I am currently working on my BSc (Hons) in Geophysics after completing a BSc in Mathematics and Geophysics at the University of Auckland. My research is in resonant ultrasound spectroscopy with Dr Kasper van Wijk

In this non-destructive method of testing we measure the resonant frequencies of rock samples and perform an inversion to calculate the elastic properties. We are looking at shale samples in order to characterise their seismic anisotropy. This is of significant interest to the energy industry as there is currently a huge growth in shale as a reservoir rock (shale gas) as oppose to its traditional role as a seal/cap rock. Understanding the anisotropy in shales can help to better characterise reservoirs and result in more accurate images of the sub-surface.

Original experimental apparatus. We have since improved our setup and no longer use three rubber bands and a paper clip to hold it together.

Earlier in my undergraduate studies, I worked with Dr Claire Postlethwaite looking at delay differential equations (DDE’s). A DDE is an equation in which the rate of change of some quantity depends on the value of that quantity at some previous time (the delay). The delay introduces a new level of complexity to the analysis as it makes the system infinitely dimensional and thus an initial history function is required rather than an initial condition to solve the equation. We looked at using delay Pyragas type feedback control to stabilise unstable periodic orbits close to Hopf and homoclinic bifurcations.