Simulations of Convection in the Earth's Mantle-Crust System

Principal Investigator

Louis Moresi

Geophysical Fluid Dynamics

Research School of Earth Sciences

The rocky outermost 3000km the earth is predominantly solid, but the constituent minerals deform over geological time in response to thermal and compositional buoyancy forces. Modeling of the flow is not simple, however, because the viscosity of the rocks is very strongly dependent on temperature, pressure, stress, composition. Furthermore, the mantle can only be studied using very indirect observations such as gravity and deformation of the Earth's surface. This project takes a two-pronged approach to the problem: (1) development of robust new algorithms for dealing with flows with strongly variable, non-linear rheology, (2) running simulations of particular mantle processes. This year, the Power Challenge was used mainly for simulation of upwelling plumes of mantle material such as that which is believed to be responsible for creating the Hawaiian Islands

Co-Investigators

David Osmond

Department of Physics

The Faculties

Projects

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What are the results to date and the future of the work?

The simulations this year were mainly performed by David Osmond as part of the work for his honours project. David developed an analytic scaling theory for the shape of hot, buoyant material rising beneath the moving surface of a very viscous fluid. His project involved using this theory to provide a new constraint on the mantle viscosity by comparing his results with similar structures in the Earth such as the Hawaiian plume. This viscosity is difficult to measure in the lab because the materials deform at very high temperatures and pressures and at very low strain rates. The viscous stresses resulting from the plume flow generate uplift of the surface which can be compared to the seafloor topography around the Hawaiian Island chain and thereby used to constrain the model parameters.

We ran a number of large scale, three dimensional simulations varying the volume flux of hot material into the system and the velocity of the surface motion. A certain amount of care was required in obtaining consistent boundary conditions and developing a grid refinement which could resolve the important features of the plume. In particular, we were interested in the way the hot material spreads sideways as it is swept downstream, and the extent to which it spreads upstream.

The results allowed us to evaluate the scaling theory and determine that the upstream flow was more complicated than assumed in deriving the analytic model. The downstream spreading was better understood and allowed us to begin to constrain the upper limit of the Hawaiian plume flux.

In a sense, however, this work is preliminary because we have concentrated on verifying the

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scaling theory, and have neglected a number of important effects present in the Earth. We entirely neglected the presence of the cold thermal boundary layer of the mantle (the Pacific tectonic plate, in the case of Hawaii) effectively we assumed a perfectly rigid, insulating plate at the surface. We also simplified the rheological model to better match that of the analytic theory. We are currently evaluating the effect of these simplifications and anticipate running further models to obtain a best-fit model for the Hawaiian plume.

In the more distant future, it would be useful to compute the melt production for plumes which fit the topography/gravity constraints. This would be a useful result because there are large-scale international efforts devoted to understanding the sequences of erupted magmas at Hawaii. These generally assume a very, very simple model of the thermal structure in the mantle.

Figure 1. Image of a plume (light grey material) impinging on the underside of a plate moving in the direction of the arrow. Material is injected into the base of the computational domain (3D arrow) where it rises under its own buoyancy until being swept downstream under the plate.

What computational techniques are used?

We used the code CITCOM which has been in active development by Louis Moresi for a number of years. It is a 3D finite element code which uses iterative multigrid methods to obtain fast, accurate solutions to the Stokes' flow equations relevant to mantle convection. The code has been demonstrated to be highly accurate for very strongly variable viscosities. Much of the development this year has been on extending the multigrid solver to work with highly non-linear and pseudo-plastic rheologies which are commonly found in Earth systems.

Publications

D. Osmond, The Shape of Mantle Plumes Under Moving Plates, ANU honours thesis, 1996.