ON THE EFFECT OF DIFFRACTION ON TRAVEL-TIME MEASUREMENTS

All observed waves are of finite frequency and are sensitive to a fini te volume of the medium through which they pass. Diffraction causes a loss of information about time contained in the initial front of a wav efield (often referred to as wavefront healing). This effect depends u pon frequency and propagation distance and imposes a low-pass filter o n the spatial resolution of time measurements. A sequence of canonical , numerical experiments that simulate the diffraction of a perturbed p lane wave at a fixed distance is described. Traveltimes are measured u sing a variety of techniques on a range of waveforms. It is empiricall y verified that a single Fresnel zone describes the spatial filtering effect of the propagation of a broad-band wavefield, even in the regim e where the initial time perturbation cannot be represented by a linea r perturbation term. For narrow-band wavefields, more Fresnel zones co me into play as the bandwidth is reduced. Measurements of time include a component of signal-generated noise coherent over a small scale whi ch scales with the Fresnel zone. It is found that, for traveltimes mea sured by automated picking, the width of the Fresnel zone is described by a time delay of \delta t\ < T/4 (here T is one period). On the oth er hand, the width of the Fresnel zone for traveltimes measured by cor relation is wider, characterized by a time delay of \delta t\ < T/4.