Traveltimes of waves in three-dimensional random media

We present the results of a comprehensive numerical study of 3-D acoustic wave propagation in weakly heterogeneous random media. Finite-frequency traveltimes are measured by cross-correlation of a large suite of synthetic seismograms with the analytical pulse shape representing the response of the background homogeneous medium. The resulting 'ground-truth' traveltimes are systematically compared with the predictions of linearized ray theory and 3-D Born-Fréchet (banana-doughnut) kernel theory. Ray-theoretical traveltimes can deviate markedly from the measured cross-correlation traveltimes whenever the characteristics scalelength of the 3-D heterogeneity is shorter than half of the maximum Fresnel zone width along the ray path, i.e. whenever a ≲ 0.5(λL)1/2, where a is the heterogeneity correlation distance, λ is the dominant wavelength of the probing wave, and L is the propagation distance. Banana-doughnut theory has a considerably larger range of validity, at least down to a ≈ 0.1 (λL)1/2 in sufficiently weakly heterogeneous media, because it accounts explicity for diffractive wave front healing and other finite-frequency wave propagation effects.