Fréchet kernels for body-wave amplitudes

We derive a 3D Fréchet sensitivity kernel relating the rms amplitude of a far-field, broad-band body-wave pulse to laterally heterogeneous seismic slowness variations within the earth. Unlike the 'banana–doughnut' sensitivity kernel for a cross-correlation traveltime, the amplitude Fréchet kernel for a turning wave is maximally sensitive, rather than completely insensitive, to the 3D slowness perturbation along the central source-to-receiver ray. In the asymptotic limit of an infinite-frequency pulse, our 3D amplitude kernel formulation is consistent with the dominant 1D integral involving the cross-path curvature of the slowness perturbation along the unperturbed geometrical ray.