On the effect of diffraction on traveltime measurements

All observed waves are of finite frequency and are sensitive to a finite volume of the medium through which they pass. Diffraction causes a loss of information about time contained in the initial front of a wavefield (often referred to as wavefront healing). This effect depends upon frequency and propagation distance and imposes a low-pass filter on the spatial resolution of time measurements. A sequence of canonical, numerical experiments that simulate the diffraction of a perturbed plane wave at a fixed distance is described. Traveltimes are measured using a variety of techniques on a range of waveforms. It is empirically verified that a single Fresnel zone describes the spatial filtering effect of the propagation of a broad-band wavefield, even in the regime where the initial time perturbation cannot be represented by a linear perturbation term. For narrow-band wavefields, more Fresnel zones come into play as the bandwidth is reduced. Measurements of time include a component of signal-generated noise coherent over a small scale which scales with the Fresnel zone. It is found that, for traveltimes measured by automated picking, the width of the Fresnel zone is described by a time delay of |δt| < T/4 (here T is one period). On the other hand, the width of the Fresnel zone for traveltimes measured by correlation is wider, characterized by a time delay of |δt| < T/4.