15:30 〜 15:45
[SIT24-07] 方解石双晶の方向データの応力インバージョン
★招待講演
キーワード：stress inversion, differential stress, statistical mixture model, polyphase tectonics
Mechanical twins are usually observed in natural calcite under a microscope. Methods of their stress inversion are briefly reviewed in this paper. Unlike faults and seismic focal mechanisms, calcite twins provide us of the opportunity to estimate stress magnitudes.
The twins have a specific crystallographic orientation. Their formation results in the simple shear of a calcite grains along the lamellae. The twinning is allowed on condition that the stress component along the shearing direction is greater than a critical value, tauc. Since the stress component depends on the orientations of planes in a crystal under a state of stress, the orientations of twinned planes in a calcite aggregate indicate the stress that formed the observed twin lamellae. The inversion determines not only the principal orientations and stress ratio, but also the non-dimensional differential stress normalized by tauc. The inverse method based on this principle (Etchecopar, 1984) has been used mainly by French researchers. Some researchers applied it to such twin lamellae that were formed under different stress conditions in different tectonic phases. However, the conventional method is unsatisfactory for dealing with such heterogeneous data sets.
It was found recently that a geometrical condition on a sphere in five-dimensional space corresponds to the twinning condition (Yamaji, 2015a). Twin data are denoted by points on the sphere, a circular area of which stands for a deviatoric stress tensor normalized by tauc. Yamaji (2015b) found that the stress inversion of heterogeneous twin data is achieved by the fuzzy clustering of the data points on the sphere. The clustering is performed by the present author using a statistical mixture model.
Unfortunately, the tauc value at 10 MPa has been often used, but its temperature and grain size dependence is not well understood. Laboratory experiments are awaited to improve our understanding on the dependence and stress magnitudes.
The twins have a specific crystallographic orientation. Their formation results in the simple shear of a calcite grains along the lamellae. The twinning is allowed on condition that the stress component along the shearing direction is greater than a critical value, tauc. Since the stress component depends on the orientations of planes in a crystal under a state of stress, the orientations of twinned planes in a calcite aggregate indicate the stress that formed the observed twin lamellae. The inversion determines not only the principal orientations and stress ratio, but also the non-dimensional differential stress normalized by tauc. The inverse method based on this principle (Etchecopar, 1984) has been used mainly by French researchers. Some researchers applied it to such twin lamellae that were formed under different stress conditions in different tectonic phases. However, the conventional method is unsatisfactory for dealing with such heterogeneous data sets.
It was found recently that a geometrical condition on a sphere in five-dimensional space corresponds to the twinning condition (Yamaji, 2015a). Twin data are denoted by points on the sphere, a circular area of which stands for a deviatoric stress tensor normalized by tauc. Yamaji (2015b) found that the stress inversion of heterogeneous twin data is achieved by the fuzzy clustering of the data points on the sphere. The clustering is performed by the present author using a statistical mixture model.
Unfortunately, the tauc value at 10 MPa has been often used, but its temperature and grain size dependence is not well understood. Laboratory experiments are awaited to improve our understanding on the dependence and stress magnitudes.