Kernel-based two-dimensional principal component analysis applied for parameterization in history matching

Mohammad Esmaeili, Mohammad Ahmadi*, Alireza Kazemi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Article number107134
JournalJournal of Petroleum Science and Engineering
Publication statusPublished - Aug 2020


  • 2DPCA
  • Data assimilation
  • History matching
  • Image processing
  • Kernel-based PCA
  • Parameterization

ASJC Scopus subject areas

  • Fuel Technology
  • Geotechnical Engineering and Engineering Geology

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