Abstract Several applications in geoscience require the generation of multiple realizations of random fields of physical properties to mimic their spatial distribution and quantify the model uncertainty. Some modeling problems present complex multivariate distributions with heteroscedasticity and non-linear relations among the variables. We propose a new algorithm, namely Direct Multivariate Simulation, for the simulation of random fields of non-parametric multivariate joint distributions. The methodology is based on a generalization of the normal score and back transformation for multivariate distributions, also called Stepwise Conditional transformation. The sequential sampling of each variable is performed by decomposing the target joint distribution into a product of univariate marginal and conditional probability density functions. We propose numerical solutions to improve the algorithm efficiency for real case applications with a large number of variables. The method is demonstrated through an application where we sample a 6-variate joint distributions with strong nonlinear dependence among the variables. The results are validated by comparing the results to the Projection Pursuit Multivariate Transform and through the computation of the experimental semi-variograms, the marginal distributions, and the bi-histograms of the simulated variables.

中文翻译：

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直接多元模拟 - 多元地质统计模拟的逐步条件转换

摘要 地球科学中的一些应用需要生成物理特性随机场的多重实现，以模拟它们的空间分布并量化模型的不确定性。一些建模问题呈现复杂的多元分布，变量之间具有异方差和非线性关系。我们提出了一种新算法，即直接多元模拟，用于模拟非参数多元联合分布的随机场。该方法基于对多元分布的正态分数和反向变换的概括，也称为逐步条件变换。每个变量的顺序采样是通过将目标联合分布分解为单变量边际和条件概率密度函数的乘积来执行的。我们提出了数值解决方案，以提高具有大量变量的实际案例应用的算法效率。该方法通过一个应用程序来演示，在该应用程序中，我们对变量之间具有强非线性相关性的 6 变量联合分布进行采样。通过将结果与 Projection Pursuit Multivariate Transform 进行比较并通过计算实验半变异函数、边缘分布和模拟变量的双直方图来验证结果。