Kinematic descriptions of the growth of geologic fault-related folding structures, including fault-bend, fault-propagation, and detachment folds, have been widely and successfully employed in quantitatively constraining predictions of subsurface structural geometries across a wide spectrum of applications in regional tectonics, petroleum systems, seismic hazard assessment, and other subsurface energy systems.

Nevertheless, application of these methods can be challenging in some situations; in particular, interpretation structures that are complex or which accommodated variable structural styles over the history of the growth of the structure often requires time-consuming manual construction of kinematic solutions using these approaches, limiting the use of these approaches to seasoned practitioners and limiting the number of alternative scenarios that can be realistically tested.

In an attempt to mitigate some of these challenges, Chris Connors (Washington and Lee University), Stephen Ball (formerly Washington and Lee University, now ExxonMobil) and I have been collaborating on developing and applying velocity-based representations of kinematic fault-related folding equations that can be numerically implemented. The full description of algorithms employed in this velocity-based description of kinematic fault-bend folding can be found in Connors, Hughes, and Ball, 2021 paper in the Journal of Structural Geology (Open Access Paper can be directly downloaded HERE).

Such numerical solutions allow fault-related folding parameters to be recalculated at each time step during simulation, permitting solution of structures more complex than is typically possible, including structures such as multi-bend fault-bend folds, splays, imbricates, and duplexes. The algorithm provides a unified representation for both extensional and contractional fault-related folding, enabling modeling of both within a single cross section, as would occur in inversion structures, or linked gravitational collapse systems.

Furthermore, because the structures are represented in a velocity-based framework, other geologic processes that can be represented as fields can also be integrated into the same framework, including erosion, compaction and subsidence.

Because the solutions are fully kinematic (meaning that the movement of material is tracked at every time step between the initial and final deformed states), then many structurally-relevant quantities may be extracted from the models beyond simply the geometry of the faults and folds, including instantaneous velocity vectors, particle paths, strain ellipses, layer parallel strain.

Additionally, we have implemented these algorithms in a Matlab-based code which operates as a stand-along executable; if you would like to use it for your own research or teaching, you can contact Chris Connors (HERE) for the latest version. If you would like advice on applying this to your research, or would like to collaborate on doing so, please send me a message!

Animated examples of the models and applications will be added soon!