CMG: Mathematical Modeling of the Dynamics of Multi-scale Phenomena During Folding and Fracturing of Sedimentary Rocks

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In this project, supported by the Collaborations in Mathematical Geosciences Program (CMG), the investigators are: 1) characterizing the geometric shapes of km-scale folded sedimentary strata using Airborne Laser Swath Mapping (ALSM) data and the principles of differential geometry; 2) investigating the dynamics of the folding process using continuum mechanics and Finite Element Methods (FEM); and 3) studying the physical interactions between km-scale folds and m-scale fractures within them using fracture and damage mechanics. Their underlying hypothesis is that the 3D shape of folded strata adequately constrains the internal deformation such that the orientation and spatial density of m-scale fractures can be predicted using these shapes. The study was motivated by the unprecedented opportunity to characterize fold shapes with decimeter precision using ALSM data and high resolution digital photography acquired by the NSF-sponsored National Center for Airborne Laser Mapping (NCALM), operated jointly by the University of Florida and the University of California. The folds selected for this study are Sheep Mountain Anticline, Wyoming, and Raplee Ridge Monocline, Utah.The team addresses three CMG theme areas: 1) mathematical modeling of large, complex geosystems; 2) analyzing large geoscience data sets; and 3) modeling geosystems with a broad range of interacting scales. The team of principal investigators includes a geoscientist with expertise in structural geology, a mathematician with expertise in differential geometry, and a civil engineer with expertise in computational mechanics. The broader impacts of this investigation stem from the fact that folds are common traps for subsurface fluids, and fractures in hydrocarbon reservoirs and groundwater aquifers are known to be conduits for fluid flow. In the environmental arena folds are being evaluated as potential reservoirs for excess CO2 storage. Furthermore, active faults commonly are associated with folds, so the mitigation of earthquake hazards requires a better understanding of the folding process. The intellectual merits of this investigation include the facts that: 1) applications of differential geometry to geological problems are rare, yet have great promise; 2) strain localization by fracturing during folding is ripe for a new approach heralded by recent advances in computational mechanics; 3) the research involves innovative applications of new technology (ALSM) that promise unprecedented data quantities and precision.