Scaling Seismic Fault Thickness From the Laboratory to the Field

Abstract

Pseudotachylytes originate from the solidification of frictional melt, which transiently forms and lubricates the fault plane during an earthquake. Here, we observe how the pseudotachylyte thickness a scales with the relative displacement D both at the laboratory and field scales, for measured slip varying from microns to meters, over 6 orders of magnitude. Considering all the data jointly, a bend appears in the scaling relationship when slip and thickness reach ∼1 mm and 100 µm, respectively, i.e., MW > 1. This bend can be attributed to the melt thickness reaching a steady-state value due to melting dynamics under shear heating, as is suggested by the solution of a Stefan problem with a migrating boundary. Each increment of fault is heating up due to fast shearing near the rupture tip and starting cooling by thermal diffusion upon rupture. The building and sustainability of a connected melt layer depend on this energy balance. For plurimillimetric thicknesses (a > 1 mm), melt thickness growth reflects in first approximation the rate of shear heating which appears to decay in D−1/2 to D−1, likely due to melt lubrication controlled by melt + solid suspension viscosity and mobility. The pseudotachylyte thickness scales with moment M0 and magnitude MW; therefore, thickness alone may be used to estimate magnitude on fossil faults in the field in the absence of displacement markers within a reasonable error margin.