Strain-rate estimation using fractal analysis of quartz grains in naturally deformed rocks

The area-perimeter fractal dimension (D) of quartz grains has earlier been proposed as a strain-rate gauge based on experimental deformation of quartz aggregates. To test the application in naturally deformed rocks, D is calculated in (a) three quartzites belonging to the Lunavada Group of rocks (Aravalli Mountain Belt, NW India) that developed textures between 420–600°C and (b) one quartz reef sample from the Malanjkhand Granite (Central India), which underwent dynamic recrystallization between 250–400°C. Using the above T ranges and calculated D values, strain-rates are calculated for the two sets of samples. A 10^−12.7 s⁻¹ strain rate at 250°C is calculated for the quartz reef sample. However, at higher temperatures the calculated strain-rate is >10⁻¹⁰ s⁻¹ for the quartz reef and the quartzite samples. The quartzites show evidence of dynamic recrystallization by grain boundary migration (GBM) and subgrain rotation (SGR), while the quartz reef is replete with evidence of bulging (BLG) recrystallization. T and calculated strainrates are plotted on available recrystallization map of quartz. It is demonstrated that whilst the T/strain-rate of the quartzites does not fall in the region of GBM and SGR, the T/strain-rate of the quartz reef falls in the BLG region. The problems with strain-rate calculations using area perimeter fractal dimension are discussed. It is concluded that the method of strain-rate calculation can be used only for lower T.