The effect of small-scale heterogeneity on the arrival time of waves

Abstract

Small-scale heterogeneity alters the arrival times of waves in a way that cannot by explained by ray theory. This is because ray theory is a high-frequency approximation that does not take the finite frequency of wavefields into account. We present a theory based on the first-order Rytov approximation that predicts well the arrival times of waves propagating in media with small-scale inhomogeneity with a length scale smaller than the width of Fresnel zones. In the regime for which scattering theory is relevant we find that caustics are easily generated in wavefields, but this does not influence the good prediction of finite frequency arrival times of waves by scattering theory. The regime of scattering theory is relevant when the characteristic length of heterogeneity is smaller than the width of Fresnel zones. The regime of triplications is independent of frequency but it is more significant the greater the magnitude of slowness fluctuations.