The role of Poiseuille flow in creating depth-variation of asthenospheric shear

Asthenospheric flow accommodates differential shear between plate and mantle motions (Couette flow) and hosts additional flow driven by horizontal pressure gradients (Poiseuille flow) that may be associated with mantle upwelling and subduction. Large uncertainties in the upper mantle flow field and its rheological structure have thus far hindered our ability to constrain the relative importance of Couette and Poiseuille flows in the asthenosphere. However, quantifying the relative contributions of asthenospheric Couette and Poiseuille flows and determining the pattern of their distribution around the globe could help discriminate among competing theories of asthenospheric origin and shed light on thermal history of the Earth. We propose a new method to quantify asthenospheric Poiseuille flow using observations of the depth-dependence of azimuthal seismic anisotropy, which can be obtained from frequency-dependent surface wave tomography models. In particular, we employ a simple 1-D Couette-Poiseuille flow model and analytically solve for depth-profiles of the strain axis orientations, which approximates the orientations of azimuthal seismic anisotropy. We show that Couette-Poiseuille flow induces rotation of azimuthal seismic anisotropy with depth provided that the horizontal pressure gradient has a component transverse to plate motion. We then construct an algorithm that uses depth rotations of azimuthal anisotropy to invert for horizontal pressure gradients everywhere in the asthenosphere and test it on a global numerical mantle flow model. A comparison of pressure gradients predicted using our method with those computed directly from the numerical model shows that our algorithm is stable and accurate, unless the pressure gradient is nearly parallel to plate motion. Applying this method to seismic data will require additional constraints on asthenospheric geometry and viscosity structure. In the numerical model, we establish that Poiseuille flow drives similar to 40 per cent of the total flow velocity amplitude in the asthenosphere, which indicates that pressure gradients from mantle convection may be an important component of asthenospheric dynamics that can, in principle, be constrained seismically.