Remarks on the Inverse Scattering Problem for Ocean Acoustics

We propose two new formulations of inverse scattering problems for ocean acoustics and give the reconstruction formula for them. Both of them use near field data instead of the far field pattern of the scattered wave

Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources

The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main features of the technique are illustrated by examples of the moving source fields in the plasma and the Cherenkov radiation. It is emphasized that the deeper insight to the wave effects in dispersive case already requires the explicit formulation of the dispersive material model. As the advanced application we have considered the Doppler frequency shift in a complex single-resonant dispersive metamaterial (Lorenz) model where in some frequency ranges the negativity of the real part of the refraction index can be reached. We have demonstrated that in dispersive case the Doppler frequency shift acquires a nonlinear dependence on the modulating frequency of the radiated particle. The detailed frequency dependence of such a shift and spectral behavior of phase and group velocities (that have the opposite directions) are studied numerically

New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations propose that the heterogeneities are compositional in nature, differing in composition from the overlying mantle, an interpretation that would be consistent with chemical geodynamic models. Numerical modeling of persistent compositional interfaces presents challenges, even to state-of-the-art numerical methodology. For example, some numerical algorithms for advecting the compositional interface cannot maintain a sharp compositional boundary as the fluid migrates and distorts with time dependent fingering due to the numerical diffusion that has been added in order to maintain the upper and lower bounds on the composition variable and the stability of the advection method. In this work we present two new algorithms for maintaining a sharper computational boundary than the advection methods that are currently openly available to the computational mantle convection community; namely, a Discontinuous Galerkin method with a Bound Preserving limiter and a Volume-of-Fluid interface tracking algorithm. We compare these two new methods with two approaches commonly used for modeling the advection of two distinct, thermally driven, compositional fields in mantle convection problems; namely, an approach based on a high-order accurate finite element method advection algorithm that employs an artificial viscosity technique to maintain the upper and lower bounds on the composition variable as well as the stability of the advection algorithm and the advection of particles that carry a scalar quantity representing the location of each compositional field. All four of these algorithms are implemented in the open source FEM code ASPECT

Crustal structure of the ocean-continent transition at Flemish Cap : seismic refraction results

Author Posting. © American Geophysical Union, 2003. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 108, B11 (2003): 2531, doi:10.1029/2003JB002434.We conducted a seismic refraction experiment across Flemish Cap and into the deep basin east of Newfoundland, Canada, and developed a velocity model for the crust and mantle from forward and inverse modeling of data from 25 ocean bottom seismometers and dense air gun shots. The continental crust at Flemish Cap is 30 km thick and is divided into three layers with P wave velocities of 6.0–6.7 km/s. Across the southeast Flemish Cap margin, the continental crust thins over a 90-km-wide zone to only 1.2 km. The ocean-continent boundary is near the base of Flemish Cap and is marked by a fault between thinned continental crust and 3-km-thick crust with velocities of 4.7–7.0 km/s interpreted as crust from magma-starved oceanic accretion. This thin crust continues seaward for 55 km and thins locally to ~1.5 km. Below a sediment cover (1.9–3.1 km/s), oceanic layer 2 (4.7–4.9 km/s) is ~1.5 km thick, while layer 3 (6.9 km/s) seems to disappear in the thinnest segment of the oceanic crust. At the seawardmost end of the line the crust thickens to ~6 km. Mantle with velocities of 7.6–8.0 km/s underlies both the thin continental and thin oceanic crust in an 80-km-wide zone. A gradual downward increase to normal mantle velocities is interpreted to reflect decreasing degree of serpentinization with depth. Normal mantle velocities of 8.0 km/s are observed ~6 km below basement. There are major differences compared to the conjugate Galicia Bank margin, which has a wide zone of extended continental crust, more faulting, and prominent detachment faults. Crust formed by seafloor spreading appears symmetric, however, with 30-km-wide zones of oceanic crust accreted on both margins beginning about 4.5 m.y. before formation of magnetic anomaly M0 (~118 Ma).This work was supported by National Science Foundation grant OCE 9819053, the Danish Research Foundation (Danmarks Grundforskningsfond), and the Natural Science and Engineering Research Council of Canada. B. Tucholke also acknowledges support by the Henry Bryant Bigelow Chair in Oceanography at Woods Hole Oceanographic Institution

