ABSTRACT The orientations of mechanical twins in calcite have been used in various areas in the world for paleopiezometry. This paper presents a new inversion scheme which determines deviatoric stress tensors normalized by the critical resolved shear stress of twinning (CRSS). The unique advantage of the technique is the ability not only to separate stresses from heterogeneous data but also to determine how many stresses should be determined from them. For this purpose, the present scheme capture clusters of data points in a five‐dimensional deviatoric stress–strain space. The accuracy and resolution of the present technique were studied using synthetic data sets. Stress axes were determined with error of a few degrees. Differential stresses normalized by CRSS, , were found to be inaccurate if the twin lamellae in question were formed under stress conditions with greater than 30. Even in such cases, principal orientations and stress ratios were accurately determined. Separation of stresses is equivalent with classification of data. The present method separated successfully even when two classes of data shared 60%–70% of data. The method was applied to a data set from a calcite vein in an Eocene limestone unit in the southern Ryukyu arc, Japan, and clearly separated two stresses. With examples from both synthetic and natural data sets, it is demonstrated that the plausibility of separated stresses can be estimated by means of the proxies of data and nondimensional deviatoric stress tensors defined in a parameter space.
Yamaji et al. (Thu,) studied this question.