Book Description

Much work is presently being done concerning small scale heterogeneities in the earth's crust. These heterogeneities range from pores in sedimentary rocks up to fluctuations in the density and seismic constants of the earth's crust with scale lengths of kilometers. The ability to study and quantify these heterogeneities using seismic methods would be a major advance in the earth sciences. Physical modeling has been shown to be a useful technique for investigating various aspects of wave propagation. In this thesis, two physical modeling experiments (one three-dimensional and one two-dimensional) are used to investigate the scattering of seismic waves from small scale heterogeneities and the changes in seismic velocity and apparent attenuation resulting from this scattering. The effects of both isotropic and anisotropic scattering on velocity and apparent attenuation are calculated. These experimental results are compared to theoretical results. The theory used for isotropic scattering for the three-dimensional experiment is a modified version of Wu's single scattering theory, where instead of calculating the scattering for a single scatterer using the Born approximation, the exact results for scattering from a cylindrical shape are used. While the results for compressional waves and both components of shear waves compare reasonably well for small scatterer volume fractions, at larger scatterer volume fractions, where the need for multiple scattering is more likely, the results for all waves do not compare as well. Many theories used to test anisotropic scattering predict changes in velocity rather than changes in apparent attenuation. The velocity changes are used primarily in this work due to geometrical focusing by a seismic lens that biases the amplitudes (and hence the estimates of apparent attenuation) at low frequencies where most theories predict apparent attenuation. Velocities are calculated from the data using travel times and low frequency phase shifts for the compressional waves and for one component of the shear waves measured in this two-dimensional experiment. Theories that are used to predict compressional and shear wave velocities for both isotropic and anisotropic scatterers are based on a fractional volume method (isotropic), two crack methods (isotropic and anisotropic), and a finely layered method (anisotropic). The isotropic experimental results have much larger, non-linear changes in the velocities than do the isotropic theoretical results. The anisotropic experimental results have similar shapes to both theoretical anisotropic methods for compressional waves and to the theoretical anisotropic crack method for shear waves. Attenuation is computed using log spectral ratios and compares as well with the theoretical results as can be expected within the limits set. A method using anisotropic apparent attenuation to help quantify the scatterers is developed for use with field data.