Preservation of Multiple Point Structure when Conditioning by Kriging

Abstract

The idea of conditioning by kriging is well known in theory and practice. It has been used for conditioning the realizations from unconditional simulation techniques such as the moving average and the turning bands simulation approaches. The basis of the conditioning by kriging approach is to use the same variogram for both the unconditional simulation and the kriging. In this paper, the focus is on using kriging for conditioning of more complex unconditional simulations. Unconditional simulated realizations with multiple point structure are generated for posterior conditioning. Two sets of data are used for kriging. After conditioning, the simulated values at data locations are the real data values, so the local data is honored. Beyond the range of correlation, the simulated values are the unconditional simulated values, which mean the multiple point structure can be preserved.The results obtained in this work show that conditioning by kriging is a simple, easy and reliable way to account for data with complex multiple point structures. Both continuous and categorical variables are used to show the performance of the conditioning by kriging approach. Moreover, kriging with different sets of data demonstrates that the multiple point structures are well preserved after conditioning.