Timescale of Short‐Term Subduction Episodicity in Convection Models With Grain Damage: Applications to Archean Tectonics

Abstract

The style of subduction that prevailed on the early Earth, or even whether subduction was prevalent at all, is an important question in the evolution of Earth's crust, mantle, and surface environment. Here, two-dimensional numerical convection models, that include grain size evolution to generate weak plate boundaries, reveal a clear transition in subduction behavior with increasing internal heating rate. Sustained subduction with a coherent slab gives way to a style where slabs periodically detach and sink rapidly into the deep mantle, with increasing internal heating rate. In this latter, "drip-like" subduction regime, repeating cycles of slab growth by subduction, followed by necking and detachment of the lower portion of the slab, are seen. These cycles are termed "slab detachment cycles," and similar behavior has been seen in regional scale subduction models of the early Earth. Fourier analysis is used to constrain the timescale of slab detachment cycles, and a simple scaling law for this timescale is developed. Applying the scaling law to the early Earth indicates that slab detachment cycles can occur on timescales of <10 Myr, even as low as <5 Myr if the lithosphere is thick and mantle temperature is >1900 K. These cycles may thus be capable of explaining repeating sequences of rocks with "arc" and "non-arc" signatures seen in some Archean cratons. The drip-like subduction regime could also have significant implications for the generation of the tonalite-trondhjemite-granodiorite (TTG) suite of rocks and exhumation of high pressure metamorphic rocks, two important features of the early Earth geologic record.

A Giant Impact Origin for the First Subduction on Earth

“…Our computations show that there is a path to developing such plumes, and it is closely linked to the presumed MGI, which happened <150 Ma before the oldest dated terrestrial zircons. Following the earliest subduction, the proto-lithosphere can usually be recycled globally, depending on lithosphere strength and plume-slab interactions, with subsequent periods of sluggish lid convection where the subducting slab periodically tears off, similar to the tectonic mode inferred for early Earth (Foley, 2020).…”

Supplemental Material: Generation of Archean TTGs via sluggish subduction

“…In the sluggish subduction regime, the sinking speed of a slab is dictated by a balance between the negative buoyancy of the slab and the viscous resistance from both the surrounding mantle and the lithospheric shear zone between overriding and downgoing plates (Foley, 2020); such a force balance gives (Eq. 1 in the main text):…”

“…where T l ≈ 900 K is the average temperature in the mid-lithosphere (Foley, 2020), A is the fineness, or inverse grain size, in lithospheric shear zones, A ref = 1000 m −1 (equivalent to 1 mm grain size) is the reference fineness (Foley, 2020), m = 2 is the grain size exponent (Hirth & Kohlstedt, 2003), and where µ l is defined as the undamaged lithospheric viscosity (i.e. the viscosity of the lithosphere when A = A ref ).…”

“…The fineness in lithospheric shear zones, A, is found by taking the grain size evolution equation for graindamage (e.g. Foley et al, 2012Foley et al, , 2014Bercovici & Ricard, 2012) in steady-state, as in Foley (2020). This gives…”

“…where f is the fraction of deformational work that partitions into surface energy and hence contributes to grain size reduction (the remainder of the deformational work contributes to shear heating, which is small unless shear zones deform very rapidly, ), τ is the second invariant of the stress tensor, γ ∼ 1 is the surface tension (Bercovici & Ricard, 2012), h l is the grain-growth, or healing, rate in the lithosphere, and p = 4 is the grain-growth exponent (Bercovici & Ricard, 2012;Foley, 2020). Like viscosity, the healing rate is also temperature-dependent following an Arrhenius law:…”