Quantifying Diapir Ascent Velocities in Power‐Law Viscous Rock Under Far‐Field Stress: Integrating Analytical Estimates, 3D Numerical Calculations and Geodynamic Applications

Abstract

Diapirism is crucial for heat and mass transfer in many geodynamic processes. Understanding diapir ascent velocity is vital for assessing its significance in various geodynamic settings. Although analytical estimates exist for ascent velocities of diapirs in power‐law viscous, stress weakening fluids, they lack validation through 3D numerical calculations. Here, we improve these estimates by incorporating combined linear and power‐law viscous flow and validate them using 3D numerical calculations. We focus on a weak, buoyant sphere in a stress weakening fluid subjected to far‐field horizontal simple shear. The ascent velocity depends on two stress ratios: (a) the ratio of buoyancy stress to characteristic stress, controlling the transition from linear to power‐law viscous flow, and (b) the ratio of regional stress associated with far‐field shearing to characteristic stress. Comparing analytical estimates with numerical calculations, we find analytical estimates are accurate within a factor of two. However, discrepancies arise due to the analytical assumption that deviatoric stresses around the diapir are comparable to buoyancy stresses. Numerical results reveal significantly smaller deviatoric stresses. As deviatoric stresses govern stress‐dependent, power‐law viscosity, analytical estimates tend to overestimate stress weakening. We introduce a shape factor to improve accuracy. Additionally, we determine characteristic stresses for representative mantle and lower crustal flow laws and discuss practical implications in natural diapirism, such as sediment diapirs in subduction zones, magmatic plutons or exhumation of ultra‐high‐pressure rocks. Our study enhances understanding of diapir ascent velocities and associated stress conditions, contributing to a thorough comprehension of diapiric processes in geology.

3D Stresses and Velocities Caused by Continental Plateaus: Scaling Analysis and Numerical Calculations With Application to the Tibetan Plateau

“…We apply only one particular value of τ C to test the first-order impact of power-law viscous flow on the crustal stress and extensional velocity. If a particular flow law, which is determined by laboratory rock deformation experiments, should be applied, then the value of τ C can be calculated for a given pressure, temperature or grain size (Macherel, Podladchikov, et al, 2023). For example, for feldspar (wet anorthite), τ C ≈ 24 MPa for a temperature of ≈600°C and a grain size of ≈0.5 mm (Macherel, Podladchikov, et al, 2023).…”

“…For the analytical estimate, we assume that the effective viscosity is controlled by the deviatoric stress estimate, τ e . τ C defines the stress magnitude at which the deformation behavior changes from a linear viscous flow law to a power-law viscous flow law (e.g., Macherel, Podladchikov, et al, 2023;Schmalholz & Podladchikov, 2013). If n = 1, then η cE = η c , and the flow is linear viscous.…”