Maarten de Hoop

 

It is often useful to treat planets as geometric objects where the geometry is defined so that the distance is measured as the travel time of seismic waves. This definition turns a planet into a Riemann or Finsler manifold with boundary. The propagation of seismic waves on rocky planets is well modelled by the geodesic flow on such a manifold, noting that the speeds of seismic waves remain bounded below up to the boundary. On gas giants, however, the (acoustic) wave speed goes to zero at the boundary, at a specific range of rates, which has a significant impact on the geometry. In fact, this property leads to a subset of conformally compact geometry. The curvature is unable to stay bounded and the boundary is a fractal in the sense of Hausdorff dimension. We present the acoustic-gravitational system of equations describing seismology, elements of the relevant geometry and show the presence of a discrete spectrum consistent with observations through Saturn's ring seismology. Moreover, we discuss some results pertaining to tomography on gas giants.

 

Joint research with J. Ilmavirta, A. Kykk\"{a}nen and R. Mazzeo