Browsing by Subject "Mantle dynamics"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Dynamics of the eastern edge of the Rio Grande Rift(2013-08) Xia, Yu; Grand, Stephen P.The Western U.S. has experienced widespread extension during the past 10’s of millions of years, largely within the Basin and Range and Rio Grande Rift provinces. Tomography results from previous studies revealed narrow fast seismic velocity anomalies in the mantle on either side of the Rio Grande Rift as well as at the western edge of the Colorado Plateau. The fast mantle anomalies have been interpreted as down-welling that is part of small scale mantle convection at the edge of extending provinces. It was also found that crust was thicker than average ab¬¬ove the possible mantle down-welling, indicating that mantle dynamics may influence crustal flow. We present results from P/S conversion receiver functions using SIEDCAR (Seismic Investigation of Edge Driven Convection Associated with the Rio Grande Rift) data to determine crustal and lithospheric structure beneath the east flank of the Rio Grande Rift. Crustal and lithosphere thickness are estimated using P-to-S and S-to-P receiver functions respectively. Receiver function migration methods were applied to produce images of the crust and lithosphere. The results show variable crustal thickness through the region with an average thickness of 45 km. The crust achieves its maximum thickness of 60km at 105W longitude, between 33.5N and 32.2N latitude. This observation confirms previous receiver function results from Wilson et al, 2005. Body wave tomography (Rocket, 2011; Schmandt and Humphreys, 2010) using similar data to what we used for the receiver function analysis, shows mantle downwelling closely associated with the thickened crust. We believe that the thickened crust might be due to lower crustal flow associated with mantle downwelling or mantle delamination at the edge of the Rio Grande Rift. In this model the sinking mantle pulls the crust downward causing a pressure gradient within the crust thus causing the flow. Our S-P images show signal from the lithosphere-asthenosphere boundary (LAB) with an average LAB thickness of 100 km but with a sharp transition at about 1050 W from 75 km to over 100 km. The region with abnormally thick crust overlies a region where the lithosphere appears to have a break. We interpret our results as showing that lower lithosphere has and is delaminating near the edge of the Great Plains accompanied by lower crustal flow in some places determined by lower crustal viscosity.Item Mixed framework for Darcy-Stokes mixtures(2014-12) Taicher, Abraham Levy; Arbogast, Todd James, 1957-; Hesse, MarcWe consider the system of equations arising from mantle dynamics introduced by McKenzie (J. Petrology, 1985). In this multi-phase model, the fluid melt velocity obeys Darcy's law while the deformable "solid" matrix is governed by a highly viscous Stokes equation. The system is then coupled through mass conservation and compaction relations. Together these equations form a coupled Darcy-Stokes system on a continuous single-domain mixture of fluid and matrix. The porosity φ, representing the relative volume of fluid melt to the bulk volume, is assumed to be much smaller than one. When coupled with solute transport and thermal evolution in a time-dependent problem, the model transitions dynamically from a non-porous single phase solid to a two-phase porous medium. Such mixture models have an advantage for numerical approximation since the free boundary between the one and two-phase regions need not be determined explicitly. The equations of mantle dynamics apply to a wide range of applications in deep earth physics such as mid-ocean ridges, subduction zones, and hot-spot volcanism, as well as to glacier dynamics and other two-phase flows in porous media. Mid-ocean ridges form when viscous corner flow of the solid mantle focuses fluid toward a central ridge. Melt is believed to migrate upward until it reaches the lithospheric "tent" where it then moves toward the ridge in a high porosity band. Simulation of this physical phenomenon required confidence in numerical methods to handle highly heterogeneous porosity as well as the single-phase to two-phase transition. In this work we present a standard mixed finite element method for the equations of mantle dynamics and investigate its limitations for vanishing porosity. While stable and optimally convergent for porosity bounded away from zero, the stability estimates we obtain suggest, and numerical results show, the method becomes unstable as porosity approaches zero. Moreover, the fluid pressure is no longer a physical variable when the fluid phase disappears and thus is not a good variable for numerical methods. Inspired by the stability estimates of the standard method, we develop a novel stable mixed method with uniqueness and existence of solutions by studying a linear degenerate elliptic sub-problem akin to the Darcy part of the full model: [mathematical equation], where a and b satisfy a(0)=b(0)=0 and are otherwise positive, and the porosity φ ≥ 0 may be zero on a set of positive measure. Using scaled variables and mild assumptions on the regularity of φ, we develop a practical mass-conservative method based on lowest order Raviart-Thomas finite elements. Finally, we adapt the numerical method for the sub-problem to the full system of equations. We show optimal convergence for sufficiently smooth solutions for a compacting column and mid-ocean ridge-like corner flow examples, and investigate accuracy and stability for less regular problems