Steven A. Stotts

Coupled‐mode solutions in generalized ocean environments

This paper presents the application of the differential equation approach to solving the second-order coupled-mode equations in inhomogeneous ocean environments. The model incorporates sound velocity profile points to construct depth-dependent, piecewise linear, ocean and bottom environments along a range grid. Modal solutions are evaluated in terms of Airy functions. The formalism to evaluate analytically the mode-coupling coefficients is presented. Comparisons to conventional expressions of the coefficients are made. The integro-differential form of the coupled equations is solved using an approach developed in nuclear theory that incorporates the Lanczos method [Knobles, J. Acoust. Soc. Am. 96, 1741-1747 (1994)]. Demonstration of the practicality of this approach is made by applying the results in actual calculations with realistic ocean environments. The formalism to evaluate analytically the mode-coupling coefficients is presented. Several benchmark examples were examined in order to validate the model and are discussed, including propagation over a hill, benchmark wedge problems, and a range-varying sound speed profile benchmark. The importance of this model is also demonstrated by the physical insight gained in having a coupled-mode approach to solving range-dependent problems.

Geoacoustic inversion in range-dependent ocean environments using a plane wave reflection coefficient approach

A new, efficient, versatile ray-based model is presented that performs geoacoustic inversions in range-dependent ocean waveguides faster than alternative forward models for which the computation time becomes extremely long, especially for broadband inversions. The water propagation is approximately separated from the seabed interaction using predetermined bathymetry and a possibly range-dependent water sound speed profile. The geometrical optics approximation is used to calculate eigenrays between sources and receivers, including bottom reflecting paths. Modeled broadband pressure fields are obtained by computing the plane wave reflection coefficient at specific angles and frequencies and by then linking this result with the bottom reflected eigenrays. Each perturbation of the seabed requires a recalculation of the plane wave reflection coefficient, but not a recalculation of the eigenrays, resulting in a highly efficient method. Range-independent problems are treated as a limiting case of the approach. The method is first described and then demonstrated with a few simple range-independent theoretical models. The versatility of addressing range-dependence in the bottom seabed is demonstrated with a simulated data set. Finally, the new model is applied to inversion from a measured data set, taken with impulsive sources, for both range-independent and range-dependent continental shelf environments.

Rough surface scattering in a Born approximation from a two-way coupled-mode formalism

Scattering from a rough surface in an ocean waveguide is described in a new derivation from a two-way coupled-mode representation. The general formalism, which contains scattering effects to all orders, is truncated to the first-order terms of an iterative (Born) expansion. Both two- and three-dimensional ocean waveguide geometries are discussed. By reducing the mode functions in terms of plane wave reflection coefficients, the off-diagonal components of the scattering kernel that is derived are shown to be consistent with a standard solution, but the diagonal components are different from the standard solution.

Numerical study of geoacoustic inversion in range-dependent ocean environments

Simulated acoustic data for two-dimensional waveguides were used to estimate the properties of a sea bed over which the depth of the water column varies with range. The simulated data were produced by a parabolic equation method. No approximate knowledge of the local sea-bed representation or parameter bounds was given prior to the inversions. In addition, little approximate information was given on the nature of the range dependence of the sea bed. The inversion methodology used a simulated annealing approach and a variation of the algorithm that generated the original acoustic data. For the purpose of consistency, a second method was employed, which used the same simulated annealing approach but with a range-dependent ray approach in which the sea-bed interaction is described by a complex plane wave reflection coefficient. Various combinations of frequencies and source-receiver positions commonly used in real acoustic measurements at sea were selected for the inversions. The goal of the inversion was to efficiently achieve a coarse description of the environment by several inversions; short-range data at low frequencies were employed for the purpose of efficiency. In the later stages of the inversion process, data from longer ranges and higher frequencies were included to provide additional details of the sea bed. Sea-bed parameters were assumed to vary linearly with range between geoacoustic profiles defined at specific ranges. Inversion results obtained prior to the reporting of the actual solutions are presented.

Geoacoustic Inversions of Horizontal and Vertical Line Array Acoustic Data From a Surface Ship Source of Opportunity

The application of an inversion methodology produces the first demonstration of a simultaneous solution for geoacoustic and source track parameters from acoustic data collected in a shallow-water, sandy sediment environment. Inversion solutions from data collected in the 2006 Shallow Water Experiment (SW06) are extracted from noise measurements of a surface ship source on an L-array. The methodology includes a screening algorithm to determine a set of frequencies for the inversion data. In addition, the methodology assesses the accuracy of the inversion solution and incorporates an estimation of parameter value uncertainties. The solution from the inversion of the horizontal component of the L-array data from the surface ship source before its closest point of approach (CPA) is used to construct modeled propagation loss for comparison with observed received level (RL) structure as the source departs from CPA. Inversion of the data from a single element in the vertical component of the L-array produces a solution that agrees with the solution obtained from the inversion of horizontal subaperture data. Also, modeled transmission loss (TL) structure obtained from the single-element inversion solution reproduces the depth dependence of the RL structure observed at other elements of the vertical component of the L-array.

