A shape-change model for isolated K-feldspar inclusions within a shear zone developed in the Teshima granite, Ryoke metamorphic belt, Japan: Estimation of the duration of deformation in a natural shear zone

A shear zone developed in the Teshima granite in the Ryoke metamorphic belt of Japan contains isolated K-feldspar inclusions showing various shapes within deformed host quartz grains. We present a shape-change model for isolated K-feldspar inclusions, which is a mathematical equation that considers stress, inclusion size, temperature, and the duration of deformation. To calculate the shape-change pattern (i.e., the aspect ratio and size of inclusions) with respect to deformation duration using the model, we used values for deformation temperature (similar to 500-600 degrees C) and paleo-stress (90 +/- 10 MPa) estimated from deformed quartz microstructures within the shear zone. Shape-change patterns were obtained by calculating the model at the estimated range of temperatures with an interval of 25 degrees C and at the estimated paleo-stress. Shape-change patterns were subsequently corrected by compensating for the effect of post-deformation annealing during exhumation of the shear zone. Deformation duration was estimated by identifying the shape-change pattern calculated by the model that most closely corresponded to the observed shape-change pattern for the shear zone and considering the cooling rate of the Ryoke belt. The resultant deformation duration of the shear zone is estimated as 16,500-8400 yr under conditions of T = 550 degrees C and sigma = 90 +/- 10 MPa. Shear strain in the shear zone is calculated as 50-260 by multiplying the shear strain rate by the deformation duration.