ISSN:
1573-8868
Keywords:
Fourier analysis
;
paleontology
;
structure
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Mathematics
Notes:
Abstract A system of strain analysis based on the application of a homogeneous strain transformation in plane polar coordinates to match deformed shapes of the same initial form is described. Two types of transformation are derived. A simple transformation between the deformed and the undeformed states, used to compare deformed shapes with a predetermined initial configuration, is recorded in the form of a plane polar coordinate Fourier series. This method allows reliable strain estimates to be made from single specimens of a fossil in an area where sufficient consistency of original shape has been established. A transformation describing the difference in relative strain between local polar coordinate systems in the same overall homogeneous deformation field, is used to compare the members of a group of deformed shapes with one another. This transformation allows the determination of the optimum initial ‘mean shape’of a group of fossils in a deformed rock as well as giving a strain measurement. The use of parabolic integration enhances the determination of the Fourier descriptions, and allows the use of irregularly spaced data. Inherent mathematical features of the method provide controls on the accuracy of the determination. The relatively mechanical nature of the input and the general form of the solution make the method readily applicable in semiautomated systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01079034
