  Using spectral-element and adjoint methods, we investigate body waves
interacting with the Earth's most dramatic interface, the core-mantle boundary
(CMB). Intermediate-to-high frequency seismograms are computed incorporating
topography models. We analyse the sensitivity of many seismic phases
interacting with the interface. The study aims at showing effects of CMB
structure on synthetics and highlights difficulties of imaging this region due
to strong trade-off between velocity variations and topography. Synthetic
waveforms computed at dominant periods of 6-18 seconds are used in order to
observe time shifts due to topography and calculate the adjoint sensitivity
kernel. We focus on diffracted, core reflected and refracted P and S waves. The
sensitivity kernel depicts first Fresnel zones of these phases and others that
may contribute to narrow time window, although unpredicted by ray theory. We
perform comparisons between time shifts due to topography models made on
full-waveform synthetics to ray theoretical predictions to assess methods
usually deployed for imaging CMB. This shows that for most phases ray theory
performs well enough with some accuracy loss. We propose that using relevant
seismic phases simultaneously in full-waveform inversion may improve CMB
topography imaging. However, it seems necessary to jointly invert for velocity
variations due to D\" layer, which is so far poorly understood and presents a
challenge when it comes to identifying its effects on traveltime data. In our
further research, a FWI workflow is being developed and aims at addressing
these issues.
