Spectral Approaches of Gaussian Conditional Simulations in History Matching Problems

In the paper we consider optimization problem arised in history matching of reservoir model. In such type of problems the unknown parameter often is a distributed field of the physical quantity such as permeability and porosity fields. The way the parameter field is parametrized greatly influences efficiency of the complete optimization approach. We propose an efficient technique of a spectral-domain parameterization based on the Cholesky decomposition of the covariance matrix in Fourier domain. The approach significantly reduce the number of simulation runs. A comparative analysis of history matching of the proposed algorithm and standard spectral method is performed using PUNQ-S3 test model.

stationary process, Gaussian fields, spectral approach, Fourier transformation, Cholesky decomposition, history matching