Exact reconstruction of ocean bottom velocity profiles from monochromatic scattering data

Submitted in partial fulfillment of the requirements for the degree of Doctor of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 1987This thesis presents the theoretical and computational underpinnings of a novel approach to the determination of the acoustic parameters of the ocean bottom using a monochromatic source. The problem is shown to be equivalent to that of the reconstruction of the potential in a Schrodinger equation from the knowledge of the plane-wave reflection coefficient as a function of vertical wavenumber, r(kz) for all real positive k z. First, the reflection coefficient is shown to decay asymptotically at least as fast as (1/kz2) for large kz and is therefore inteqrable. The Gelfand-Levitan inversion procedure is extended to include the case of basement velocity higher than the velocity of sound in water. The neglect of bound states is shown to be justified in both clayey silt and silty clay at the 220 Hz frequency of operation. Three methods for the numerical solution of the integral equation are investigated. The first one is an "Improved Born approximation" wherein the solution is given as a series expansion the first term of which is the Born approximation while the second term represents a substantial and yet easy to implement improvement over Born. The two other methods are based on a discretization of the Gelfand-Levitan integral equation, and both avoid a matrix inversion: one by employing a recursive procedure, and the other by coupling the Gelfand-Levitan equation with a partial differential equation. Bounds are obtained on errors in the solution due either to discretization or to data inaccuracy. These methods are tested on synthetic data obtained from known geoacoustic models of the ocean bottom. Results are found to be very accurate particularly at the top of the sediment layer with resolution of less than the wavelength of the acoustic source in the water. Several effects are investigated, such as sampling, attenuation, and noise. Also examined is the gradual restriction of the reflection coefficient to a finite range of vertical wave numbers and the consequent progressive deterioration of the reconstruction. The analysis shows how to reconstruct velocity profiles in the presence of density variation when the experiment is conducted at two frequencies. Our results provide a good understanding of the issues involved in conducting a monochromatic deep ocean bottom experiment and constitute a promising technique for processing the experimental data when it becomes available.Support for this thesis was provided in part by the education office at WHOI and by the Office of Naval Research

Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media

The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes

Internal tidal modal ray refraction and energy ducting in baroclinic Gulf Stream currents

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 1969-1993, doi:10.1175/JPO-D-18-0031.1.Upstream mean semidiurnal internal tidal energy flux has been found in the Gulf Stream in hydrodynamical model simulations of the Atlantic Ocean. A major source of the energy in the simulations is the south edge of Georges Bank, where strong and resonant Gulf of Maine tidal currents are found. An explanation of the flux pattern within the Gulf Stream is that internal wave modal rays can be strongly redirected by baroclinic currents and even trapped (ducted) by current jets that feature strong velocities above the thermocline that are directed counter to the modal wavenumber vector (i.e., when the waves travel upstream). This ducting behavior is analyzed and explained here with ray-based wave propagation studies for internal wave modes with anisotropic wavenumbers, as occur in mesoscale background flow fields. Two primary analysis tools are introduced and then used to analyze the strong refraction and ducting: the generalized Jones equation governing modal properties and ray equations that are suitable for studying waves with anisotropic wavenumbers.The Woods Hole research was supported by National Science Foundation Grant OCE-1060430 and by the Office of Naval Research Grants N00014-11-1-0701 and N00014-17-1-2624. The USM research was supported by ONR Grant N00014-15-1-2288 and National Science Foundation Grant OCE-1537449.2019-02-2