All of our observations that constrain the Earth's interior structure are made at the surface. Hence there is always an `inverse problem' in making use of indirect observations to perform inferences about the Earth at depth. Inverse problems occur in many areas of the Physical sciences, and it is the subject of on going research of how best to solve them.
In Geophysics many inverse problems are nonlinear, for example using seismic waveforms or travel times of waves to constrain the structure at depth. Recent research in the seismology group has led to a new fully nonlinear approach to certain types of inverse problem.
Projects are available in the study of nonlinear inverse problems and methods for their solution. Questions include: How do we best parametrize an inverse problem ? How do efficiently search large dimensional parameter spaces ? How do we handle severe nonlinearity ? Projects are likely to involve a combination of mathematics, advanced computation, and physics applied to a particular geophysical inverse problem.
Contact the supervisor directly for more information.