One of my more theoretical interests relates to how we create 3-D images of the earth's interior. Since we cannot drill more than a few kilometers into the earth, and we don't have rock samples from much below 100 km below the surface, we must rely on information gleaned from seismic waves to learn more about the earth's interior.
Different types of seismic waves travel along different paths within the earth. For example, teleseismic body waves, both compressional (P) and shear (S) waves, travel through the body of the earth. Surface waves, not too surprisingly, travel along the surface of the earth. Each of these types of waves have been used independently to create 3-D images of the earth. The process of creating these images is commonly known as "seismic tomography".
Seismic tomography is for the earth what a CAT scan is for humans. What we are actually measuring is the velocity with which a particular type of seismic wave travels through a particular volume of rock within the earth. To do this, we calculate how much time we think that wave should take to get from an earthquake to a particular location, and look at the difference between that "predicted travel time" and the actual "observed travel time".
We can also calculate the paths of each of these rays, so given enough seismic stations and enough earthquakes distributed around these stations, we can calculate what volumes in the earth are fast, and what volumes are slow. Resolution depends on the availability of stations, and the distribution of earthquakes. The first we have some control over, the second, very little...
What we can do, though, is combine different types of waves into a single 3-D model. For example, surface waves travel horizontally across the earth's surface, whereas teleseismic body waves are traveling nearly vertically as they approach the seismic station. That means that these two different types of waves have very complementary spatial resolution. I've recently been funded to develop a joint surface wave-teleseismic body wave methodology that would exploit the strengths of these two different types of data.
If this sounds like an interesting project to you, drop me an email. I'm currently looking for a graduate student to work on this project. I have funding for one year of support under my current grant, and have access to additional funding from the department as well. Once developed, this methodology can then be applied to a range of datasets, making for a great dissertation project for the right student. Oh, and did I mention Chapel Hill is a great place to live?