Bayesian Balancing: Inverse Modeling of Fault-Related Folds for Seismic Hazard and Natural Resource Applications

David Oakley, University of Nebraska Omaha
Donald Fisher, The Pennsylvania State University
Nestor Cardozo, University of Stavanger
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Abstract

Kinematic models that relate fault geometry and displacement to resulting fold geometries and deformation are important and widely used methods in structural geology. They can help to produce balanced cross sections, and sometimes 3D models, and to reconstruct the history of deformation. They can be used to predict subsurface structural geometry where data are lacking, which is important for many applications in natural hazards preparedness and natural resource exploration, among others. These models are, however, non-unique. When only a single model is made, it may not be the best fit to the available data, and it will almost certainly not be the only possible interpretation. Without a full understanding of the range of possible solutions, it can be difficult to make reliable, actionable predictions based on models. To find the best-fitting models and to quantify uncertainty in them, we turn to data inversion methods. We first apply the Markov Chain Monte Carlo (MCMC) method to the problem of fitting trishear models to fault-propagation folds, showing that probability distributions of model parameters may be multimodal. We apply this method to fault-related folds in the North Canterbury region of New Zealand—a seismically active region where faults associated with folding pose poorly quantified seismic hazards, and fault geometry at depth is largely unknown. We include the uplift of dated marine terraces in our models, which helps to narrow the space of possible solutions, and, critically for seismic hazard analysis, allows us to quantify fault slip rates and their uncertainty. The MCMC method, however, is difficult to apply to problems with many unknown model parameters. In this case, we turn to a method better suited for large parameter spaces: ensemble Kalman inversion. We apply this method to a 3D oil field model containing five faults to quantify along-strike variations in fault throw and estimate the associated uncertainty. Further development of the data inversion approach to structural modeling and model balancing is in progress; areas of ongoing and future research include selection among different kinematic models, use of mechanical instead of kinematic models, and joint inversion of structural and geomorphic data to better quantify deformation rates.

Session

Societal relevance of structural geology and tectonics