Robert I. Odom

Modal scattering: A key to understanding oceanic T‐waves

The excitation mechanism of oceanic T-waves has been a puzzle for almost fifty years, with refraction from a sloping seafloor and seafloor scattering as two of the most commonly invoked mechanisms. By representing the earthquake source field as a normal mode sum, it can be seen that both mechanisms are very closely related. Strict modal orthogonality prohibits the existence of T-waves in a laterally homogeneous semi-infinite half-space or radially symmetric sphere, as energy cannot be transferred from one mode to another in an homogeneous medium. Deterministic non-planar bathymetry, random boundary roughness, upper crustal heterogeneity, or a combination of these provides a physical mechanism to break the strict orthogonality. We show that modal scattering from the rough seabottom in the epicentral region converts energy from the directly excited ocean crustal/water column modes to the propagating acoustic modes comprising the oceanic T-wave. Submarine earthquake fault orientation also appears to be reflected in the T-wave excitation.

A geoacoustic bottom interaction model (GABIM)

The geoacoustic bottom interaction model (GABIM) has been developed for application over the low-frequency and midfrequency range (100 Hz to 10 kHz). It yields values for bottom backscattering strength and bottom loss for stratified seafloors. The model input parameters are first defined, after which the zeroth-order, nonrandom problem is discussed. Standard codes are used to obtain bottom loss, uncorrected for scattering, and as the first step in computation of scattering. The kernel for interface scattering employs a combination of the Kirchhoff approximation, first-order perturbation theory, and an empirical expression for very rough seafloors. The kernel for sediment volume scattering can be chosen as empirical or physical, the latter based on first-order perturbation theory. Examples are provided to illustrate the various scattering kernels and to show the behavior predicted by the full model for layered seafloors. Suggestions are made for improvements and generalizations of the model.

Sounds in the Ocean at 1–100 Hz

Very-low-frequency sounds between 1 and 100 Hz propagate large distances in the ocean sound channel. Weather conditions, earthquakes, marine mammals, and anthropogenic activities influence sound levels in this band. Weather-related sounds result from interactions between waves, bubbles entrained by breaking waves, and the deformation of sea ice. Earthquakes generate sound in geologically active regions, and earthquake T waves propagate throughout the oceans. Blue and fin whales generate long bouts of sounds near 20 Hz that can dominate regional ambient noise levels seasonally. Anthropogenic sound sources include ship propellers, energy extraction, and seismic air guns and have been growing steadily. The increasing availability of long-term records of ocean sound will provide new opportunities for a deeper understanding of natural and anthropogenic sound sources and potential interactions between them.

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

Most marine sediments exhibit transverse isotropy (TI) 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, ...

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

Modal investigation of elastic anisotropy in shallow-water environments: anisotropy beyond vertical transverse isotropy.

Theoretical and numerical results are presented for modal characteristics of the seismo-acoustic wavefield in anisotropic range-independent media. General anisotropy affects the form of the elastic-stiffness tensor, particle-motion polarization, the frequency and angular dispersion curves, and introduces near-degenerate modes. Horizontally polarized particle motion (SH) cannot be ignored when anisotropy is present for low-frequency modes having significant bottom interaction. The seismo-acoustic wavefield has polarizations in all three coordinate directions even in the absence of any scattering or heterogeneity. Even weak anisotropy may have a significant impact on seismo-acoustic wave propagation. Unlike isotropic and transversely isotropic media with a vertical symmetry axis where acoustic signals comprise P-SV modes alone (in the absence of any scattering), tilted TI media allow both quasi-P-SV and quasi-SH modes to carry seismo-acoustic energy. Discrete modes for an anisotropic medium are best described as generalized P-SV-SH modes with polarizations in all three Cartesian directions. Conversion to SH is a loss that will mimic acoustic attenuation. An in-water explosion will excite quasi-SH.

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

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

Coupled mode theory is applied to acoustic/elastic wave propagation in shallow water to examine the effects of lateral heterogeneities and transverse isotropy on mode coupling and signals. A numerical code is developed by applying the invariant imbedding technique to the coupled mode theory. From the code, the reflection and transmission matrices and the forward/backward-propagating wave fields in the frequency domain are generated for a range-dependent medium. The effect of transverse isotropy of bottom sediment layers is also considered. Time domain signals are synthesized with a 2-Hz bandwidth between 10 Hz and 12 Hz for the excitation by a unit line force and for an incident fundamental mode. The generation of higher overtones and the decay of the fundamental mode propagating in a range-dependent medium are clearly shown.

Adapting results in filtering theory to inverse theory, to address the statistics of nonlinear geoacoustic inverse problems

The intrinsically non‐Gaussian statistics of nonlinear inverse problems, including ocean geoacoustic problems, is explored via analytic rather than numerical means. While Monte Carlo Bayesian methods do address the non‐Gaussian statistics in nonlinear inverse problems, they can be very slow, and intuitive interpretation of the results are at times problematic. There is great theoretical overlap between recursive filters/smoothers, such as the extended Kalman filter, and methods of linear and nonlinear geophysical inversion. The use of recursive filters in inversion is not in itself new, but our interest is in adapting statistical developments from one to the other. Classic analytic methods in both filtering theory and inverse theory assume Gaussian probability distributions, but newer nonlinear filters do not all make this assumption and are explored for their potential application to nonlinear inverse problems. The similarities and differences between the frameworks of filtering theory and inverse theory...

The second order resolution operator of a nonlinear ocean acoustics inverse problem.

The resolution operator for a linear inverse problem indicates how much smearing exists in the map between the true model and the estimated model. The trace of the resolution operator provides an estimate of the number of model parameters model that are resolved. In a series representation of the resolution operator for a nonlinear problem, the higher‐order terms indicates how much spurious nonlinear leakage there is from the true model to the estimated model. In previous work, the solution of a simple nonlinear ocean acoustic inverse problem as a perturbation series in the horizontal wavenumber was constructed, and the linear data kernels were presented. This linear problem permitted the quantification of the magnitude of the perturbation and indicated when nonlinear effects must be taken into consideration. In this extension of previous work, the second order resolution kernel is constructed, which describes how effectively nonlinear effects can be removed from the reconstructed model. [Work supported b...