Structural geologic modeling and restoration using ensemble Kalman inversion

Abstract

We demonstrate the use of Ensemble Kalman Inversion (EKI) for building three-dimensional, multi-fault, kinematically restorable structural geologic models, by means of a workflow in which fault geometry, the distribution of slip on a fault, and the geometry of folded horizons are all modeled. The models are constrained by observations of faults and horizons in the present deformed state together with the expectation that horizons should restore flat. Two modeling approaches are tested: restoration from the deformed state, and forward modeling from the restored state. We first test these methods on a synthetic model involving a single fault, and then apply them to a real-field example involving five faults. Models are prone to ensemble collapse, which results in underestimation of uncertainty at small ensemble sizes, but localization and covariance inflation can mitigate this issue. With these methods, EKI can recover the true parameter values in the synthetic case and produce a solution consistent with the data in the real case, as well as quantify uncertainty in both cases. EKI, therefore, shows promise as a tool for building complex, restorable structural geologic models, and it holds the potential for integration of fault kinematics with other ensemble-based subsurface modelling workflows.