Citation
Chapple, William Massee (1964) Mathematical Study of Finite-Amplitude Rock-Folding. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FCVB-NS79. https://resolver.caltech.edu/CaltechTHESIS:05152013-140445759
Abstract
The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.
Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.
The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.
Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.
Item Type: | Thesis (Dissertation (Ph.D.)) |
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Subject Keywords: | (Geology and Mathematics) |
Degree Grantor: | California Institute of Technology |
Division: | Geological and Planetary Sciences |
Major Option: | Geology |
Minor Option: | Mathematics |
Thesis Availability: | Public (worldwide access) |
Research Advisor(s): |
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Thesis Committee: |
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Defense Date: | 10 September 1963 |
Record Number: | CaltechTHESIS:05152013-140445759 |
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:05152013-140445759 |
DOI: | 10.7907/FCVB-NS79 |
Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 7714 |
Collection: | CaltechTHESIS |
Deposited By: | Benjamin Perez |
Deposited On: | 15 May 2013 21:49 |
Last Modified: | 29 Jan 2024 20:10 |
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