P. E. van Keken

A comparison of methods for the modeling of thermochemical convection

We have compared several methods of studying thermochemical convection in a Boussinesq fluid at infinite Prandtl number. For the representation of chemical heterogeneity tracer, marker chain, and field methods are employed. In the case of an isothermal Rayleigh-Taylor instability, good agreement is found for the initial rise of the unstable lower layer; however, the timing and location of the later smaller-scale instabilities may differ between methods. For a simulation of entrainment by thermal convection of a dense layer at the bottom of the mantle we found good agreement for a few overturn times. After this, differences between the results can be large. We propose intrinsic differences between the methods and possibly chaotic mixing effects may be the cause of the lack of detailed agreement. The comparison shows that high resolution is necessary for a reasonable thermochemical study. This will pose severe restrictions on the applicability of these methods to three-dimensional situations.

Dynamical models of mantle volatile evolution and the role of phase transitions and temperature-dependent rheology

Helium isotopic variations demand the preservation of a primitive volatile source for ocean island basalts (OIB) in conjunction with a well-mixed and more radiogenic source for mid-oceanic ridge basalts (MORB). Dynamical models of the Earths evolution should be able to predict this basic geochemical observation. We have developed a number of increasingly more realistic models of mantle convection that satisfy present-day heat loss and plate velocities to study the eects of convective mixing, radiogenic ingrowth, and degassing on the mantle 3 He/ 4 He evolution. We have included mechanisms that have been proposed to enhance the isolation of individual reservoirs in the mantle such as high lower mantle viscosity, strongly temperature- and pressure-dependent rheology, and an endothermic phase transition at 670 km depth. Although the combination of these mechanisms can produce regions of lower mixing eciency, our models cannot satisfactorily explain the existence of two distinct OIB and MORB 3 He= 4 He sources. If further improvements to the model, such as simulated plates and continents, still fail to explain the geochemical constraints, it may be prudent to consider sources of primitive helium beyond the current paradigm requiring them to be stored within the terrestrial mantle since early in the Earths history.

Rheological control of oceanic crust separation in the transition zone

Mineral physics observations suggest that distinct density and rheological differences exist between the crustal component of oceanic lithosphere and the underlying mantle. We have conducted numerical experiments to investigate the influence of both density and viscosity on the effectiveness of recycling of oceanic crust into the lower mantle. Confirming previous results, the density inversion at 670 km depth alone is not sufficient to prevent crustal recycling. However, a soft layer may exist between the strong garnet crust and cold slab interior. Models employing a simplified Newtonian sandwich model show that this thin, weak layer can effectively decouple the crust and slab. Once entrained into the lower mantle, the then lighter crust can rise sufficiently fast as a Rayleigh-Taylor instability to avoid further entrainment. These results suggest that the crustal component of slabs may be trapped at 670 km depth, leading to a garnet enriched transition zone.

Deep storage of oceanic crust in a vigorously convecting mantle

[1] Fractionated isotopic ratios in some oceanic basalts indicates the presence of recycled oceanic crust in the mantle. This crust must have escaped complete remixing for a significant period of time. Gravitational settling into a dense layer at the base of the mantle may facilitate this preservation. Christensen and Hofmann (1994) first demonstrated the dynamics of this process by developing scaling laws for extrapolating low convective vigor models to conditions estimated for the mantle. Here this sequestration is studied in models with more Earth-like convective vigor. Scaling laws for geodynamic parameters are updated and the isotopic evolution of the U-Pb and Sm-Nd systems examined. Significant accumulation is still found at high Rayleigh number, but only when the excess density of oceanic crust in the lower mantle is larger than currently suggested from laboratory experiments. These accumulations are found to maintain the fractionated isotopic signature of ancient crust for models with moderate to moderately high convective vigor relative to mantle estimates. At the highest convective vigor tested, the accumulations are not isotopically distinct.

GeoWall: Stereoscopic visualization for geoscience research and education

The GeoWall lets people visualize the structure and dynamics of the Earth in stereo, aiding their understanding of spatial relationships. Making use of inexpensive, polarized 3D glasses, entire classrooms or conference audiences can share the 3D experience. Since the hardware is portable, its easy to bring visualizations to the audience. In this article we describe the GeoWall hardware and software and discuss how the GeoWall Consortium was instrumental in creating a community of users in a variety of disciplines. Using case studies, we show how the GeoWall helped research and education. Finally, we describe our recent work in high-resolution tiled displays

DASPK: A new high order and adaptive time-integration technique with applications to mantle convection with strongly temperature-and pressure-dependent rheology

Abstract A new technique is presented for the efficient time-integration of the equations that describe the slow deformation in the Earths mantle. This method is based on the adaptive, high order implicit solver for differential-algebraic equations (DASPK) and is independent of the choice of spatial discretization technique. Using a standard finite element package for the spatial discretization, it is shown that the solution of the 2-D convection-diffusion equation for temperature can be performed at much lower computational cost, but at the same or higher accuracy, compared to a traditional implicit second-order method. The solution to the full set of 2-D mantle convection equations is 3 to 4 times more efficient. Both in 2-D and 3-D, the memory and CPU-usage of this implementation depends linearly on the number of grid points and has good properties with respect to vectorization and parallelization. As an application of this technique, convection in the Earths mantle with strongly temperature and pres...

Convective mixing in the Earth's mantle

This chapter focuses on the use of mantle convection modeling in the development of our understanding of the chemical evolution of the Earth by providing a short review of the main observations, a discussion of the physical approaches to characterize mantle mixing, and an overview of the historical and current modeling approaches to the formation, preservation, and destruction of chemical heterogeneity.

2.12 – Convective Mixing in the Earth's Mantle

cp heat capacity dx distance between two points after time t dX original infinitesimal distance between two points D stretching tensor Di dissipation number ĝ gravity vector h depth of convecting layer H(r) two-particle correlation function P dynamic pressure Ra thermal Rayleigh number t time T temperature ui components of the velocity tensor v velocity w upward velocity a thermal expansivity _ e strain-rate tensor em mixing efficiency h dynamic viscosity k thermal diffusivity l Luyaponov exponent m infinitesimal stretching length