| Using Differential Geometry to Quantify Geologic Structures | |
| Personnel: David D. Pollard, Ian Mynatt Collaborators: Stephan Bergbauer, Raymond Fletcher, Rafe Mazzeo Sponsor: Stanford Rock Fracture Project, NSF Collaborations in Mathematics and Geosciences | |
| Description: This project has three major aims: 1) The development and distribution of highly functional, user-friendly
MATLAB-based codes for the geometric analysis of geologic surfaces and structures using the mathematics of differential geometry. 2)
The implementation of these algorithms on geologic structures in order to both describe and analyze them, as well as to expand and
explore the uses of differential geometry in the geologic arena. 3) The presentation of these methods to the geologic community with
the goal of encouraging others to implement and investigate the uses of differential geometry for quantifying geologic structures.
Differential geometry allows for the precise calculation of geometric attributes of discretely sampled surfaces. Shown are the maximum normal curvature calculations for a sub-surface horizon in the North Sea and the so-called "shape curvature" calculations for a joint surface. Each of these calculations provides unique, insightful descriptions of the surface analyzed. 
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| Selected Publications: Mynatt, I., S. Bergbauer, D.D. Pollard, in prep., Using differential geometry to describe and quantify 3-D folds: four examples at multiple scales. Pollard, D. D., S. Bergbauer, and I. Mynatt, 2004, Using differential geometry to characterize and analyze the morphology of joints. In: The Initiation, Propagation and Arrest of Joints and Other Fractures. Geological Society, London, Special Publications, 231, 153-182. Bergbauer, S., D.D. Pollard, 2003, How to calculate normal curvatures of sampled geologic surfaces. Journal of Structural Geology. Vol. 25, no. 2, 277-289. | |