Constraining Poiseuille flow in the asthenosphere using depth-dependence of azimuthal seismic anisotropy

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. Determining the relative importance and spatial distribution of Poiseuille flow in the asthenosphere could help discriminate among competing theories of asthenospheric origin and shed light on thermal history of the Earth. Large uncertainties in the flow field and rheological structure of the upper mantle have thus far hindered our ability to constrain the relative importance of Couette and Poiseuille flows in the asthenosphere. We propose a new method to quantify Poiseuille flow in the asthenosphere using observations of the depth-dependence of azimuthal seismic anisotropy. In particular, we employ a simple one-dimensional Couette-Poiseuille flow model and analytically solve for the depth-profiles of the strain axis orientation in the asthenosphere, which approximates the orientation of azimuthal seismic anisotropy. We find 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 utilizes observed rotations of azimuthal seismic anisotropy with depth and analytical depth-profiles of the strain axis to invert for the horizontal pressure gradients everywhere in the asthenosphere. We test our method on the output of a global numerical mantle flow model. A comparison of our predicted pressure gradients with those computed directly from the numerical model shows a high degree of agreement, indicating that our method is robust. We show that our algorithm is stable, except for the case in which the component of the pressure gradient transverse to plate motion is close to zero. We establish that Poiseuille flow drives about 40% of the total flow velocity amplitude in the asthenosphere of the numerical model, which indicates that pressure gradients from mantle convection may be an important component of asthenospheric dynamics.