Darin J. Soukup

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.

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.

Modal scattering and T‐waves: Sediment amplification and source effects

If the Earth were a plane‐layered semi‐infinite half‐space or a radially symmetric sphere oceanic, T‐waves could not exist. This is apparent because the source depth of T‐wave producing earthquakes is greater than the depth at which the low order modes comprising the T‐waves have any significant amplitude. Bottom roughness provides a mechanism by which energy from high order source modes can be scattered into the lower order modes. The efficiency of this scattering is improved when there is a layer of sediments overlying the higher speed upper ocean crust. Some of the source modes develop a large anti‐node, reminiscent of a Scholte wave, at the water sediment interface. Bottom roughness serves as a sheet of secondary sources placed directly on the anti‐node of these modes, and contributes a significant amount of energy to the T‐waves. However, a significant fraction of the total T‐wave energy is also provided by small scattered contributions from many higher modes of the continuum spectrum, which is model...

Anisotropy, range dependence and seismo‐acoustic propagation in shallow water.

The shallow water environment may be highly variable, with both range dependence and anisotropy almost ubiquitous in the seafloor bottom/sub‐bottom regions. Some common causes of range dependence include marine‐sediment composition, non‐planar boundaries, rough surfaces, strong density, or velocity contrasts, and variation in water‐column depth and/or sediment‐cover thickness. Common causes of elastic anisotropy are compositional layering or vertically aligned cracks. There is an apparent trade‐off between anisotropy and range dependence, and difficult to separate the two effects in a propagating signal. If the symmetry axis of a compositionally layered sediment is not exactly normal to the seafloor, the seismo‐acoustic wave field has particle‐motion polarizations in all three coordinate directions. Even in a one‐dimensional medium, an explosion source excites sediment particle motion with all three polarizations. Assuming sediment isotropy when it is not justified can cause errors in layer‐thickness comp...

Seismo‐acoustic modal scattering by volume heterogeneities in shallow water sediments.

Elastic anisotropy is a nearly ubiquitous feature of marine sediments. The simplest type of sediment anisotropy is transverse isotropy, characterized by five elastic constants, and results from layered deposition. A modal scattering theory for volume perturbations of the sediment elastic moduli is presented. The scattering theory is based on the coupled mode formulation for propagation in range dependent fluid‐elastic media. The Born approximation is employed to derive a modal scattering matrix. Although the perturbations of the elastic moduli are random, they may not be arbitrary in the sense that certain symmetry and energy constraints among the moduli must be respected. Mode‐mode coupling matrices are computed for quasi‐P‐SV‐SH seismo‐acoustic modes, which show mode mixing and the importance of non‐nearest neighbor interactions. The effects of volume scattering can be combined with rough surface scattering and also incorporated into mode coupling caused by deterministic range dependence of the material...

Local coupled modes and volume scattering in heterogeneous anisotropic shallow water environments

Seafloor bottom/subbottom interactions are significant for low frequency acoustic wave propagation in shallow water environments. We investigate the significance of deterministic and stochastic volume scattering for generally anisotropic seafloor bottoms. The following assumptions are made: (i) the model is laterally heterogeneous with an elastic bottom/subbottom, (ii) anisotropy is hexagonally symmetric, (iii) the bottom/subbottom structure is dominated by deterministic elastic moduli with additional small‐scale stochastic variations. The local coupled mode rough interface scattering theory of Park and Odom [Geophys. J. Int. 136, 123 (1999)] is extended by including volume scattering terms. New volume scattering terms are derived by applying perturbation theory to the elastic equations of motion. The acoustic wavefield is expressed as a sum of a mean deterministic wavefield and a small‐scale scattered wavefield. Perturbations in the elastic moduli contribute to energy loss and the loss of signal coherenc...

T‐wave sources, slopes, rough bottoms and continuum

Bathymetry plays a strong role in the excitation of T‐waves by breaking strict mode orthogonality and permitting energy from higher order modes to couple to the lower order modes comprising the T‐phase. Observationally (Dziak, 2001) earthquakes with a strong strike‐slip component are more efficient at generating T‐waves than normal fault mechanisms with the same moment magnitude. It is shown that fault type and orientation correlates strongly with T‐wave excitation efficiency. For shallow sources, the discrete modes contribute to the majority of the seismic source field, which is then scattered into the acoustic modes by irregular bathymetry. However, the deeper the earthquake source, the more important the continuum component of the spectrum becomes for the excitation. Deterministic bathymetry and random roughness enter the modal scattering theory as separate terms, and allow the relative contributions from the slope conversion mechanism and bottom roughness to be directly compared. [Work supported by th...

Modal conversion by rough surface scattering: The key to the T‐phase

The amplitudes of the propagating acoustic modes associated with T‐waves decay exponentially below their ray equivalent turning points, and cannot be excited directly by an earthquake. The modal decomposition for a T‐wave producing earthquake that occurred near the western tip of the Blanco TFZ has been computed. The directly excited higher order modes are characterized by relatively large amplitudes in the ocean crust, significant water‐borne components, and often strong interface components at the ocean‐bottom boundary. Employing the modal scattering theory of Park and Odom (1999), it is found that energy has been transferred from higher order modes to the Stoneley fundamental and the lower order modes have significant amplitude at the water‐bottom interface. Scattering from irregular ocean bottom bathymetry is the mechanism for the energy transfer. The lowest order acoustic modes, modes 1 and 2, are only very weakly excited because they have very small amplitudes at the bottom. This is consistent with the interpretation of de Groot‐Hedlin and Orcutt (1999). [Work supported by the NOPP Program and ONR.]

Coupling to SH as a loss mechanism in shallow‐water acoustic propagation

Since horizontally polarized shear waves (SH) are polarized normal to the propagation and polarization direction of a bottom interacting shallow‐water acoustic signal, they are generally not considered as a loss mechanism. However, most marine sediments are anisotropic to some degree as a result of the bedding process with a symmetry axis normal to the bedding planes. Particle motions of compressional (P), vertically polarized shear waves (SV), and SH waves are no longer independent. Dispersion calculations show that the quasi‐P‐SV and quasi‐SH mode branches attract and repel as the symmetry axis is rotated. For certain ranges of the symmetry axis angle, the phase velocities of the quasi‐P‐SV and quasi‐SH approach each other. Coupled‐mode computations have been performed, which indicate that energy can be efficiently redistributed among modes with both P‐SV and SH components in the bottom. The coupling is induced by range dependence in the waveguide, and energy is distributed among all propagating modes. ...