Combining Methods for Subsurface Prediction

The depth to subsurfaces in a multi-layer model is obtained by adding the thickness of layers. However, the choice of layering is not unique so there will often be alternative ways of obtaining the depth to a particular subsurface. Each layer thickness can be described by a stochastic model accounting for uncertainties in the thickness. Stochastic models for the depth to subsurfaces are obtained from these. Alternative layer models will give alternative stochastic models and thus alternative depth predictions for the same subsurface. Two approaches to resolve this ambiguity is proposed. The first uses an established method of unbiased linear combination of predictors. The second and new approach combines the alternative stochastic models into a single stochastic model giving a single predictor for subsurface depth. This predictor performs similarly to the approach combining several predictors while drastically reducing computational costs. The proposed method applies to layered geological structures using a combination of universal or Bayesian kriging and cokriging.