It is well known that the geoid is affected by the deformation of all
interfaces associated with a change in density. While the two major
interfaces of Earth, its surface and its core-mantle boundary, are
relatively easy to account for, the contribution of internal interfaces,
such as the discontinuities at 410 and 660 km depth, is more difficult
to model. The aim of this project is to implement a method for taking
into account the effects of internal deformations on the geoid and
dynamic topography of Earth.
Possible extension for Master's thesis:
Impact of the imposed surface velocities on dynamic topography and Geoid
The forward/inverse modelling of mantle circulation is done via the
imposition of surface velocities derived from a paleo-reconstruction
of the plates. However, the theoretical geoid is modelled by a pseudo-analytical method, which
assumes a free-slip boundary condition at the top surface. These calculations do not take into account the impact of the moving plates on the top boundary and are not capable of producing the toroidal component of the velocities. Thus, it is reasonable to assume that the dynamic topography obtained from these
models will differ from the dynamic topography produced by Earth's mantle. The main goal of this
project is to modify the existing numerical code to account for the plate velocities at the top surface and to perform comparisons between the classical and the new implementation.
Geoid and dynamic topography are important observables that can be used to test numerical models of mantle convection against real world data. There are elegant mathematical procedures for the calculation of the Geoid from the governing Stokes equations, and we use these on a regular basis to test our numerical models against reality. As of yet, these procedures assume an incompressible mantle, which is a limitation that we would like to overcome. In this project, compressibility would be implemented into an existing C++-code and its effects would be investigated.
Estimates of the present-day temperature field within Earth's mantle are required to reconstruct the evolution of mantle flow backwards in time. This information can be derived from seismic tomography models together with thermodinamically self-consistent models of mantle mineralogy. In addition to the uncertainties and approximations of mineralogy models, the estimation is complicated by the fact that the velocity-to-temperature relation is not bijective: due to the presence of phase transitions, different temperatures can result in the same seismic velocity. Possible projects include: a general review of mantle mineralogy models; a more in-depth comparison of the main models, their differences, and their significance in terms of mantle dynamics (including simple simulations); and the development of an algorithm to automatically choose the most likely temperature when multiple choices are possible.
In mantle convection simulations the stationary flow field is described by a Stokes-type system which strongly depends on the underlying, potentially highly discontinuous viscosity profile. Thus, deriving robust and efficient solvers for this system can be very challenging. In order to improve our numerical methods we plan to set-up a new benchmark scenario. First we want to define a suitable radial viscosity profile. Next, a semi-analytic solution, i.e. a flow field u can be computed based on an propagator matrix method. With this solution at hand, we can verify our numerical solver. Furthermore, we want to compare this semi-analytic flow field against a second solution from our numerical solver that is obtained by a novel, potentially more efficient approach. Possible tasks for the student include 1) literature review about benchmarks for Stokes system with variable viscosity; 2) construction of suitable viscosity profiles (e.g., including a jump and local oscillations with variable amplitude and wavelength); 3) minor modification and systematic application of the numerical testbed (HHG); and 4) comparison between numerical and semi-analytic solution and 5) additionally generate and compare a computationally more efficient approximate (in a numerical sense) solution to the exact numerical and semi-analytic solutions.
Seismological observations represent the largest dataset used to constrain present-day mantle structure. The arrival times of direct body-waves play an important role, as they have been measured (i.e., picked) for many decades now using millions of seismic recordings of many thousands of earthquakes. The picked arrival times represent the ray-theoretical traveltimes of the waves according to Fermat's principle and they have been used in many tomographic inversions for mantle structure. Alternatively, one can use them to assess mantle models derived from dynamic flow calculations. In this project, the available seismic datasets should be used to test existing mantle circulation models. To this end, the seismic observations need to be collected from the relevant datacenters. In addition, ray-tracing through the geodynamic model will be performed for as many earthquakes as possible to obtain an equivalent synthetic dataset for comparison to the observations.
Today, a variety of numerical techniques exists to compute full waveform seismograms for 1-D Earth structures on a global scale. The three software packages of interest here all follow rather different approaches leading to significant differences in computational requirements. In case of special setups (e.g., huge numbers of seismograms for each earthquake) it is not clear upfront, which of the methods will be best suited. The project will concentrate on comparing the results of the three methods in terms of similarity of the waveforms as well as in terms of memory and runtime requirements.
We have recently developed a new 2-D mantle convection testbed in modern Fortran. The two-dimensional nature of the calculations results in low computational requirements even at high grid resolutions. Thus, a large range of scenarios for the convection in the mantle can be simulated. The project aims at visualizing the simulations and creating movies of convection over time for various combinations of input parameters. The resulting images and movies are intended to be used in lectures and scientific talks.
Determining the Earth's heat budget and heat production is critical for understanding plate tectonics, mantle convection and the thermal evolution of the Earth. The main possible sources of heat inside the Earth are well understood: radiogenic heat in the crust, mantle and possibly the core and secular cooling of the core and mantle. However, their relative importance is highly unknown and still debated, due to the lack of primary observations. Moreover, the total surface heat flux is not very well known, with recent estimates ranging between 40 and 50 TW. Different assumptions lead to different dynamic regimes for both present-day and past Earth's convection. This thesis project aims at exploring different scenarios of Earth's heat budget.