CAN WE PREDICT THE WIDTH OF DUCTILE SHEAR ZONES?

Exhumed crustal shear zones range in width from millimeters to tens of kilometers. Intuitively, we expect ductile shear zones to be wider if they accommodate more displacement or faster displacement rates; if they form at higher temperatures; or if they occur in relatively weak rocks. Based on these understandings, previous studies have proposed theoretical scaling laws relating shear zone width to imposed displacement rate (such as plate velocity) and strain rate (which is a function of the rheology). However, few studies have tried to quantify this relation, largely because actual measured values are difficult to obtain from active shear zones at depth.

We therefore targeted the crustal-scale, normal-sense Simplon Shear Zone in the central Alps. Due to progressive strain localization during exhumation and cooling, the footwall preserves a structural zonation, from a broad zone of high-T deformation, through progressively narrower zones of lower-T mylonitization, to a brittle fault adjacent to the hangingwall. Using field- and microstructural mapping, quartz paleopiezometry, mineral chemistry thermobarometry, and published displacement rates based on thermochronological modeling, we have therefore been able to estimate the shear zone width, stress, P-T conditions, and strain rate for deformation at a range of depths. By combining our measured data with existing scaling laws and theoretical relations, we propose the following equation:

W = BV/σ^n+mp

Where W is the width of the shear zone, V is the displacement rate across it, σ is the stress with exponent n, m is the grain-size sensitivity, p is the piezometric exponent, and B is a “rheological parameter” that varies from ~1E+18 in quartz-rich granite, to ~3.5E+19 in feldspar-dominated granite.

To answer the title question: yes, we can predict the width of a ductile shear zone, if we know the displacement rate across it (which can be estimated from thermochronology or other constraints); the stress (which can be determined with paleopiezometry); the appropriate stress exponent, piezometric exponent, and grain-size sensitivity (which are available in the literature, and can be chosen based on microstructural determination of the deformation mechanisms); and the rheological parameter (which this study provides for quartz-, mica-, and feldspar-dominated granitic rock).