采样(信号处理)
地质统计学
克里金
点(几何)
统计
计算机科学
变异函数
蒙特卡罗方法
数学
环境科学
重要性抽样
插值(计算机图形学)
抽样设计
计量经济学
空间变异性
滤波器(信号处理)
计算机视觉
几何学
作者
Gregoire Mariethoz,Philippe Renard,Julien Straubhaar
摘要
[1] Multiple-point geostatistics is a general statistical framework to model spatial fields displaying a wide range of complex structures. In particular, it allows controlling connectivity patterns that have a critical importance for groundwater flow and transport problems. This approach involves considering data events (spatial arrangements of values) derived from a training image (TI). All data events found in the TI are usually stored in a database, which is used to retrieve conditional probabilities for the simulation. Instead, we propose to sample directly the training image for a given data event, making the database unnecessary. Our method is statistically equivalent to previous implementations, but in addition it allows extending the application of multiple-point geostatistics to continuous variables and to multivariate problems. The method can be used for the simulation of geological heterogeneity, accounting or not for indirect observations such as geophysics. We show its applicability in the presence of complex features, nonlinear relationships between variables, and with various cases of nonstationarity. Computationally, it is fast, easy to parallelize, parsimonious in memory needs, and straightforward to implement.
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