# BSc/MSc projects

**Bachelor and Master's thesis topics in Geodynamics**

**Benchmarking numerical methods for the Stokes system with****local variable viscosity in radial direction**(Level: Bachelor/Masters; Contact: 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.

**P-wave anisotropic tomography of the whole Pacific Ocean**(Level: Bachelor/Masters; Contact: Jincheng Ma)

P-wave anisotropy tomography is a new but powerful tool for mapping three-dimensional variations of azimuthal and radial seismic anisotropy in the Earth’s interior. Seismic anisotropy is a very useful and important physical parameter, because it can provide a wealth of new information regarding dynamic processes in the crust and mantle. The Pacific plate, as the largest tectonic one, is the best place to study large-scale subduction dynamics and mantle plumes in the world because of the high level of seismicity and availability of the dense and high-sensitivity seismic networks from China, Japan, America, Australia, Chile and so on. In this project, the main goal is to clearly depict the geometry of kinds of subducting slabs and mantle plumes, and then discuss the depth-varying azimuthal anisotropy inside the mantle wedge, subducting slab and sub-slab mantle in different subduction zones. Possible tasks for student includes 1): Literature review about Seismic anisotropy and Ray-based tomography theory; 2): master the tomography code written in Fortran (very easy); 3): collect all available arrival-time data; 4): build 3-D tomography model. The final results are intended to be used in comparison with the near future full waveform tomography of the whole Pacific Ocean.

**Effect of debris cover on glacier dynamics**(Level: Bachelor/Masters, Contact: Christoph Mayer, christoph.mayer@keg.badw.de)

Debris cover affects the surface energy balance of glaciers, because debris either increases ice melt due to effective thermal conductivity, or inhibts melt by shielding the ice from solar radiation. However, this change in surface mass balance also has consequences on the dynamic state of the glacier, because variations in ice loss affect the geometry of the glacier itself. As debris is continuously evacuated from glacier ice, the debris distribution on the glacier surface is always in a transient state. This implies that debris covered glaciers are never able to reach a steady state, but are in a continuous adaptation state. We aim on investigating this system with a full-Stokes ice dynamic flow-line model (Elmer-Ice) by implementing the appropriate boundary conditions and run a series of different configurations in order to see the effect of debris on the ice-dynamic conditions. The numerical model is already established and the task of the candidate will be to implement a (already existing) melt model for debris covered ice. Then different set-ups of boundary conditions should be tested in order to cover the parameter space and investigate the potential transient glacier reactions. The results are highly relevant for region wide glacier studies, as these are at the moment based on steady state assumptions.

**Calculation of ray-theoretical arrival times of seismic body waves in mantle convection models**

(Level: Bachelor; Contact: Schuberth/Freissler)

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 data centers. 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 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. Three leading software packages in this regard are SPECFEM, YSPEC and AxiSEM that all follow rather different approaches. As a consequence, there are 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: 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.