Traveltimes of waves in three‐dimensional random media

SUMMARY 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(λ L ) 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(λ L ) 1/2 in sufficiently weakly heterogeneous media, because it accounts explicitly for diffractive wave front healing and other finite‐frequency wave propagation effects.