Modeling the Uncertainty in the Layout of Geological Units by Implicit Boundary Simulation Accounting for a Preexisting Interpretive Geological Model

An implicit simulation algorithm that uses signed distance functions is proposed to represent subsurface geological configuration while accounting for two sources of information: drillhole data considered as 'hard' (error-free) information and a preexisting interpretive geological model viewed as 'soft' information. The proposed algorithm follows a hierarchical workflow and relies on the calculation of the down-the-hole distance between every drillhole data and the closest geological boundary (primary variable) together with the omnidirectional distance between each node of the interpretive model and the closest boundary (covariate). The level of influence of the latter on the former can be controlled by tuning their cross-correlation so that one can increase or reduce the effect of the geological interpretation in the simulation, depending on the confidence of the expert in such an interpretation. The key parameters for a successful implementation of the proposed approach are the choice of a binary tree to control the topological relationships between the simulated geological units, of a spatial correlation model to control the geological continuity and the boundaries regularity, and of a coefficient to control the trustworthiness given to the soft data. The specification of these parameters can be assessed by geological considerations and by cross-validation techniques. The proposal was applied to a synthetic and a real case study, where it was shown that incorporation of soft data allowed reproduction of geological zonations in areas with few drillhole data. Some implementation issues and possible improvements to the method are also discussed.

Automated summary

The proposed algorithm utilizes signed distance functions to represent subsurface geological configuration, taking into account drillhole data as 'hard' information and a preexisting interpretive geological model as 'soft' information. The level of influence of the geological interpretation in the simulation can be controlled by tuning the cross-correlation between the two sources of information. Key parameters for successful implementation include the choice of a binary tree, a spatial correlation model, and a coefficient to control the trustworthiness of the soft data. The application of the algorithm in synthetic and real case studies showed that incorporation of soft data allowed for reproduction of geological zonations in areas with limited drillhole data.