Dependence of the brittle ductile transition on strain-rate-dependent critical homologous temperature

Abstract

Earthquakes mainly occur in crust or mantle that is below a critical temperature for the tectonic strain-rate, ˙et, such that stress builds up to the breaking point before it can relax due to creep. Then long-range stress correlation gives rise to power law seismicity including large events. The limiting temperature depends on pressure, which is taken into account by finding a critical homologous temperature THc = T/TM above which earthquakes are rarely observed (where T, TM are temperature and average melting temperature of constituent minerals). We find that THc for ocean plates is ∼0.55. For California earthquakes, it is also close to 0.55. The uppermost mantle layer of oceanic plates of thickness ∼50 km is composed of harzburgite and depleted peridotite from which basalt has been removed to form ocean crust. Thus it has a higher melting temperature than the peridotite of the surrounding mantle, or the lower halves of plates. Thicknesses of seismicity in deep subduction zones, determined from 2-D polynomial fits to a relocated catalogue, are ∼50 km, which suggests that the earthquake channel is confined to this layer. We construct models to find homologous temperatures in slabs, and find that seismicity thicknesses are also, on average, confined to TH ≤ 0.55 ± 0.05. The associated rheology is compared with that obtained from flexure models of ocean lithosphere. The brittle-ductile transition occurs where viscosity drops from high values in the cold cores of slabs to values of 1022-1023 Pa s, that is, where creep strain-rates become comparable to tectonic rates. The cut-off for deep earthquakes is not sharp. However they appear unlikely to occur if homologous temperature is high TH > 0.55. Exceptions to the rule are anomalously deep earthquakes such as those beneath the Iceland and the Hawaiian hotspots, and the Newport Inglewood Fault. These are smaller events with short-range stress correlation, and can be explained if strain-rates are two to three orders of magnitude higher than those associated with earthquakes located where TH ≤ 0.55. We conclude that the brittle-ductile transition corresponds to the transition from long-range (regional) to short-range (localized on asperities) stress correlation.