Diffraction effects upon finite‐frequency travel times: A simple 2‐D example

The widespread availability of broad‐band digital seismic data makes it possible to measure travel‐time anomalies by cross‐correlation with spherical‐earth synthetic seismograms. Finite‐frequency diffraction effects render such measurements sensitive to wave‐speed perturbations off of the infinite‐frequency geometrical ray path. We show, by consideration of a simple 2‐D example, that the Born approximation provides an excellent description of these off‐path sensitivity effects, in the absence of caustics and for travel‐time shifts that are small compared to the wave period. Remarkably, an isolated low‐velocity anomaly may produce fringing fast travel‐time anomalies, as measured by cross‐correlation.