Frechet kernels for finite-frequency traveltimes - II. Examples

3-D Born-Frechet traveltime kernel theory is recast in the context of scala r-wave propagation in a smooth acoustic medium, for simplicity. The predict ions of the theory are in excellent agreement with 'ground truth' traveltim e shifts, measured by cross-correlation of heterogeneous-medium and homogen eous-medium synthetic seismograms, computed using a parallelized pseudospec tral code. Scattering, wave-front healing and other finite-frequency diffra ction effects can give rise to cross-correlation traveltime shifts that are in significant disagreement with geometrical ray theory, whenever the cros s-path width of wave-speed heterogeneity is of the same order as the width of the banana-doughnut Frechet kernel surrounding the ray. A concentrated o ff-path slow or fast anomaly can give rise to a larger traveltime shift tha n one directly on the ray path, by virtue of the hollow-banana character of the kernel. The often intricate 3-D geometry of the sensitivity kernels of P, PP, PcP, PcP2, PcP3, ... and P + pP waves is explored, in a series of c olourful cross-sections. The geometries of an absolute PP kernel and a diff erential PP - P kernel are particularly complicated, because of the minimax nature of the surface-reflected PP wave. The kernel for an overlapping P pP wave from a shallow-focus source has a banana-doughnut character, like that of an isolated P-wave kernel, even when the teleseismic pulse shape is significantly distorted by the depth phase interference. A numerically eco nomical representation of the 3-D traveltime sensitivity, based upon the pa raxial approximation, is in excellent agreement with the 'exact' ray-theore tical Frechet kernel.