Abstract

The joint modeling of the petrophysical properties (i.e., porosity, permeability) from wells in the presence of one or more seismic attributes (i.e., impedance) may be cumbersome, as the linear model of coregionalization needs to be simultaneously fitted to all experimental direct and cross-variograms, and the strong assumptions are required in the collocated cokriging system. Transforming each petrophysical property to an uncorrelated factor through the projection-pursuit multivariate transform allows each uncorrelated factor to be simulated independently. However, considering the case where there is an exhaustive secondary variable, the uncorrelated factors can no longer be simulated independently, as they are still conditionally dependent through the secondary variable. The aim of this paper is to provide a solution to this problem through the simulation of each uncorrelated factor in a subsequent fashion; that is, the first uncorrelated factor is cosimulated using the available secondary variable as a covariate; the second uncorrelated factor is cosimulated using a super-secondary variable generated by merging the previously simulated first uncorrelated factor and the secondary variable, and the kth uncorrelated factor is cosimulated using a super-secondary variable generated by merging all previously simulated uncorrelated factors \((1,\ldots ,k-1)\) as well as the secondary variable. This hierarchical simulation framework preserves the correlation structure between the uncorrelated factors themselves and between the uncorrelated factors and the secondary variable. The methodology is demonstrated in case studies using synthetic and real reservoir datasets. It is shown that the use of PPMT approach and the hierarchical simulation workflow in combination achieves: (1) multivariate complexity in the data is accounted for through the PPMT approach, and (2) the reproduction of the observed bivariate relationships in the simulated realizations of the petrophysical properties themselves and the secondary information is ensured by the hierarchical simulation workflow.

Highlights

• Application of multivariate Gaussian transform to the spatially correlated variables.

• Simulation of each factor independently.

• Reproduction of the bivariate statistics in the realizations.

中文翻译：

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使用地震数据进行高效的多元属性建模

摘要

在存在一种或多种地震属性（即阻抗）的情况下，对井的岩石物理特性（即孔隙度、渗透率）进行联合建模可能很麻烦，因为共区化的线性模型需要同时拟合所有实验直接和交叉变异函数，并且在并置的协同克里金系统中需要强假设。通过投影-追踪多元变换将每个岩石物理特性转换为不相关的因素，允许独立模拟每个不相关的因素。然而，考虑到存在穷举次要变量的情况，不相关的因素不能再独立模拟，因为它们仍然通过次要变量有条件地依赖。本文的目的是通过以后续方式模拟每个不相关因素来提供解决此问题的方法；也就是说，第一个不相关的因素使用可用的次要变量作为协变量进行协同模拟；使用通过合并先前模拟的第一个不相关因子和次要变量而生成的超二级变量对第二个不相关因子进行联合模拟，并且第k个不相关因子使用通过合并所有先前模拟的不相关因子\((1,\ldots ,k-1)\)生成的超二级变量进行协同模拟以及次要变量。这种分层模拟框架保留了不相关因素本身之间以及不相关因素与次要变量之间的相关结构。该方法在使用合成和真实油藏数据集的案例研究中得到了证明。结果表明，结合使用 PPMT 方法和分层模拟工作流程可实现：（1）通过 PPMT 方法考虑数据中的多元复杂性，以及（2）在模拟实现中再现观察到的双变量关系分层模拟工作流程确保了岩石物理特性本身和次要信息。

强调

• 多元高斯变换对空间相关变量的应用。

• 独立模拟每个因素。

• 在实现中重现双变量统计数据。