HR: 1330h
AN: H42B-1070    [PDF]
TI: Constraining Fold-shape Models With Simultaneous Non-linear Regression to Characterize Fold Related Fractures
AU: * Hoaglund, J R
EM: hoaglund@essc.psu.edu
AF: Pennsylvania State University EMS Environment Institute, 2217 Earth-Engineering Sciences, University Park, PA 16802 United States
AB: Bedding-plane partings and axial-plane spaced cleavage are examples of fractures in sedimentary rocks that can be related to field scale fold structures. These fracture systems can be modelled regionally if the fold structure can be approximated mathematically through the use of fold shape models. The theory of a new technique to estimate parameters of fold shape models using geologic horizon elevation and bedding plane data is presented. Observations of the elevation of a geologic horizon are used to regress the parameters of a model of the horizon in a fold, while observations of bedding planes are used to regress the same parameters in the gradient of an isotimic surface function that reduces to the horizon model when the isotimic constant is zero. The gradient thus corresponds to the normal to the tangent (bedding) plane to the horizon, i.e. the pole to bedding. Therefore the normalized components of the gradient correspond to the direction cosines of the pole to bedding, and comprise three models in the same parameters as the horizon model. A simultaneous regression can be constructed using both the horizon elevation and bedding plane observations. The sensitivities of both the horizon model and gradient models depend upon the values of the parameters, and thus the regression is non-linear. The theory is developed and an example using a sum-of-sines function is presented for upright, symmetric folds in the Mahantango Creek watershed of Pennsylvania.
DE: 1829 Groundwater hydrology
DE: 1894 Instruments and techniques
DE: 1899 General or miscellaneous
SC: Hydrology [H]
MN: 2003 Fall Meeting