Novel observations on the structure and deformation of the overriding plate in subduction zones and their implications for slow slip

Abstract:

We discover that subduction zones all around the world exhibit a beautiful relationship between the inter-tremor time interval and the slenderness ratio of the overriding plate, as shown in the accompanying figure. In order to understand this phenomenon better, we perform numerical simulations of deformation as well as study the 3D surficial deformation of the overriding continental crust in Cascadia and Alaska using GPS data.

In solid mechanics, the buckling of beams is determined by the material’s Young’s modulus and its slenderness. Slenderness is a measure of the tendency of the beam to buckle and is quantified by the slenderness ratio – the ratio between the effective length of the beam and its radius of gyration. For a wedge geometry, we redefine the slenderness ratio to be the ratio of the length of the wedge to the maximum thickness, which is also equal to the inverse of the slope of the plate interface in subduction zones. For a given slenderness ratio, there is a critical load (lower than the yield stress of the material), at which the wedge will bend (buckling/folding) before it can break. We perform numerical simulation of the buckling process of wedges by subjecting them to similar forces and boundary conditions encountered at subduction zones.

The results from the above numerical modeling show that critical load and slenderness ratio have an inverse nonlinear relation between them (almost identical to the classical Euler’s critical load relation), and very similar to the non-linear relationship in the accompanying figure. Assuming that all continental wedges experience similar stress rates, then the critical stress should be approximately directly proportional to the inter-tremor time interval (because stress equals the product of stress rate and time). Therefore, we can use inter-tremor time interval as a proxy for critical stress. From the above analysis, we conclude that the remarkable relationship between the inter-tremor time interval and the slenderness ratio of the overriding plate is a result of buckling of the overriding continental plate.

In addition to the above numerical analysis, we analyze the surficial 3D spatio-temporal displacements of the overriding plates in Cascadia and Alaska using 3-component GPS data. We find that these deformations are consistent with the buckling of a wedge-shaped body.