Mantle circulation with partial shallow return flow: Effects on stresses in oceanic plates and topography of the sea floor

Abstract

Fully two‐dimensional analytic boundary layer solutions are used to model the thermomechanical structure of the oceanic upper mantle when a shallow horizontal return flow helps balance the lithospheric transport of mass from ridge to trench. The following are all incorporated in the solutions: horizontal and vertical advection of heat, vertical heat conduction, viscous dissipation, adiabatic heating and cooling, buoyancy, and the pressure‐ and temperature‐dependent nonlinear rheology of olivine. Depth profiles of horizontal and vertical velocities, temperature, and shear stress are calculated for several ages of the ocean floor. Such solutions are used to construct accurate isotherm and streamline patterns within the rigid lithosphere and high‐shear, return flow asthenosphere of the oceanic upper mantle boundary layer. Ocean floor topography is inferred from the thermal contraction of the cooling lithosphere and asthenosphere and from the adverse horizontal pressure gradient required by the dynamics to drive the shallow return flow. The flattening of the topography of the old ocean floor can be attributed to the retardation of boundary layer cooling by shear heating and/or to the adverse pressure gradient of a shallow return flow. The latter effect would be dominant if a shallow return flow did occur in the earth's upper mantle. Solutions which provide adequate fits to the ocean floor bathymetry data for the Pacific plate can be found if the activation volume for the creep of olivine is small, i.e., about 11 cm3/mol, and if the deep mantle temperature T is high, i.e., if T is about 1500°C at depths of 100–200 km (depending on age) for dry olivine or about 1400°C at similar depths for wet olivine. The upper mantle temperatures required for a shallow return flow to be compatible with bathymetry data imply partial melting in the lower lithosphere and upper asthenosphere from the ridge axis to ages of about 10 m.y. Shear stresses at the base of the rigid lithosphere generally range from about 1 to several tens of bars, and horizontal adverse pressure gradients at great depth vary from about 10 to 100 mbar/km for wide variations in the extent of return flow and deep mantle temperature. For a relatively cold deep mantle, shear stresses in the lower lithosphere and asthenosphere decrease almost linearly with depth, implying horizontal pressure gradients essentially constant with depth. For a hot deep mantle, shear stress versus depth profiles show curvature in the lower lithosphere and upper asthenosphere and a linearly decreasing pattern at greater depths. Under such circumstances, horizontal pressure gradients exhibit considerable depth variation including the possibility of a reversal in sign between the top and the bottom of the asthenosphere.

On the thermal evolution of passive continental margins, thermal depth anomalies, and the Norwegian‐Greenland Sea

“…To this approximation, as was stated earlier, the lateral motion of the lower half of the region is insignificant (i.e., the model is not meant to suggest a 400-kmthick lithosphere). Below 200 km, the model produces •ertical temperature gradients which are nearly adiabatic, so the temperature field in the lower region is not greatly different from that produced by some convective models [e.g., Schubert et aL, 1978]. For these reasons, the model presented here may be considered an approximation to its more elegant but less tractable convective cOUnterpart.…”

Stress field and kinematics for diffuse microseismicity in a zone of continental transpression, South Island, New Zealand

“…The directions of azS Hmax , derived above for the plate boundary channel flow model, are virtually identical to the average directions of strain rate from high-resolution decadal GPS measurements of velocity [Beavan et al, 2016], which are~100°for the Southern Lakes region and~105°for the central Southern Alps (Figure 5). This would make sense if the GPS-derived strain rates reflect uniform elastic straining of the brittle crust, which in dynamical terms implies that it is either coupled to an underlying uniform ductile flow [Lamb, 1994, Bourne et al, 1998 or the result of edge forces imposed by the bounding plates on an isotropic uniform elastic layer [Solomon et al, 1975;Forsyth and Uyeda, 1975;Richardson et al, 1976;Schubert et al, 1978, Wallace et al, 2004, Wallace et al, 2007, Lamb and Smith, 2013, so long as gravitationally induced stresses are a negligible component of the stress field [Jeffreys and Singer, 1959;Artyushkov, 1973;Wortel et al, 1991;Flesch et al, 2000Flesch et al, , 2007. However, the topography of the Southern Alps in central South Island suggests that gravity is likely to be a contributing part of the stress field.…”

On Presence of Seismic Anisotropy in the Asthenosphere beneath Continents and its Dependence on Plate Velocity: Significance of Reference Frame Selection

“…(a) AM1-2 model; a peak marked by reversed triangle may be the effect of Eurasian motion which is a perpendicular relation to those of other models, (b) HS2-NUVEL1 model, and (c) NNR-NUVEL1 model. If masses of vertical velocity profile balance within shallower upper mantle, return flow will be produced in the asthenosphere (TURCOTTE and SCHUBERT, 1982) as calculated in SCHUBERT and YUEN (1978) and CHASE (1979). The idea of return flow is also presumed to explain Pacific shrinkage (ALVAREZ, 1982).…”