from this model. Fitting the model to data of two real diamond deposits of a totally different nature - small rich clusters of Namibia versus larger but less rich clusters of Guinea - demonstrates its flexibility. Non-conditional simulations are setup by means of random tesselation of the reference space. The characteristics of these tesselations are inferred from variograms of the deposit. The mixing properties of the Poisson density of these point processes is then visualised by assigning a Poisson intensity to each polygon. By using the cluster characteristics derived from the above statistical model a non-conditional simulation representing the major geological characteristics of a diamond deposit is performed. Once the model has been set up, conditional simulation by means of simulated annealing can be completed. Simulated annealing is an optimization technique used in various sciences, but is mainly used in electronical applications. Its purpose is to minimize an object function subject to specific constraints or properties. The above developed non-conditional simulation is regarded as a model or training image for this optimization problem. From the non-conditional simulation, the spatial model is extracted in the form of block distributions, blockvariogram or any other multivariate statistical properties. Thereafter, an objectfunction is constructed using these statistics and making the conditional simulation sample from random sets constrained on both conditioning data and spatial model. By this, any kind of estimation, local and global with proper confidence limits can be extracted. Other methods based on Markov Random Field properties of the simulated annealing approach are investigated. Publications Gelders, J. (1995), "Geostatistische beschrijving van industriële en siersteen diamantafzettingen; discrete en continue benadering". M.Sc. thesis K.U.Leuven. Promotor: Prof. A. Vervoort. Caers, J. (1996), "A General Family of Counting Distributions Suitable for Modelling Cluster Phenomena", Math. Geology, Vol. 28, No. 5, p. 27 Caers, J., Gelders, J., Rombouts, L. & Vervoort, A. (1996), "Non-Conditional Simulation of an Infinitely Divisible Marked Point Process applied to Diamond Deposits", Paper presented at the Fifth International Geostatistics Congress, Sept. 22-27, Wollongong, Australia. J. Caers (1996), "Statistical and geostatistical valuation of diamond deposits", Ph.D. thesis, K.U.Leuven, Faculty of Engineering, Leuven. Promotor A. Vervoort