Three-dimensional sensitivity kernels for surface wave observables

We calculate three dimensional (3-D) sensitivity kernels for fundamental-mode surface wave observables based on the single-scattering (Born) approximation. The sensitivity kernels for measured phases, amplitudes and arrival angles are formulated in the framework of surface wave mode summation. We derive kernels for cross-spectral multitaper measurements; as a special case, the results are applicable to single-taper measurements. Cross-branch mode-coupling effects are fully accounted for in the kernels; however, these effects can probably be ignored at the present level of spatial resolution in global phase-delay tomography. The narrowly concentrated spectra of the windows and tapers commonly used in global surface wave studies enable the kernels to be computed extremely efficiently.