Quantitative geology and geostatistics. Geostatistics BANFF 2004. Volume 1 / Количественная геология и геостатистика. Геостатистика BANFF 2004. Том 1

Geostatistical simulation makes strong assumptions of stationarity in the mean and the variance over the domain of interest. Unfortunately, geological nature usually does not reflect this assumption and we are forced to subdivide our model area into stationary regions that have some common geological controls and similar statistical properties. This paper addresses the significant complexity introduced by boundaries. Boundaries are often soft, that is, samples near boundaries influence multiple rock types.
We propose a new technique that accounts for stationary variables within rock types and additional non-stationary factors near boundaries. The technique involves the following distinct phases: (i) identification of the rock types and boundary zones based on geological modeling and the timing of different geological events, (ii) optimization for the stationary statistical parameters of each rock type and the non-stationary mean, variance and covariance in the boundary zones, and (iii) estimation and simulation using non-stationary cokriging. The resulting technique can be thought of as non-stationary cokriging in presence of geological boundaries.
The theoretical framework and notation for this new technique is developed. Implementation details are discussed and resolved with a number of synthetic examples. A real case study demonstrates the utility of the technique for practical application <....>