Wavefield smoothing and the effect of rough velocity perturbations

S U M M A R Y Geometr ic ray theory is a n extremely efficient tool for modelling wave propagat ion through heterogeneous media. Its use is, however, only justified when the inhomogeneity satisfies certain smoothness criteria. These criteria a re often n o t satisfied, for example in wave propagat ion through turbulent media. I n this paper , the effect of velocity per turbat ions o n the phase a n d ampli tude of transient wavefields is investigated for the situation tha t the velocity per turbat ion is not necessarily smooth enough t o justify the use of ray theory. It is shown tha t the phase a n d ampli tude per turbat ions of transient arrivals can to first o rder be written as weighted averages of the velocity per turbat ion over the first Fresnel zone. The resulting averaging integrals are derived for a homogeneous reference medium as well as for inhomogeneous reference media where the equat ions of dynamic ray tracing need t o be invoked. T h e use of the averaging integrals is illustrated with H numerical example. This example also shows tha t t h e derived averaging integrals form a useful starting point for further approximat ions. The fact t h a t the delay time due t o t h e velocity per turbat ion can be expressed as a weighted average over the first Fresnel zone explains the success of tomographic inversions schemes that a re based on ray theory in situations where ray theory is strictly not justified; in that situation o n e merely collapses the t rue sensitivity function over t h e first Fresnel zone t o a line integral a long a geometric ray.