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

Abstract

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 (~500–600 °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 °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 °C and σ = 90 ± 10 MPa. Shear strain in the shear zone is calculated as 50–260 by multiplying the shear strain rate by the deformation duration.