Serrated quartz grain boundaries, temperature and strain rate: testing fractal techniques in a syntectonic granite

AbstractIn the past fractal (ruler) dimension (Dr) of quartz grain-boundary sutures and area–perimeter fractal dimension (Da) of quartz grains, respectively, have been shown to depend on temperature (T) and strain rate. However, the application of these methods to gauge temperature and strain rate in naturally deformed intrusive rocks has not yet been tested. In the present studyDrandDaare calculated in 12 thin sections from different parts of a syntectonic granite (Godhra Granite, India). Of these, six belong to the northern part, two to the central part and four to the southern part of the granite. Earlier work on the Godhra Granite showed both a strain and a temperature gradient, with high temperature in the north and high strain in the south. Microstructural studies reveal that the quartz grain-boundary sutures are less serrated in the northern samples compared to those from the remaining part of the granite. The northern samples contain abundant high-temperature solid-state deformation fabrics that formed between 675 and 725 °C (quartz chessboard pattern thermobarometry). Using aDrv.Tplot given by earlier workers, aDrvalue of 1.05–1.14 is expected for the aboveTrange.Drcalculations of quartz sutures from the northern samples give a median of 1.11 and most of the sutures haveDr<1.14. These data fit well with the expected temperature range in which the quartz chessboard pattern formed in the Godhra Granite. The central and southern parts of the granite are dominated by myrmekites (500–670 °C), recrystallized feldspars (450–600 °C), deformation twins in feldspar (400–500 °C) and kinked biotite (<300 °C). The expectedDrof quartz sutures under the above medium–low temperature ranges are 1.07–1.23, 1.11–1.25, 1.16–1.28 and <1.27, respectively.Drcalculations reveal that most of the quartz sutures from the central+southern part haveDr>1.14, and the median values are 1.18 (centre) and 1.17 (south). Using theDrv.Tplot, theseDrvalues indicate that most of the textures in the central+southern part of the Godhra Granite formed in the temperature range of 450–600 °C, which fits well with the temperature range required for the development of medium–low temperature fabrics that dominate this part of the granite. Thus, it is concluded thatDrof quartz sutures can be used as a geothermometer in syntectonic granites.Dafor northern and southern samples is 1.10 and 1.14, respectively. Strain rates of the order of approximately 10−7and 10−11s−1, respectively, are obtained for high (675 °C) and low temperature (300 °C) using area-perimeter fractal dimension (Da) values. Although these are higher than geological strain rates that are known in nature (10−12–10−15s−1), the calculated values for the lower-temperature range are similar to strain rates estimated for intrusions (10−10–10−12s−1). The calculations indicate that the method to calculate strain rate usingDaof quartz grains fails to give geologically reasonable strain rates for high temperature in a syntectonic granite. However, the method maybe useful in obtaining reasonable strain rate estimates for lower temperatures.