Physical modeling observations of wave velocity and apparent attenuation in isotropic and anisotropic two-phase media

We study wave propagation through isotropic and anisotropic scatterer distributions in order to observe azimuthal variations in velocity and apparent attenuation. Using thin aluminum plates as physical models, we obtained seismograms for compressional and shear wave propagation through heterogeneous media. Three random distributions of scatterers are studied: circular scatterers in isotropic distributions (modeling circular scatterers), elongated scatterers in isotropic distributions (modeling randomly oriented elliptical scatterers), and elongated scatterers in anisotropic distributions (modeling aligned elliptical scatterers). All scatterers had approximately the same cross-sectional area and were filled with epoxy in order to reduce the impedance contrast. In addition to seismograms recorded for no scatterers, seismograms were recorded for several scatterer volume fractions. Azimuths were measured relative to the long axis of the aligned elongated scatterers. Velocities were calculated using travel times and phase shifts at low frequencies. The velocities measured from the data were compared to simple low-frequency average-velocity theories based on thin lamellae or on distributions of penny-shaped cracks. The apparent attenuation for different scatterer distributions was computed using spectral ratios.Comparisons of the results for circular and randomly oriented elongated scatterers were made to determine the effects of scatterer shape. As expected, the circular and randomly oriented elongated scatterers showed no systematic azimuthal variation in velocity. The velocity anomalies were systematically larger for the randomly oriented elongated scatterers than for the circular scatterers. Both methods of theoretical estimation for the isotropic velocities produced velocities significantly larger than those measured. The spectral ratios showed more apparent attenuation for the randomly oriented elongated scatterers than for the circular scatterers.Comparisons of the results for the randomly oriented and aligned elongated scatterers were made to determine the effects of anisotropy in the scatterer distribution. Compressional waves for the aligned elongated scatterers with wave propagation parallel to the scatterers had larger velocities than for the aligned elongated scatterers with wave propagation perpendicular to the scatterers for all velocity calculations. Shear wave velocities were complicated by an anomalous phase change in the shear wave seismograms for azimuths less than 40° and were not as conclusive. The general trend of the theoretical velocities is similar to the velocities calculated from the data. There are, however, what appear to be significant differences. The spectral ratios showed more apparent attenuation for the randomly oriented elongated scatterers than for the aligned elongated scatterers with wave propagation parallel to the scatterers, and less attenuation than for the aligned elongated scatterers with wave propagation perpendicular to the scatterers.