Project description
This project applies a methodological framework that has driven seismic exploration since the 1980s. It has not yet been applied to MHD models of the Earth's outer core. Wave propagation through a heterogeneous medium can be treated as a perturbation problem: a chosen smooth `background' produces a reference wave field, and the deviation from this background acts as a `scattering potential' that produces additional, smaller scattered waves. At leading order in the perturbation strength (the Born approximation), the scattered field is linear in the deviation, and the inverse problem of recovering the deviation from observations becomes mathematically tractable.
The project transfers this framework from seismology to the linearised wave system that has been proposed as the mechanism for geomagnetic jerks (rapid changes in the geomagnetic field). The mathematical work is to linearise the rotating MHD equations around a smooth symmetric background magnetic field, identify the resulting scattering potential, derive the corresponding wave Green's function (the response of the medium to a point source) and the Born-approximation forward operator, and construct the adjoint imaging operator that turns observed data into a reconstructed image of the medium. A key piece of theoretical work is to check whether the symmetry properties on which standard seismic-imaging theory relies still hold here: the Coriolis force changes the symmetry of the wave operator in a way that requires careful examination rather than direct transfer. The first part is spent reproducing a benchmark from the seismic-imaging literature, the imaging response (point-spread function) for a point scatterer on a homogeneous background, which characterises the spatial resolution of the imaging operator.
The scientific outcome is a linearised inverse-imaging framework for the heterogeneity of the deep internal magnetic field, applied to vector measurements at long-running geomagnetic observatories during the well-recorded jerk events. The wave source is assumed known (using estimates from existing inversions); the imaging target is the magnetic-field structure of the medium itself. If time permits, the framework can be extended to stronger heterogeneity (using higherorder versions of the Born expansion) and to joint inversion for both source and medium simultaneously, in the spirit of seismic full-waveform inversion.
The student taking on this project needs to have a bachelor degree in geophysics, or equivalent.