Wavefront healing: a banana-doughnut perspective

Wavefront healing is a ubiquitous diffraction phenomenon that affects cross -correlation traveltime measurements, whenever the scale of the 3-D, variat ions in wave speed is comparable to the characteristic wavelength of the wa ves. We conduct a theoretical and numerical analysis of this finite-frequen cy phenomenon, using a 3-D pseudospectral code to compute and measure synth etic pressure-response waveforms and 'ground truth' cross-correlation trave ltimes at various distances behind a smooth, spherical anomaly in an otherw ise homogeneous acoustic medium. Wavefront healing is ignored in traveltime tomographic inversions based upon linearized geometrical ray theory, in as much as it is strictly an infinite-frequency approximation. In contrast, a 3-D banana-doughnut Frechet kernel does account for wavefront healing beca use it is cored by a tubular region of negligible traveltime sensitivity al ong the source-receiver geometrical ray. The cross-path width of the 3-D ke rnel varies as the square root of the wavelength lambda times the source-re ceiver distance L, so that as a wave propagates, an anomaly at a fixed loca tion finds itself increasingly able to 'hide' within the growing doughnut ' hole'. The results of our numerical investigations indicate that banana-dou ghnut traveltime predictions are generally in excellent agreement with meas ured ground truth traveltimes over a wide range of propagation distances an d anomaly dimensions and magnitudes. Linearized ray theory is, on the other hand, only valid for large 3-D anomalies that are smooth on the kernel wid th scale root lambdaL. In detail, there is an asymmetry in the wavefront he aling behaviour behind a fast and slow anomaly that cannot be adequately mo delled by any theory that posits a linear relationship between the measured traveltime shift and the wave-speed perturbation.