Three-dimensional passive mantle flow beneath mid-ocean ridges: an analytical approach

Abstract

S U M M A R YWe discuss theoretical and computational method on plate-driven mantle flow beneath midocean ridges. We consider a steady-state flow induced by motion of overlying rigid plates in an incompressible viscous mantle beneath a generic ridge-transform-ridge plate boundary. No assumption of orthogonal and symmetric spreading at ridge axis is made. Analytical solutions for viscosity flow in a half-space and in a layered viscosity mantle beneath an infinitesimal thickness lithosphere and beneath plates that thicken with increasing age, are presented. Numerical calculations were carried out using a standard fast Fourier transform algorithm. The difficulty of using standard Fourier methods to predict accurately the mantle flow field in the proximity of the plate boundaries is overcome by applying the Gegenbauer reconstruction post-processing technique to the Fourier pseudo-spectral solutions. Finally, we present some examples of flow computations. We consider, for both models, two different ridge-transformridge geometries consisting of 100 and 1000 km offsets of two ridge segments spreading at 15 mm/yr half rate. We found a significant difference in the flow structure between the two flow models close to ridge axis and ridge-transform intersections. The proposed model and methods are useful for fast mantle flow calculations to investigate melting processes beneath spreading centres, and to predict the relationship between mantle temperature, crustal thickness and geochemistry of the oceanic crust.

Birth of an ocean in the Red Sea: Initial pangs

“…We considered first a steady state mantle flow induced by motion of the overlying rigid plates in an incompressible, homogeneous, isoviscous mantle. The steady state three‐dimensional passive mantle flow has been solved via the Fourier pseudo‐spectral technique outlined in Ligi et al [2008] both for thin plates and for plates that thicken away from the ridge.…”

Serpentinization of mantle peridotites along an uplifted lithospheric section, Mid Atlantic Ridge at 11° N

“…Sub-lithospheric mantle flow and thermal structure were obtained by solving Stokes and heat equations with semi-analytical-pseudo-spectral (Ligi et al, 2008) and finite difference techniques (Morgan and Forsyth, 1988), respectively. We calculated basaltic crust thickness following computational methods on plate-driven subridge mantle flow for a lithosphere that thickens with age (Ligi et al, 2008) assuming a mantle temperature of 1350°C at 150 km depth (base of our model), fractional hydrous melting (100 ppm of H 2 O content in the mantle source) and complete melt extraction . The base of rigid plates in the plate-thickening model, assumed to correspond to the depth of the 800°C isotherm, was obtained iteratively, starting from a constant-thickness plate-flow model.…”

Post-Mesozoic Rapid Increase of Seawater Mg/Ca due to Enhanced Mantle-Seawater Interaction

“…We calculated it (see Supplementary Information) following computational methods on plate-driven subridge mantle flow for a lithosphere that thickens with age44 (Fig. 4).…”

“…Assuming a plate spreading velocity for each sector by averaging spreading rates and directions, we calculated passive mantle flow, thermal structure and melt production beneath each ridge segment following methods of ref. 44. We calculated along-axis crustal thickness assuming pure-fractional melting and complete melt extraction.…”

“…We solved for the steady-state three-dimensional passive mantle flow via a Fourier pseudo-spectral technique44. The base of rigid plates, assumed to correspond to the depth of the 800°C isotherm, was obtained iteratively solving each time the mantle temperature field, starting from a constant-thickness plate-flow model.…”