Abstract:Classical multiple-point geostatistics based on stationary assumption has shortcomings in non-stationary modeling application.This paper proposes a new non-stationary simulation based on segmentation by using anisotropy.The new method uses rose diagram consisting of different directions' variogram range to quantify characterization of train image's local anisotropy.In combination with multidimensional scaling and K-means,the proposed method can automatically segment non-stationary train image into several sub-regions which are independent of each other.In the sub-region,classical MPS algorithms are used to simulate sub-regions' geological model which eventually form a whole non-stationary realization.Using fracture network modeling as an example,the proposed method simulated and reproduced non-stationary train image perfectly.The results obtained by the authors provide reference for non-stationary modeling of multiple-point geostatistics.
[1] 石书缘,尹艳树,冯文杰.多点地质统计学建模的发展趋势[J].物探与化探,2012,36(4):655-660. [2] 尹艳树,张昌民,李少华.多点地质统计学原理、方法及应用[M].北京:地质出版社,2013:2-4. [3] Honarkhah M.Stochastic simulation of patterns using distance-based pattern modeling[D].Paloma Alto:Stanford University,2011. [4] 张仁铎.空间变异理论及应用[M].北京:科学出版社,2005. [5] Journel A G.The deterministic side of geostatistics[J].Journal of the International Association for Mathematical Geology,1985,17(1):1-15. [6] Strebelle,Zhang T.Non-stationary multiple-point geostatistical models in:Leuangthong O,Deutsch C V.Quantitative Geology and Geostatistics[M].Springer Netherlands,2005:235-244. [7] Zhang T.Multiple-point simulation of multiple reservoir facies[D].Stanford:Stanford University. [8] Arpat G B.Sequential simulation with patterns[D].Stanford:Stanford University,2005. [9] Honarkhah M,Caers J.Direct pattern-based simulation of non-stationary geostatistical models[J].Mathematical Geosciences,2012,44(6):651 672. [10] 尹艳树,张昌民,李少华,等.一种基于沉积模式的多点地质统计学建模方法[J].地质论评,2014,1:216-221. [11] Arpat G B.Sequential simulation with patterns[D].Stanford:Stanford University,2005. [12] Matheron G F.The Theory of regionalized variables and its application[J].école Nationale Supérieure des Mines de Paris,1971:5. [13] 王仁铎,胡光道.线性地质统计学[M].北京:地质出版社,1988. [14] 侯景儒,尹镇南,李维明,等.实用地质统计学[M].北京.地质出版社,1998:36-45. [15] 靳松,朱筱敏,钟大康.变差函数在沉积微相自动识别中的应用[J].石油学报,2006,3:57-60. [16] 施小清,姜蓓蕾,卞锦宇,等.以地质统计方法推估上海第三承压含水层渗透系数的分布[J].工程勘察,2009,1:36-41. [17] Deutsch C V,Journel A G.GSLIB:Geostatistical software libarary and user's guide[M].New York:Oxford University Press,1992:39-53. [18] 刘焕荣.实验变异函数及其理论模型的计算与拟合研究[D].昆明:昆明理工大学,2014. [19] Ding C,He X,Zha H,et al.Adaptive dimension reduction for clustering high dimensional data[C]//IEEE International Conference on Data Mining IEEE Computer Society,2002:147. [20] Bécavin C,Tchitchek N,Mintsa-Eya C,et al.Improving the efficiency of multidimensional scaling in the analysis of high-dimensional data using singular value decomposition[J].Advance Access publication,2011,27(10):1413-1421. [21] Kruskal J B.Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis[J].Psychometrika,1964,29(1):1 27. [22] Mardia K V.Some properties of clasical multi-dimesional scaling[J].Communications in Statistics-Theory and Methods,1978,7(13):1233-1241. [23] Kanungo T,Mount D M,Netanyahu N S,et al.An efficient k-means clustering algorithm:Analysis and implementation[J].Pattern Analysis and Machine Intelligence,IEEE Transactions,2002,24(7):881-892. [24] Boucher A.Considering complex training images with search tree partitioning[J].Computers and Geosciences,2009,35(6):1151-1158.