Development and application of one-way elastic wave propagators in generally-anisotropic, heterogeneous, three-dimensional media

A finite-difference narrow-angle one-way wave equation is implemented and is applied to various wave propagation problems to verify the method as well as to study frequency-dependent three-component waveform effects. The narrow-angle wave equation is the most approximate, yet most computationally practical, of the one-way wave equations derived by Thomson (1999). Although the vector narrow-angle wave equation is limited to a certain propagation distance, it is still a viable and powerful modelling approach to wave propagation in three-dimensional elastic media.; A FORTRAN finite-difference code is developed that is second-order accurate in the lateral and forward propagation direction and requires only three extrapolation planes to be stored during each propagation step. Numerical analysis of the finite-difference algorithm indicates that the scheme is stable for appropriate initial conditions and, for the propagation path-lengths of interest, angular range of forward propagation and source-pulse spectral content, numerical grid-anisotropy is minimal.; The narrow-angle propagator is sufficiently accurate for angles up to +/-15° to the preferred direction of propagation and is stable within singular regions of slowness space. For reasonable velocity gradients, the travel-times and amplitudes of transmitted and converted body-waves are in good agreement with an exact reference solution.; The conical-point singularity is the main focus of the homogeneous, anisotropic wave propagation examples, because it represents the most extreme anisotropic singularity and poses the greatest difficulty for ray-based methods. The results of wave propagation along the acoustic axis display characteristic and potentially diagnostic waveform effects, such as wavefront folding and tearing, merging and splitting pulses, growth of anomalous components and bipolar waveforms.; The results of wave propagation in isotropic heterogeneous media are consistent with various published results. Some familiar frequency-dependent wave-diffraction and pulse-distortion effects such as geometrical spreading, wavefront triplication and creeping-wave diffraction are observed when the length-scale of the heterogeneities is large relative to the seismic wavelength. The averaging effects due to smooth variations in medium parameters that vary on the sub-Fresnel zone level as well as frequency-dependent forward scattering are observed for wave propagation in stochastic media for a range of correlation lengths with respect to the seismic wavelength.