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 characteristic 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 explicitly for diffractive wave front healing and other finite-frequency wave propagation effects.