Non-lithostatic pressure in subduction zones

The pressure at depth is not directly observable and no one knows precisely to which extent the pressure conditions in subduction zones, recorded by high-pressure metamorphic rocks, deviate from mantle lithostatic pressure. As an alternative to large-scale complex numerical models of subduction zones, the analytical subduction channel model can give us some insight on the physical processes that control the development of non-lithostatic pressure, as well as some estimation of its amplitude. We propose a new approach coupling the flow of crust within the channel to the deformation of the mantle bounding the channel, occurring as the pressure within the channel deviates from mantle lithostatic values. While for very weak crust within the subduction channel, the channel walls are rigid and channel geometry does not vary, for stronger crust, our coupled approach unravels a new domain of behaviour where the mantle is no longer completely rigid and the deformation of the channel walls prevents arbitrarily large non-lithostatic pressure to develop. This new regime poses an upper bound on the amplitude of non-lithostatic pressure within the channel that depends only on the mantle viscosity. The transition from one regime to another is dependent on an adimensional parameter α=μmμch03L3, incorporating not only mantle and crust viscosity but also the geometry of the channel. The development of larger non-lithostatic pressure in thinner channels than in larger ones, predicted in the rigid channel model, is partly inhibited in the fully coupled model as thinner channels more easily induce channel wall deformation. The lengthscale of the channel width perturbations influences the amplitude of non-lithostatic pressure, as small-scale ones, inducing a more rigid response of the mantle, potentially trigger larger non-lithostatic pressure.