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# BSc and MSc Projects

Bachelor and Masters thesis topics in geodynamics 2016

• Calculation of the geoid and dynamic topography for an internally deforming Earth
(Level: Bachelor/Masters; Contact: Colli/Ghelichkhan/Schuberth)

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.

• Calculation of the geoid and dynamic topography in compressible Earth models
(Level: Bachelor; Contact: Ghelichkhan)

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.

• Seismic anomalies, temperature anomalies and mineral physics
(Level: Bachelor/Masters; Contact: Colli/Ghelichkhan/Schuberth)

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.

• Dynamics of the asthenosphere and pressure flow between infinite plates
(Level: Bachelor/Masters; Contact: Colli)

The dynamics of a thin and low-viscosity asthenosphere can be approximated via pressure (Poiseuille) flow between two parallel and infinite plates. Sources of overpressure are large-scale upwellings and mantle plumes, while sinking slabs generate regions of low pressure. Analytical solutions for simple Cartesian 2-D geometries with translational symmetry are well known, and can be used to explore the role of subduction. This type of solution, however, is not a very good approximation for the role of plume heads, which can be better studied in cylindrical symmetry. This thesis project will involve the study of 2-D solutions in translational symmetry (Bachelor level) or the derivation and study of new analytical or numerical solutions in cylindrical symmetry (Master level).

• Benchmarking numerical methods for the Stokes system with local variable viscosity in radial direction
(Level: Bachelor/Masters; Contact: Bauer/Mohr)

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.

• Calculation of ray-theoretical arrivals times of seismic body waves in mantle convection models
(Level: Bachelor; Contact: Schuberth)

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.

• Comparison of SPECFEM3D, YSPEC and AXISEM seismograms for synthetic 1-D Earth models
(Level: Bachelor/Masters; Contact: Schuberth)

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.

• Visualization of 2-D and 3-D convection for educational and scientific purposes
(Level: Bachelor/Masters; Contact: Schuberth/Mohr)

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.

• Earth's heat budget
(Level: Bachelor/Masters; Contact: Colli/Schuberth)

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.

• Chaos in mantle convection
(Level: Masters; Contact: Colli)

Convection in the Earth's mantle is chaotic, and a little error in the initial state is bound to grow exponentially and lead to a completely uncorrelated state. In this projects, the importance and evolution of different types of error will be assessed and compared.

• Seismological constraints for oceanic plate stresses, driving forces and rheology
(Level: Masters; Contact: Colli/Bunge)

In a couple of outstanding papers, Seth Stein and coworkers pointed out that the source parameters of intraplate seismicity within the oceanic lithosphere provide valuable information about the stress in the lithosphere, plate tectonic forces, and the rheology of the lithosphere and of the asthenosphere. The project aims at repeating the analysis of Stein et al. with new data from the global seismic catalogues.

• Volatile diffusion, bubble nucleation and bubble growth in high viscosity fluids
(Level: Bachelor/Masters; Contact: Colli, in collaboration with people from the volcanology section: Don Dingwell, Corrado Cimarelli, Fabian Wadsworth, Laura Spina)

Although bubble nucleation and growth in decompressing magmas is a key driving mechanism of volcanic eruptions, degassing phenomena and their link with the wide variety of eruptive styles observed during volcanic activity still remain quite enigmatic. We can provide a variety of possible bachelor and master projects ranging from literature reviews to the refinement of analytical solutions to numerical modeling; topics include e.g.: across-surface volatile diffusion, single bubble nucleation and growth in newtonian and non-newtonian fluids, bubble-bubble interaction, bubble-grain interaction, bubble deformation due to an externally imposed flow.