A Mohr-Cyclide Construction for Finite Deformation and its Application to 3-d Analysis of Deformed Vein Sets

2D finite deformation analysis commonly relies on simplified assumptions such as plane strain and isovolume, which are insufficient to fully characterize 3D geological structures, leading to incomplete tectonic interpretations. To overcome these limitations, this study proposes the Mohr-cyclide for finite deformation as a new geometrical tool to fully visualize and quantify 3D deformation. We present a practical method for constructing Mohr-cyclides directly from field data. By constraining the parameters of 2D Mohr circles on the rotation profile plane (RPP) and elongation parallel to the finite rotation axis, the strain ellipsoid’s shape, size, rotation, and volume change can all be quantified from the same dataset. Application of this method to deformed quartz veins in the Ryoke metamorphic belt of the Hongu-san area in SW Japan reveals significant volume reduction in the rock and a top-to-the-SE sense of shear. The proposed volume change has implications for mass transfer that can occur associated with metamorphism. The shear sense is opposite to that reported in neighboring outcrops, but the same dextral shear has been locally documented elsewhere in the Ryoke belt. The observed reversals in the sense of shear are potentially useful in constraining tectonic models for SW Japan at the time of deformation. The Mohr-cyclide is a powerful analytical tool that can help resolve complex 3D rock deformation histories and provide new insights into tectonic processes.