Effects of transverse isotropy on modes and mode coupling in shallow water

Abstract

Most marine sediments exhibit transverse isotropy ͑TI͒ that can have a significant effect on the signal properties of strongly bottom interacting sound. Locally, transverse isotropy has the greatest effect on the fundamental and near fundamental modal overtones. The local shallow water TI modes have reduced amplitude in the sediment relative to the corresponding shallow water modes for an isotropic bottom. Even a small departure from isotropy ͑2.4%͒ can have a significant ͑15%͒ effect on the phase velocity of bottom interacting modes. Calculations of mode-mode coupling coefficients for a range-dependent medium indicate that mode coupling is more strongly confined to modal nearest neighbors for a TI medium characterized predominantly by shear wave anisotropy, when compared to the corresponding isotropic medium. As the frequency increases, the strongest coupling occurs between higher overtones and also becomes more strongly peaked around nearest neighbors. The coupled mode theory of Maupin ͓Geophys. J. 93, 173-185 ͑1988͔͒ is employed to model the coupling. This theory can treat smooth gradients and sloping layer boundaries for all five of the bottom elastic moduli in a TI medium, the densities, and the range dependence of the water column itself. This coupled mode formulation also properly accounts for the continuity of stress and displacement boundary conditions in an exact way at irregular interfaces.

Estimating shallow shear velocities with marine multicomponent seismic data

“…In land surveys with vibroseis or buried explosive sources, however, they are apparent and may provide useful information complementary to the Rayleigh waves. For example, with observations of both Rayleigh and Love waves one can infer information about transverse isotropy e.g., Bachman, 1983;Odom et al, 1996. If information from Love w aves is desired, sources on towed sleds have b e e n d e v eloped by marine geophysicists to generate them Stoll et al, 1994a and a few studies have beencompleted on Love waves in marine sediments e.g., Bautista and Stoll, 1995. It should bementioned, however, that Love waves complicate the seismograms such that unambiguous simultaneous determination of Rayleigh and Love w ave dispersion may bechallenging.…”

Shallow Water Acoustic Propagation in Anisotropic Scattering Environments: Student Support

“…In isotropic media such as fluids and isotropic elastic bottom material, and in transversely isotropic (TI) elastic media, the mode coupling is mostly dominated by the 1/∆k term in the mode coupling matrix B qr . The result is that the strongest interactions occur between nearest neighbors in phase velocity, and the coupling matrix is nearest neighbor dominant with the strongest interactions closest to the diagonal (Odom et al 1996). If the bottom sediments are layered in such a way so that the normal to the layering is not also normal to the water surface, the symmetry of the TI medium is broken and the anisotropy of the bottom sediments takes on a more general form.…”

Effects of elastic heterogeneities and anisotropy on mode coupling and signals in shallow water

“…This source F 0 depends linearly on the solution of the local plane layered problem. We refer the reader to Maupin's ͑1988͒ original work or to the summary given in Odom et al ͑1996͒ for details. The square brackets ͓•͔ m in Eq.…”

“…These coupling matrices become the coefficient matrices of the coupled matrix DRE which will be solved in the following subsection. The plots of B are presented in Odom et al ͑1996͒.…”

“…Only a brief outline of the theory, required for the development in the following subsections, is therefore given in this paper. Details are given in Maupin ͑1988͒ and summarized in Odom et al ͑1996͒. For the numerical implementation in the following section, the range dependence is assumed to be confined in the interval ͓x L ,x R ͔ as illustrated in Fig.…”