Surface Wave Scattering From 3-D Obstacles

Abstract

The scattering of surface waves from 3-D, discrete obstacles in both the near- and far-fields is described using a T-matrix formulation which relates the incident and scattered wavefields via expansions over surface wave modes. the scatterer resides in an otherwise laterally homogeneous, stratified medium and can exhibit an arbitrarily large contrast in material properties with its surroundings. the method relies on the expansion of the incident and scattered wavefields in terms of regular and outgoing surface wave basis functions which depend upon wavetype (Love, Rayleigh), modal order and azimuthal order, and are orthogonal with respect to a specific class of closed surface integral. By expanding the wavefield inside the scatterer in an appropriate set of basis functions, this orthogonality can be exploited to relate the unknown coefficients of the scattered wavefield to those in the known expansion of the incident wavefield via the surface wave T-matrix. This quantity, which depends only on the size and shape of the obstacle, provides a complete description of the scattering response to any incident harmonic wave and permits a broad range of scattering measures (e.g. mode coupling, wavetype conversion, radiation patterns) to be readily constructed. The theory is applied to a suite of simple, geometric models to investigate the influence of obstacle dimension and geometry on the nature of mode coupling and wavetype conversion in the scattered wavefield. the method is computationally tractable when the product of the wavenumber k and the typical obstacle radius a is less than or equal to 10, and thus allows the consideration of a wide range of interactions. Results indicate that discordance between the surface wave eigenfunctions in the obstacle and surroundings dictates to large degree the general distribution of energy in the scattered modes especially for obstacles with vertical boundaries. the effect of dimension is to increase (i) the ratio of energy in the unconverted mode to other scattered modes, and (ii) the ratio of forward- to back-scattered energies with an accompanying increase in the complexity of radiation patterns. the total scattered energy from obstacles whose horizontal cross-sections deviate from circularity depends on the orientation of the incident wave and, in the case of an elliptic cylinder, the direction of maximum scattered energy differs by ˜45° between incident Love and Rayleigh waves. Obstacle boundaries which depart from vertical surfaces can have a marked effect on modal coupling especially in the incident wavetype. Slight departures cause strong coupling to orders immediately adjacent to the incident mode while the effect of more pronounced variations is felt across larger portions of the modal spectrum.