His research encompasses various aspects of solid-earth geophysics. More specifically, he studies the physical properties of the lithosphere, focusing on the elastic and thermomechanical properties of the continents, by seismic tomography and the spectral analysis of gravity and topography. With his colleagues, Frederik has developed mathematical methods for the analysis of processes on the sphere, for geodesy, geomagnetism, and cosmology, designed wavelet-based signal processing methods for seismology, and developed oceanic instrumentation to close the seismic coverage gap over the Earth's oceans.