Broadband modeling of downslope propagation in a penetrable wedge

Sound propagation in a wedge-shaped environment with a penetrable bottom is simulated with broadband adiabatic mode, coupled mode, and parabolic equation model computations. Simulated results are compared to measured data taken in a tank experiment by Tindle et al. The coupled mode formalism is shown to predict, in agreement with that experiment, that modal wave fronts in penetrable wedges are approximately circular arcs centered at the apex of the wedge for a source near the apex. It is also shown that for wedge angles up to 6 degrees, the received waveforms are well approximated by the adiabatic waveforms time-shifted by a depth-dependent interval to account for the curvature of the modal wave fronts. A small deviation from circularity in the modal wave fronts is possibly observed in the 6 degrees case.

Multiple-source localization using GPS technology and received arrival time structure analysis in an air-deployed system

An efficient and robust method has been developed to locate multiple impulsive sources in an ocean environment. Global position system (GPS) receivers were installed on sonobuoys to obtain their locations within a few meters of accuracy. A sonobuoy field was deployed in a ring-type pattern. Charges were then set off at arbitrary locations within the ring, High-resolution plots were used to obtain direct path and/or first bottom bounce arrivals on each buoy. A model grid of arrival times was constructed, corresponding to the dimensions of the buoy field. A ray model previously developed here at the Applied Research Laboratories at the University of Texas at Austin (ARL:UT) was used to obtain model travel times. The minimum value of the least-square-type error between the real arrival times and the modeled travel times resulted in an unambiguous location of the source, within the limits of the grid spacing chosen. This value was calculated by picking one receiver as the reference and then summing the timing errors of the remaining receivers relative to the reference. Successive iterations with finer grid spacings result in source localization within the accuracy of the buoy locations. The localization routine was extended by allowing permutations of the pulse arrivals on each buoy to account for multiple sources closely separated in time and/or space. An automated correlation technique is presented as an alternative to the leading edge-detection method used here for obtaining relative arrival times. Two proof-of-concept experiments were performed and some results of data obtained at Lake Travis and the Gulf of Mexico are presented.

Scattering in a Pekeris waveguide from a rough bottom using a two‐way coupled mode approach.

Scattering from a rough ocean bottom is described numerically with a two-way coupled-mode formalism that contains scattering effects to all orders and provides an exact solution to the wave equation. Both scattered field and direct blast components are computed within the formalism framework. A comparison of the scattered component solution from the coupled mode with the Born approximation (BA) solution for scattering from a rough bottom Pekeris waveguide shows that the BA predicts correctly the scattered field levels but not detailed structure. The transition from direct blast to scattered field dominance is identified in the total field time series.

Geoacoustic inversion of short range source data using a plane wave reflection coefficient approach

Acoustic time series data were collected in a shallow, hard bottom lake environment located in central Texas using both short range (2 m) implosive data, obtained with the source and a single hydrophone located near mid-depth in the waveguide, along with longer range implosive and explosive data from a near surface source to a bottom mounted hydrophone. Matched field inversions using simulated annealing were performed with a ray trace plus complex plane wave reflection coefficient forward propagation model that was validated in previous work. Isolating bottom interacting paths to perform the inversions is shown to be essential to reduce parameter uncertainties in the hard bottom environment and enables a systematic approach to the inversions which establishes the number of layers needed to represent the lake environment. Measured transmission loss data from a towed source were compared through a RMS error analysis to modeled transmission loss, constructed with the parameters from inversions of data from several source types, to further establish the validity of the inversion approach for this environment. Geoacoustic parameters obtained by inversions of short range, low frequency impulsive data are used to predict transmission loss at longer ranges and higher frequencies. The range dependence of the global minimum is discussed.

Source bearing determination from a tri-axial seismometer using Rayleigh wave propagation

Bearing determinations for ground vehicles have been made, using a single buried three-axis seismometer. The method, based on Rayleigh wave detection, exploits the phase difference between measured wave components to obtain vehicle bearing estimates. It is referred to as a Rayleigh wave retention method and uses both prograde and retrograde motion. Determination of the propagation direction is based upon analysis of maximum correlation values obtained by cross-correlating the vertical wave components with horizontal beam components. Theoretical simulations demonstrate the technique. Methods for obtaining direction of travel and vehicle speed estimates are also discussed. Applications of the method to real data obtained from several vehicles at different test sites are presented.