Finite Strain Analysis Using Shape and Point Data

Abstract Understanding the finite strain state of a rock or its spatial variation is an important component of structural geology. In this chapter the problem of calculating finite strain using shape data and point data is considered in detail. The first step in strain analysis is data acquisition, and the first section is concerned with semiautomatic extraction of data for strain analysis from digital images. Two methods for strain analysis are considered: the first method (MRL, mean radial length) uses the shapes of strain markers, and the second method (Delaunay triangulation nearest neighbor method) uses the relative positions of strain marker centroids. In each case, relevant image files, data, and C++ code are provided. Background theory is discussed, and an example application is considered emphasizing that finite strain analysis is best used in conjunction with a range of structural observations.

[1]  M. McNaught.  Modifying the normalized fry method for aggregates of non-elliptical grains , 1994 .

[2]  D. Dunnet,et al.  Non-random sedimentary fabrics and their modification by strain , 1971 .

[3]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  G. Gutiérrez-Alonso,et al.  Factors affecting finite strain estimation in low-grade, low-strain clastic rocks , 2009 .

[5]  F. Hrouda,et al.  Theoretical models for the relationship between magnetic anisotropy and strain: effect of triaxial magnetic grains , 1999 .

[6]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[7]  P. Labaume,et al.  Strain decoupling across the decollement of the Barbados accretionary prism , 1996 .

[8]  P. Robin.  Determination of geologic strain using randomly oriented strain markers of any shape , 1977 .

[9]  A. Yamaji.  Theories of strain analysis from shape fabrics: A perspective using hyperbolic geometry , 2008 .

[10]  K. Mulchrone,et al.  Finite strain estimation using the mean radial length of elliptical objects with bootstrap confidence intervals , 2003 .

[11]  N. Fry,et al.  A comparison of methods of strain determination in rocks from southwest Dyfed (Pembrokeshire) and adjacent areas , 1979 .

[12]  N. Fry.  Random point distributions and strain measurement in rocks , 1979 .

[13]  A statistical examination of the Fry method of strain analysis , 2011 .

[14]  D. Dunnet,et al.  A technique of finite strain analysis using elliptical particles , 1969 .

[15]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[16]  F. Hrouda,et al.  A technique for numerical modeling of magnetic anisotropy to strain relationship , 2002 .

[17]  Tian-Yuan Shih,et al.  Improvements on Sloan's algorithm for constructing Delaunay triangulations , 1998 .

[18]  T. Shimamoto,et al.  A simple algebraic method for strain estimation from deformed ellipsoidal objects. 1. Basic theory , 1976 .

[19]  Objective fitting of ellipses in the centre-to-centre (Fry) method of strain analysis , 2007 .

[20]  Patrick A. Meere,et al.  Mathematica code for image analysis, semi-automatic parameter extraction and strain analysis , 2013, Comput. Geosci..

[21]  J. Ramsay.  Folding and fracturing of rocks , 1967 .

[22]  R. Lisle.  Strain analysis from point fabric patterns: An objective variant of the Fry method , 2010 .

[23]  Kieran F. Mulchrone.  Application of Delaunay triangulation to the nearest neighbour method of strain analysis , 2003 .

[24]  K. Mulchrone,et al.  SAPE: a program for semi-automatic parameter extraction for strain analysis , 2005 .

[25]  J. Jezek,et al.  SUSIE: A program for inverse strain estimation from magnetic susceptibility , 2007, Comput. Geosci..

[26]  David Hart,et al.  Least-squares fit of an ellipse to anisotropic polar data: Application to azimuthal resistivity surveys in karst regions☆ , 1997 .

[27]  R. Lisle.  Clastic grain shape and orientation in relation to cleavage from the Aberystwyth Grits, Wales , 1977 .

[28]  P. E. Matthews,et al.  An algebraic method of strain analysis using elliptical markers , 1974 .

[29]  D. Elliott.  Determination of Finite Strain and Initial Shape from Deformed Elliptical Objects , 1970 .

[30]  K. Mulchrone,et al.  Fitting an ellipse to an arbitrary shape: implications for strain analysis , 2004 .

[31]  E. Erslev.  Normalized center-to-center strain analysis of packed aggregates , 1988 .