Simplicial Indicator Kriging for Boundary Assessment
In 1993, Pawlowsky et al. suggested the use of indicator kriging (IK) for delimiting the extent of a geological body. The approach was based on the conversion of available data into a binomial variable, whether a sample falls within/outside the body, and ordinary kriging to interpolate it. Obtained results were interpreted as the probability to be in the body for a given location. But, as kriging does not place any constraint to produce interpolations inside the (0,1) interval, some impossible probability estimates were obtained. As an alternative, one can treat the problem from the point of view of compositional data analysis, understanding that the purpose is to estimate not the binomial variable itself, but the probabilities of a sample falling within and outside the body. By combining a preliminary estimation of the binomial probability parameter at sampled locations, with kriging in a logistic scale, one always obtains valid probabilities, without need of any further correction. Moreover, they have some interesting geometric-statistic optimality properties: e.g., they are BLUE in the Aitchison geometry of the simplex. The approach is illustrated with the same example corresponding to the delimitation of the oil field Lyons West, located in Kansas, USA.
J. J. Egozcue R. Tolosana-Delgado V. Pawlowsky-Glahn
Technical University of Catalonia, Department of Applied Mathematics Ⅲ, Campus Nord, edificio C2, E- Department of Sedimentology and Environmental Geology, Georg-August-Universit(a)t G(o)ttingen, D-370 University of Girona, Department of Computer Science and Applied Mathematics, Campus Montilivi, edif
国际会议
The 12th Conference of the International Association for Mathematical Geology(第12届国际数学地质大会)
北京
英文
36-38
2007-08-26（万方平台首次上网日期，不代表论文的发表时间）