Contribution of Elasticity in Slab Bending

Previous studies have shown that plate rheology exerts a dominant control on the shape and velocity of subducting plates. Here, we perform a systematic investigation of the, often disregarded, role of elasticity in slab bending at the trench, using simple, yet fully dynamic, set of 2.5D models where an elastic, visco-elastic or visco-elasto-plastic plate subducts freely into a purely viscous mantle. We derive a scaling relationship between the bending radius of visco-elastic slabs and the Deborah number, De, which is the ratio of Maxwell time over deformation time. We show that De controls the ratio of elastically stored energy over viscously dissipated energy and find that at De exceeding 10-2, it requires substantially less energy to bend a visco-elastic slab to the same shape as a purely viscous slab with the same viscosity (90% less for De=0.1). Elastically stored energy at higher De facilitates slab unbending and hence favours retreating modes of subduction, while trench advance only occurs for some cases with De<10-2. We use our scaling relation to estimate apparent Deborah numbers, Deapp, from a global compilation of subduction-zone parameters. Values range from 10-3 to >1, where most zones have low Deapp<10-2, but a few young plates have Deapp>0.1. Slabs with Deapp ≤ 10-2 either have very low viscosities, ≤10 times mantle viscosity, or they may be yielding, in which case our apparent Deborah number may underestimate actual De by up to an order of magnitude. If a significant portion of the low Deapp slabs yield, then elastically stored energy may actually be important in quite a large number of subduction zones. Interestingly, increasing Deapp correlates with increasing proportion of larger seismic events (b-value) in both instrumental and historic catalogues, indicating that increased contribution of elasticity may facilitate rupture in larger, less frequent earthquakes.