The success in modelling diversity and natural variability of geological media depends on the capability of a particular algorithm to reproduce realism of complex multi-scale reservoir characteristics and agree with data at the same time. Adequate representation of uncertainty in spatial properties is determined by the choice of appropriate model parameterisation and its ability to match the data. The problem of agreement between geostatistical simulations and preservation of the a priori spatial features is subject to uncertainty in conditioning data and assumptions about the model properties (e.g. connectivity, continuity, correlation, stationarity, etc.).
We propose a novel approach to tackle the problem of matching the data from different sources and keeping the model realism to produce reliable reservoir prediction. This high level overview presents a way to bring together prior geological knowledge and relevant data under uncertainty by means of intelligent data fusion through kernel learning. The kernel learning approach balances model complexity with goodness of fit by selecting and reproducing relevant model features. Impact from data at different sources is combined by means of kernels functions, which represent spatial correlation. Kernel regression in the hyper space of features ensures representation of non-linearity and overcomes heavy stationarity assumption. Use of the kernel transformation allows us to reproduce continuity along data manifolds and represent correlation at multiple scales. Support vector formalism ensures the data influence the pattern according to their relevance to the modelled phenomenon (spatial dependency) and the target problem (matching the data). Furthermore, the impact of noisy and atypical data is handled in a rigorous way to prevent loss of predictive capability of the model.
Several examples demonstrate how kernel based models integrated into the Bayesian optimisation framework quantify the uncertainty of reservoir predictions and provide multiple history matches.