Modeling frictional melt injection to constrain coseismic physical conditions

- We develop 2D time-dependent models of pseudotachylyte injection vein formation.
- Vein formation times are ∼1 s, 102 to 103 times slower than previously predicted.
- We conclude that vein growth may often be limited by frictional melt transport.
- The occurrence and shape of veins can constrain minimum melt temperature.
- We propose that vein shapes require high coseismic stress and wall rock softening.

Pseudotachylyte, a fault rock formed through coseismic frictional melting, provides an important record of coseismic mechanics. In particular, injection veins formed at a high angle to the fault surface have been used to estimate rupture directivity, velocity, pulse length, stress drop, as well as slip weakening distance and wall rock stiffness. These studies have generally treated injection vein formation as a purely elastic process and have assumed that processes of melt generation, transport, and solidification have little influence on the final vein geometry. Using a pressurized crack model, an analytical approximation of injection vein formation based on dike intrusion, we find that the timescales of quenching and flow propagation may be similar for a subset of injection veins compiled from the Asbestos Mountain Fault, USA, Gole Larghe Fault Zone, Italy, and the Fort Foster Brittle Zone, USA under minimum melt temperature conditions. 34% of the veins are found to be flow limited, with a final geometry that may reflect cooling of the vein before it reaches an elastic equilibrium with the wall rock. Formation of these veins is a dynamic process whose behavior is not fully captured by the analytical approach. To assess the applicability of simplifying assumptions of the pressurized crack we employ a time-dependent finite-element model of injection vein formation that couples elastic deformation of the wall rock with the fluid dynamics and heat transfer of the frictional melt. This finite element model reveals that two basic assumptions of the pressurized crack model, self-similar growth and a uniform pressure gradient, are false. The pressurized crack model thus underestimates flow propagation time by 2-3 orders of magnitude. Flow limiting may therefore occur under a wider range of conditions than previously thought. Flow-limited veins may be recognizable in the field where veins have tapered profiles or smaller aspect ratios than expected. The occurrence and shape of injection veins can be coupled with modeling to provide an independent estimate of minimum melt temperature. Finally, the large aspect ratio observed for all three populations of injection veins may be best explained by a large reduction in stiffness associated with coseismic damage, as injection vein growth is likely to far exceed the lifetime of dynamic stresses at any location along a fault.