Marching Acoustic Fields Parallel to a Surface of Discontinuity

The development of a phase-space marching algorithm in the presence of an interface between two media, with discontinuous variation of acoustic parameters is described. Beginning with the concept of representation of functions and operators, an acoustic field call be expressed as a synthesis of basic wave species, e.g. plane waves, point-source fields (both volume and surface), and Gaussian beams. Propagators in specific experimental scenarios are accordingly developed. Propagator of Gaussian type is emphasized for its limited content in both spatial and spectral domains. The suggestion of propagation modeling as a wavefield marching is extensively discussed and phase-space marching technique is proposed to incorporate the interpretation of wave propagation as an ordered sequence of local events. Combining the wavefield marching strategy with windowed-Fourier-transformation technique, a model for phase-space marching of local spectrum is then set up. A number of numerical simulations is presented to enhance the understanding of an important acoustic propagation/scattering problem, determining the scattered and transmitted acoustic fields generated by an internal surface of discontinuity. The results reveal some underlying physics of propagation and scattering of wave fields, such as bifurcation, lateral wave, wave interference and beam displacement. The change of marching direction is also addressed in the thesis to accommodate the situation of an inclined ocean bottom. The interpretation for phase-space representation that it represents a decomposition of the field into spatially local components which generate spatially local wave species is emphasized. It is this interpretation that allows a change of marching direction. A beamed wave species propagating in a wedge -shaped waveguide is investigated and the local turning -around phenomenon is clearly seen in the phase space. The reported algorithm is a significant advance in the predictive modeling of realistic ocean application.