Traveltimes of waves in three-dimensional random media

Abstract

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-Frechet (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. In this paper, we conduct a comprehensive numerical investiga- tion of the validity of both linearized ray theory and 3-D Born- Frechet kernel theory in weakly heterogeneous random media. We use a pseudospectral method to solve the 3-D acoustic wave equation in a suite of Gaussian and exponentially correlated random media, characterized by their root-mean-square slowness variation and their correlation scalelength. Finite-frequency traveltime shifts are mea- sured at a variety of source-receiver distances, by cross-correlation of the numerically computed synthetic seismograms with the cor- responding analytical response of the background homogeneous medium. This study extends the analyses of Nolet & Dahlen (2000) and Hung et al. (2001), who investigated the wave front healing effects downstream of an isolated, slow or fast, spherically sym- metric slowness anomaly using the parabolic approximation and the pseudospectral method, respectively. In a statistically homoge- neous random medium, the diffractive healing of wave front corru- gations produced by near-source slowness anomalies is continually being augmented by new corrugations produced by more distant anomalies, as the wave propagates away from the source. Because of this, a ray-theoretical skeptic might argue that conclusions based upon the study of a 'lonely bowling ball' are not pertinent to seis- mic wave propagation in the Earth's mantle. Spetzler & Snieder's (2001b) study of picked traveltimes of plane waves in 2-D random media shows that, for their case, Rytov scattering theory predicts traveltimes more accurately than ray theory. Similarly, we use our 'ground-truth' numerical results to place empirical constraints upon the validity of both linearized ray theory and 3-D Born-Frechet ker- nel theory in spatially extended 3-D random heterogeneous media.