| It is essential for the techniques of paleostress analysis to separate stresses from
heterogeneous data (e.g., Tikoff et al., 2013). A statistical mixture model is shown in this
paper to be effective for calcite twinning paleopiezometry: Given the orientations of
twinned e-planes and their gliding directions, the present inverse method based on the
mixture model determines not only deviatoric stress tensors, but also estimates the
number of tensors that should be read from a data set using Bayesian information
criterion.
The present method is based on the fact that mechanical twinning occurs on an e-plane if
the resolved shear stress along its gliding direction, τ, is greater than a critical value, τc (e.g.,
Lacombe, 2010). The orientation data from e-planes corresponds to points on a
5-dimensional unit sphere, a spherical cap on which indicates a deviatoric stress tensor. The
twinning condition, τ > τc, is identical with the condition that the points corresponding to
the orientation data are distributed upon the spherical cap (Yamaji, 2015a). It means that
the paleostress analysis of calcite twins comes down to the problem of fitting a
spherical cap to data points on the sphere (Yamaji, 2015b). Given a heterogeneous data
set, two or more spherical caps should be fitted to the data point on the sphere. A
statistical mixture model is employed for this fitting in the present work. Such a
statistical model enables us to evaluate the number of stresses recorded in the data
set.
The present method was tested with artificial data sets and a natural data set obtained
from a Miocene graben in central Japan. From the former type of data sets, the method
determined the deviatoric stress tensors that were assumed to generate the data sets. The
natural data were inverted to give two stresses that appeared appropriate for the tectonic
setting of the area where the data were obtained. |