The Transition Between the Scale Domains of Ray and Effective Medium Theory and Anisotropy: Numerical Models

The anisotropy of a periodically layered isotropic medium is numerically modeled in order to study the effect of the scale of heterogeneity on seismic observations. An important motivation is to delineate the wavelength ranges over which a pulse propagating obliquely through the structure will be described by either ray (short wavelength) or effective medium (long wavelength) theory. The same band-limited pulse is propagated obliquely at a variety of incidence angles through a compositionally uniform layered structure as a function of the layer thicknesses. The resulting seismograms display similar behavior to that encountered for normal incidence including the effects of stop- and pass-bands. Velocities determined from time picks on these seismograms show a large difference in velocities between the long and short wavelength limits as has been previously demonstrated for normal incidence propagation. The bulk of the transition between these two limits is independent of incidence angle and occurs when the ratio between the wavelength and the layering thickness is near a value of 10. Two more geologically reasonable models show that these effects are diminished with smaller contrasts between the layers