EFFECT OF MATERIAL CONTRAST ON ANISOTROPY AND DISPERSION OF LAYERED PERIODIC MEDIUM

In order to research the anisotropy and dispersion features of media with aligned fractures, models which approximately describe the media are constructed. For the case in which crack density is very high and aspect ratio may be very low, the cracked medium can be described as a layered periodic medium, in which the aligned fractures in question are described as layers. Given a layered periodic medium consisting of all solid layers, the effect of the contrast between individual layers on the behavior of anisotropy is examined. The effect of shear modulus contrast on anisotropy is essential. If shear moduli of two layers are equal, the effective medium is isotropic. The increase of bulk modulus contrast shifts the maximum SV -wave velocity point to that of smaller angle. For the layered periodic medium consisting of alternating solid and fluid layers, the effects on both anisotropy and frequency dispersion are then examined. There will be dispersion for propagating P-wave, and thereby stop-bands exist. For the wave propagates perpendicular to the layering, the stop-bands as a function of phys- ical properties of individual layers are studied. When wavelength is much greater than the spatial period of the medium, there are two modes of P-wave, the fast and slow P-wave. For cases in which crack density is low and aspect ratio is relatively high, the anisotropy is characterized using the Eshelby-Cheng method. The increase of bulk modulus contrast will increase the anisotropy of the effective medium. As the aspect ratio increases from 0.1 to 0.5, the anisotropy of P-wave and SV -wave increases.