Surface-wave group-delay and attenuation kernels

We derive both 3-D and 2-D Fréchet sensitivity kernels for surface-wave group-delay and anelastic attenuation measurements. A finite-frequency group-delay exhibits 2-D off-ray sensitivity either to the local phase-velocity perturbation δc/c or to its dispersion ω(∂/∂ω)(δc/c) as well as to the local group-velocity perturbation δC/C. This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of δC/C a dubious procedure, unless the lateral variations in group velocity are extremely smooth.