Self-affinities of Folds and Incomplete Similarity

Kazuhei Kikuchi, Hiroyuki Nagahama

Abstract


A method to analyze self-affinities is introduced, and
applied to the large scale fold geometries of the Quaternary and
Tertiary in the inner belt of the Northeast Honshu Arc. Based on
this analysis, their geometries are found to be self-affine and can
be differently scaled in different directions. We recognize the selfaffinities
for the amplitude and the wavelength of folds, and
discover a crossover from local to global altitude (vertical)
variation of the geometries of folds in the Northeast Honshu Arc.
Buckingham's Pi-theorem has been applied to similar systems of
inhomogeneous viscous Newtonian fluid under similar boundary
condition. However, Buckingham's Pi-theorem cannot give us the
self-affinities of folds. A general renormalization-group argument
is proposed to the applicability of the similarity theory. By this
argument, we derive the self-affinities for the amplitude and the
wavelength of folds as a parameter for the anisotropic stress field.


Keywords


Self-affinities; Folds; Incomplete similarity

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References


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