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首页> 外文期刊>Computers & geosciences >HOSIM: A high-order stochastic simulation algorithm for generating three-dimensional complex geological patterns
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HOSIM: A high-order stochastic simulation algorithm for generating three-dimensional complex geological patterns

机译：HOSIM：一种用于生成三维复杂地质图案的高阶随机模拟算法

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摘要

The three-dimensional high-order simulation algorithm HOSIM is developed to simulate complex nonlinear and non-Gaussian systems. HOSIM is an alternative to the current MP approaches and it is based upon new high-order spatial connectivity measures, termed high-order spatial cumulants. The HOSIM algorithm implements a sequential simulation process, where local conditional distributions are generated using weighted orthonormal Legendre polynomials, which in turn define the so-called Legendre cumulants. The latter are high-order conditional spatial cumulants inferred from both the available data and training images. This approach is data-driven and reconstructs both high and lower-order spatial complexity in simulated realizations, while it only borrows from training images information that is not available in the data used. However, the three-dimensional implementation of the algorithm is computationally very intensive. To address his topic, the contribution of high-order conditional spatial cumulants is assessed in this paper through the number of Legendre cumulants with respect to the order of approximation used to estimate a conditional distribution and the number of data used within the respective neighbourhood. This leads to discarding the terms of Legendre cumulants with negligible contributions and allows an efficient simulation algorithm to be developed. The current version of the HOSIM algorithm is several orders of magnitude faster than the original version of the algorithm. Application and comparisons in a controlled environment show the excellent performance and efficiency of the HOSIM algorithm.
机译：开发了三维高阶仿真算法HOSIM，以仿真复杂的非线性和非高斯系统。 HOSIM是当前MP方法的替代方法，它基于新的高阶空间连接性度量（称为高阶空间累积量）。 HOSIM算法执行顺序仿真过程，在该过程中，使用加权的正交勒让德多项式生成局部条件分布，而多项式又定义了所谓的勒让德累积量。后者是从可用数据和训练图像两者推断出的高阶条件空间累积量。这种方法是数据驱动的，并在模拟实现中重构了高阶和低阶空间的复杂性，而它仅从训练图像中借用了所用数据中不可用的信息。但是，该算法的三维实现在计算上非常密集。为了解决他的话题，本文通过勒让德累积量的数量相对于用于估计条件分布的近似阶数和各个邻域内使用的数据数量，来评估高阶条件空间累积量的贡献。这导致以微不足道的贡献丢弃勒让德累积量的术语，并允许开发有效的仿真算法。当前版本的HOSIM算法要比原始版本的算法快几个数量级。在受控环境中的应用和比较表明，HOSIM算法具有出色的性能和效率。

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