MODELING ACOUSTIC-WAVES WITH PARAXIAL EXTRAPOLATORS

Modeling by paraxial extrapolators is applicable to wave-propagation problems in which most of the energy is traveling within a restricted angular cone about a principal axis of the problem. Using this technique, frequency-domain finite-difference solutions accurate for propagation angles out to 60° are readily generated for both 2-D and 3-D models. Solutions for 3-D problems are computed by applying the 2-D paraxial operators twice at each extrapolation step. The azimuthal anisotropy is essentially eliminated by adding a phase-correction operator to the extrapolation system. For heterogeneous models, scattering effects are incorporated by determining transmission and reflection coefficients at structural boundaries within the media. The chief advantages of the paraxial approach are that 1) active storage is reduced, 2) the decomposition in frequency allows the technique to be implemented on highly parallel machines, 3) attenuation can be modeled as an arbitrary function of frequency, and 4) only a small number of frequencies are needed to produce time slices. -from Authors