Sensitivity kernels for receiver function misfits in a full waveform inversion workflow

Receiver functions have been used for decades to study the Earth's major discontinuities by focusing on converted waves. Deconvolution, which is the mathematical backbone of the method, is assumed to remove the source time function and the far-field dependence on structure, making it a useful method to map the nearby Earth structure and its discontinuities. Ray theory, a plane incoming wavefield, and a sufficiently well-known near-receiver background velocity model are conventionally assumed to map the observations to locations in the subsurface. Many researchers are aware of the shortcoming of these assumptions and several remedies have been proposed for mitigating their consequences. Adjoint tomography with a quasi-exact forward operator is now within reach for most researchers, and we believe is the way forward in receiver function studies. A first step is to calculate adjoint sensitivity kernels for a given misfit function. Here, we derive the adjoint source for a receiver function waveform misfit. Using a spectral element forward code, we have calculated sensitivity kernels for P-to-S converted waves using several 2-D models representing an average crust with an underlying mantle. The kernels show profound differences between P- and S-wave speed sensitivity. The sensitivity to P-wave speed is wide-ranging and related to the scattered P-wavefield which interferes with that of the P-to-S converted wave. The S-wave speed sensitivity is more local and mostly associated to potential locations of P-to-S conversion, although more distant sensitivity is also observed. Notably, there is virtually no sensitivity to impedance. We further observe the well-known trade-off between depth of the discontinuity and wave speed, but find that considering a longer waveform that includes more surface reverberations reduces this trade-off significantly.

Automated summary

Receiver functions have long been used to study Earth's major discontinuities. The traditional assumptions for mapping locations in the subsurface have been found to have limitations, but the use of adjoint tomography provides a potential solution. Sensitivity kernels for P-to-S converted waves have been calculated, revealing differences in sensitivity to P-wave speed and S-wave speed. The well-known trade-off between depth of the discontinuity and wave speed has also been observed, but can be significantly reduced by considering longer waveforms that include more surface reverberations.