A Caltech Library Service

Mathematical Study of Finite-Amplitude Rock-Folding


Chapple, William Massee (1964) Mathematical Study of Finite-Amplitude Rock-Folding. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FCVB-NS79.


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.))
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):
  • Kamb, W. Barclay
Thesis Committee:
  • Unknown, Unknown
Defense Date:10 September 1963
Record Number:CaltechTHESIS:05152013-140445759
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7714
Deposited By: Benjamin Perez
Deposited On:15 May 2013 21:49
Last Modified:29 Jan 2024 20:10

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page