Three-dimensional strain analysis using Mathematica

A suite of geological computer programs written in Mathematica is currently available both within the online repository for the Journal of Structural Geology as well as on the first author’s website (http://www.sonoma.edu/users/m/mookerje/ProgramPage.htm). The majority of these programs focus on three-dimensional strain analysis (e.g., determining best-fit strain ellipsoids, plotting elliptical data on either a Flinn or Hsu diagram, and determining error bounds for three-dimensional strain data). This program suite also includes a ternary diagram plotting program, a rose diagram program, an equal area and equal angle projections program, and an instructional program for creating two-dimensional strain path animations. The bulk of this paper focuses on a new method for determining a best-fit ellipsoid from arbitrarily oriented sectional ellipses and methods for determining appropriate error bounds for strain parameters and orientation data. This best-fit ellipsoid method utilizes a least-squares approach and minimizes the error associated with the two-dimensional data-ellipse matrix elements with the corresponding matrix elements from sectional ellipses through a general ellipsoid. Furthermore, a kernel density estimator is utilized to yield reliable error margins for the strain parameters, octahedral shear strain, Flinn’s k-value, and Lode’s ratio. By assuming a gamma distribution for the simulated principal axes orientations, more realistic error bounds can be estimated for these axes orientations.