The process of minimizing the difference between observed and simulated data by adjusting the input model parameters is typically called history matching. Geological parameterization approaches allow high-dimensional geological models to be replaced by relatively low-dimensional parameters in history matching problem. It is important because of the incompetence of optimization algorithms in problems with numerous decision variables. The principal component analysis (PCA) method is commonly used for the representation of geological models in terms of a few parameters. Though, it can only preserve two-point statistics of a random field which is inadequate for regenerating the complicated structures. Kernel-based PCA (KPCA) has been developed to allow the conservation of higher-order statistics in random fields. The most important deficiency of these methods is the consideration of geological realizations in vector forms that causes parameterization methods can only survey the structure of realizations in one direction. As a major disadvantage for fields with anisotropic covariance, spatial correlations in different directions are not properly preserved. We employ two-dimensional principal component analysis (2DPCA) rather than PCA for surveying the structure of two-dimensional realizations in both directions. We consider the realizations as two-dimensional matrices and perform original KPCA in two directions. This method is applied for regenerating Gaussian and non-Gaussian geological random fields with smaller normal random fields and as a parameterization method in history matching. In the Gaussian case, the superiority of 2DPCA over PCA is demonstrated. For non-Gaussian case, both methods lack adequate precision. Hence, a kernel-based 2DPCA (K2DPCA) is developed that exhibits better performance in the regeneration of channelized geological structures compared with KPCA. It is demonstrated that K2DPCA allows preserving the higher-order statistics behind the complex channelized structures when used as a parameterization method for history matching problem in a channelized reservoir.

通过调整输入模型参数来最小化观察到的数据与模拟数据之间的差异的过程通常称为历史匹配。地质参数化方法允许在历史匹配问题中将高维地质模型替换为相对低维参数。由于具有众多决策变量的问题中优化算法的不足，这一点很重要。主成分分析（PCA）方法通常用于通过几个参数来表示地质模型。但是，它只能保留随机字段的两点统计信息，这不足以再生复杂的结构。已经开发了基于内核的PCA（KPCA），可以保留随机字段中的高阶统计信息。这些方法最重要的缺陷是考虑了矢量形式的地质实现，这导致参数化方法只能在一个方向上调查实现的结构。对于具有各向异性协方差的场的主要缺点，没有正确保存不同方向上的空间相关性。我们使用二维主成分分析（2DPCA）而不是PCA来研究两个方向上的二维实现的结构。我们将实现视为二维矩阵，并在两个方向上执行原始KPCA。该方法适用于以较小的法向随机场再生高斯和非高斯地质随机场，并作为历史匹配中的参数化方法。在高斯情况下，证明了2DPCA优于PCA。对于非高斯情况，两种方法都缺乏足够的精度。因此，与KPCA相比，开发了基于核的2DPCA（K2DPCA），在通道化地质结构的再生中表现出更好的性能。结果表明，K2DPCA用作通道化储层中历史匹配问题的参数化方法时，可以保留复杂通道化结构背后的高阶统计量。