Self-affinities of Folds and Incomplete Similarity

Kazuhei Kikuchi, Hiroyuki Nagahama


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.


Self-affinities; Folds; Incomplete similarity

Full Text:



K. Kikuchi, K. Abiko, H. Nagahama, H. Kitazato, and J. Muto, “Selfaffnities

of landforms and folds in the Northeast Honshu Arc, Japan,”

Acta Geophysica, vol. 61, pp. 1642-1658, December 2013.

G.W. Hunt, and M.K. Wadee, “Comparative Lagrangian formulations

for localized buckling,” Proc. R. Soc. London, vol. A434, pp. 485-502,

September 1991.

A. Ord, and B. Hobbs, “Microfabrics as energy minimisers: Rotation

recrystallisation as an example,” Journal of Structural Geology, vol. 33,

pp. 220-243, March 2011.

T. Shimamoto, “Application of the Pi-theorem to the similarity criteria

of slow deformation of inhomogeneous viscous fluids,” Tectonophysics,

vol. 22, pp. 253-263, June 1974.

E. Buckingham, “On physically similar systems; illustrations of the use

of dimensional equations,” Physical Review, vol. 4, pp. 345-376,

October 1914.

G.I. Barenblatt, Similarity, Self-similarity, and Intermediate

Asymptotics: Consultants Bureau, New York, 1979.

K. Kikuchi, and H. Nagahama, “Self-affinities of Folds and Incomplete

Similarity”, Proceedings of Annual International Conference on

Geological and Earth Sciences 2016, Singapore, October 10, 2016, PP.

-56, October 2016.

M.A. Biot, “Folding instability of a layered viscoelastic medium under

compression”, Proc. R. Soc. London, vol. A242, pp. 444-454,

November 1957.

K. Kikuchi, K. Abiko, H. Nagahama, and J. Muto, “Self-affinities

analysis of fault-related folding,” Episodes, vol. 38, pp. 308-311,

December 2014.


  • There are currently no refbacks.