Fractal analysis of quartz boundaries as a strain rate proxy for tracing Earth’s stress history

Abstract

Understanding strain rates in naturally deformed rocks is crucial for reconstructing the tectonic history of orogenic belts. This study focuses on the Chahzar Thrust Zone, located within the Sanandaj-Sirjan metamorphic zone of southwestern Iran, an ideal setting for investigating deformation dynamics through microstructural analysis. We employ fractal analysis of quartz grain boundaries to estimate strain rates and assess deformation conditions. Although quartz microstructures such as bulging (250–400 °C), subgrain rotation (400–500 °C), and grain boundary migration (500–750 °C) have been historically linked to specific temperature ranges, recent studies emphasize that these features are also strongly influenced by strain rate, fluid content, and other variables (Law, 2014). In this context, we apply the box-counting method to quantify the fractal dimension (D) of recrystallized quartz grains, using it as a semi-quantitative proxy for combined deformation conditions. Our results yield estimated strain rates ranging from 10⁻1⁰.⁹ s⁻1 to 10⁻⁶.⁸ s⁻1, which are notably higher than previously reported typical natural strain rates (10⁻12–10⁻15 s⁻1). These findings suggest a deformation regime with episodic or localized strain intensification, contributing to a better understanding of strain accommodation in mid-crustal rocks and offering insights into tectonic processes in similar orogenic systems worldwide.