Adjoint sources and sensitivity kernels of a receiver function waveform misfit

In global seismology, receiver functions are used to detect large, near-receiver discontinuities. A receiver function is the deconvolution of the radial with the vertical component. They detect similar patterns in the two components and are sensitive to P-to-S conversions and reflections, particularly those that convert or reflect near the receiver. Our objective is to determine the receiver function sensitivity in global seismic data to image near-receiver structure and topography on mantle discontinuities. To find the Fréchet derivatives, we derive the adjoint source for a simple least-squares receiver function waveform misfit. We calculate the sensitivity kernels for a synthetic example, using PREM (as a reference model) and two slightly modified versions of PREM (as synthetic 'data'). For one modified PREM model we added topography on the discontinuity, for the other a 3D-velocity model in the mantle. We focus on the P-to-S wave converted at the 660-discontinuity (P660s). The P, S and density sensitivity kernels show a complex dependency throughout the mantle, with the strongest sensitivity to the (scattered) primary wave, its free-surface reflections and other reverberation in the upper mantle. Additionally, the boundary sensitivity kernels for topography are calculated. The boundary kernels have the strongest sensitivity near the conversion point region, as well as some sensitivity to the primary wave scatterers. The results indicate that receiver functions are sensitive to the primary wave field scatterers and to the Fresnel zone of the P660s-phase. They also indicate that a change in velocity far from the conversion point and a change in topography of the discontinuity can have similar effects on the misfit.