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High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines.
Mathematical Geosciences ( IF 2.6 ) Pub Date : 2018-05-17 , DOI: 10.1007/s11004-018-9741-2
Ilnur Minniakhmetov 1 , Roussos Dimitrakopoulos 1 , Marcelo Godoy 2
Affiliation  

High-order sequential simulation techniques for complex non-Gaussian spatially distributed variables have been developed over the last few years. The high-order simulation approach does not require any transformation of initial data and makes no assumptions about any probability distribution function, while it introduces complex spatial relations to the simulated realizations via high-order spatial statistics. This paper presents a new extension where a conditional probability density function (cpdf) is approximated using Legendre-like orthogonal splines. The coefficients of spline approximation are estimated using high-order spatial statistics inferred from the available sample data, additionally complemented by a training image. The advantages of using orthogonal splines with respect to the previously used Legendre polynomials include their ability to better approximate a multidimensional probability density function, reproduce the high-order spatial statistics, and provide a generalization of high-order simulations using Legendre polynomials. The performance of the new method is first tested with a completely known image and compared to both the high-order simulation approach using Legendre polynomials and the conventional sequential Gaussian simulation method. Then, an application in a gold deposit demonstrates the advantages of the proposed method in terms of the reproduction of histograms, variograms, and high-order spatial statistics, including connectivity measures. The C++ course code of the high-order simulation implementation presented herein, along with an example demonstrating its utilization, are provided online as supplementary material.

中文翻译:

使用类勒让德正交样条的高阶空间模拟。

在过去的几年里,复杂的非高斯空间分布变量的高阶顺序模拟技术得到了发展。高阶模拟方法不需要对初始数据进行任何变换,也不对任何概率分布函数做出任何假设,同时它通过高阶空间统计将复杂的空间关系引入到模拟实现中。本文提出了一种新的扩展,其中使用勒让德式正交样条来近似条件概率密度函数 (cpdf)。样条近似的系数是使用从可用样本数据推断的高阶空间统计来估计的,并另外补充了训练图像。相对于之前使用的勒让德多项式,使用正交样条的优点包括能够更好地逼近多维概率密度函数、再现高阶空间统计数据以及使用勒让德多项式提供高阶模拟的概括。首先使用完全已知的图像测试新方法的性能,并与使用勒让德多项式的高阶模拟方法和传统的顺序高斯模拟方法进行比较。然后,在金矿中的应用证明了所提出的方法在直方图、变异函数和高阶空间统计(包括连通性测量)的再现方面的优势。本文提供的高阶仿真实现的 C++ 课程代码以及演示其使用的示例作为补充材料在线提供。
更新日期:2018-05-17
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