THREE-DIMENSIONAL STRAIN ANALYSIS USING MATHEMATICA

The author has made available a suite of Mathematica-based geological computer programs at the following web page: http://www.sonoma.edu/users/m/mookerje/ProgramPage.htm. The majority of these programs focus on three-dimensional strain analysis using a new method for determining best fit ellipsoids from planar sections. This method takes a least-squares approach by minimizing the difference between the matrix elements of the input two-dimensional data-ellipses and the matrix elements from the corresponding sectional ellipses through a general ellipsoid. This method works both for data sets that include the absolute size of the sectional ellipses as well as for those where only axial ratios are known. Also included in this program suite are best fit ellipsoid programs that incorporate a statistical analysis component to facilitate the evaluation of the quality of the initial input data set and to ultimately constrain and guide the kinematic interpretations. These programs take a simulation-based approach and utilize a kernel density estimator to calculate reliable error margins for the strain parameters, octahedral shear strain, Flinn’s k-value, and Lode’s ratio. Additionally, these statistical programs determine error margins for the principal axes orientations of the strain ellipsoid by assuming a gamma distribution for the angle between the simulation-derived axes orientations and the corresponding best fit principle axis. These programs will facilitate the undertaking of three-dimensional strain analysis and will assist investigators in choosing the most appropriate number and orientations of sectional data planes for a given sample as well as encourage investigators to report error bounds associated with their kinematic data. This program suite also includes graphical programs for plotting geological data sets, including both a Flinn and Hsu diagram plotting program (with and without error margins), as well as 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.