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. ¿ 1998 American Geophysical Union