How hot is the bottom of Earth’s mantle?

Can you combine geophysics, fluid dynamics and mineralogy to construct a deep-Earth thermometer and better constrain Earth’s energy budget?

Convection in Earth’s rocky mantle controls the long-term evolution of the planet, drives surface tectonics and is intimately linked to planetary habitability. It also permits magnetic field generation by cooling the liquid iron outer core. At first sight the fluid dynamics of mantle convection appears quite simple as the high viscosity implies that flow is not turbulent, although it is chaotic. The rich and complex dynamics exhibited by Earth, and the other terrestrial planets, arise because the physical properties that characterise mantle materials, and in particular the rheology, are enormously sensitive to small changes in temperature, pressure and composition. The complex feedbacks between mantle physical properties and mantle flow are most prevalent in the uppermost and lowermost boundary layers of the mantle, and it is the rheology in these regions that is largely responsible for the diversity of planetary behaviour and evolution. In this project you will make use of a range of geophysical observations and models to constrain the thickness, lateral variability and temperature of the lower boundary layer of the mantle. You will then use this information to probe the evolution of the planet.

In this project you will make use of two complimentary approaches designed to constrain the temperature of the lowermost few hundred kilometres of the mantle. The first will involve the further development and use of a new low-resolution model of the lower mantle, which we call LEMA. This Earth model is designed to simulate the properties and dynamics of the lower mantle based on proposed models of its temperature and composition making use of self consistent mineral physics to translate these input parameters into descriptions of the mantle’s elasticity and density. These can be compared with models derived from seismic tomography, and with other constraints such as observations of the long-wavelength surface gravity field and of the shape of the core-mantle boundary. One of the major advantages of our approach is its high performance: an Earth model can be created and compared to the full gamut of observations in less than a third of a second. This leads to the ability to make use of LEMA in a Bayesian approach where very large numbers of models are randomly constructed and compared with observations in order to generate a statistical view of the range of possible temperature distributions in the lower mantle that are consistent with the observations, and with what is know of the physical properties of mantle minerals. Our initial experience of LEMA is that it is capable of placing robust constraints on the radial structure of the thermal boundary layer at the base of the mantle, but further work remains to examine lateral variability in this layer.

The second approach will involve a more detailed analysis of the behaviour of boundary layers in mantle-like dynamical systems. Although the influence of depth-dependent material properties has been extensively analysed in models of 2D mantle convection, the way that rheological complexity, itself caused by temperature variation, alters this idealisation of mantle convection has not been subject to significant study. This part of the project will involve an analysis of the properties and behaviour of complex mantle-like systems. Starting with a simplified 2D analysis, you will explore convection in models with increasingly complex material properties using a combination of theoretical and numerical tools. This understanding will permit a numerical study of the 3D case where statistical measures of boundary layer behaviour can be compared with observations of the Earth, and boundary layer heat-flux can be used to explore the long-term evolution of the terrestrial planets.