A laboratory and numerical study was conducted to investigate the impact of scale-dependent seismic wave propagation in randomly layered media, as applied to sonic logs, surface seismic, and vertical seismic profiles (VSPs). Analysis of the laboratory results (1) confirmed the wavelength dependence of velocities inferred from traveltimes, (2) indicated that scale effects can introduce traveltime errors when upscaling from logs to surface seismic and VSPs, and (3) illustrated that erroneous VSP interval velocities can result when layer thicknesses are smaller than about one-tenth of the wavelength. A simple approximate recipe is presented for estimating these traveltimes by successively filtering the medium using a running Backus average and ray theory. The scale-dependent dispersion was also predicted well using a more rigorous invariant imbedding formulation. The predicted traveltimes, using the approximate recipe, compare well with the times observed in the laboratory stack of steel and plastic layers and in numerical studies of stratified media. The dispersion curves predicted by the approximate method also show the overall behavior computed with the more rigorous invariant imbedding formulation.

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