Determining relative bulk viscosity of kilometre-scale crustal units using field observations and numerical modelling

Though the rheology of kilometre-scale polymineralic rock units is crucial for reliable large-scale, geotectonic models, this information is difficult to obtain. In geotectonic models, a layer is defined as an entity at the kilometre scale, even though it is heterogeneous at the millimetre to metre scale. Here, we use the shape characteristics of the boundaries between rock units to derive the relative bulk viscosity of those units at the kilometre scale. We examine the shape of a vertically oriented ultramafic, harzburgitic-lherzolitic unit, which developed a kilometre-scale pinch and swell structure at mid-crustal conditions (~ 600 °C, ~ 8.5 kbar), in the Anita Shear Zone, New Zealand. The ultramafic layer is embedded between a typical polymineralic paragneiss to the west, and a feldspar-quartz-hornblende orthogneiss, to the east. Notably, the boundaries on either side of the ultramafic layer give the ultramafics an asymmetric shape. Microstructural analysis shows that deformation was dominated by dislocation creep (n = 3). Based on the inferred rheological behaviour from the field, a series of numerical simulations are performed. Relative and absolute values are derived for bulk viscosity of the rock units by comparing boundary tortuosity difference measured on the field example and the numerical series. Our analysis shows that during deformation at mid-crustal conditions, paragneisses can be ~ 30 times less viscous than an ultramafic unit, whereas orthogneisses have intermediate viscosity, ~ 3 times greater than the paragneisses. If we assume a strain rate of 10⁻ ¹⁴ s⁻ ¹ the ultramafic, orthogneiss and paragneiss have syn-deformational viscosities of 3 × 10²², 2.3 × 10²¹ and 9.4 × 10²⁰ Pa s, respectively. Our study shows pinch and swell structures are useful as a gauge to assess relative bulk viscosity of rock units based on shape characteristics at the kilometre scale and in non-Newtonian flow regimes, even where heterogeneity occurs within the units at the outcrop scale.