George V. Frisk

A comparison between the Born and Rytov approximations for the inverse backscattering problem

We compare the Born and Rytov approximations in solving the inverse acoustic backscattering problem, i.e., determining medium properties from reflections. For the one‐dimensional problem, we show that the Rytov approximation is generally better than the Born approximation in predicting sound speed changes, while both methods have the same error in determining the positions of reflectors. This is shown analytically for simple models and numerically for more general models. The performance of the Rytov approximation is degraded when low‐velocity regions are present in the medium being probed. The accuracy of the inversion depends on the manner in which the sound speed perturbation is linearized. The location of the receiver affects the accuracy of the inversion, and, in the case of the Rytov approximation, best results are obtained when the receiver is at the interface between the known and unknown regions. Furthermore, the Rytov method is less sensitive to the choice of reference sound speed used in the in...

On the determination of modal attenuation coefficients and compressional wave attenuation profiles in a range-dependent environment in Nantucket Sound

Techniques for determining modal attenuation coefficients and the compressional wave attenuation profile of the bottom in shallow water are presented. The input data consists of spatially well-sampled measurements of the pressure field versus range due to a monochromatic point source, which can be provided by either real or synthetic aperture horizontal arrays. Several methods are described for obtaining modal attenuation coefficients from the pressure field or its Hankel transform. The bottom attenuation profile is related to the modal attenuation coefficients through an integral equation that is solved using linear inverse theory. The methods are demonstrated using both noise-free and noisy synthetic data. The results of inverting experimental data from Nantucket Sound at 140 Hz and 220 Hz are presented. including the resolution and variance estimates of the inferred bottom attenuation profiles. Separation of the contributions of other attenuating mechanisms that can be confused with compressional wave attenuation (shear, rough surface scattering) is also discussed. >

The determination of geoacoustic models in shallow water

A technique for determining geoacoustic models in shallow water is described. For a horizontally stratified ocean and bottom, the method consists of measuring the magnitude and phase versus range of the pressure field due to a CW point source and numerically Hankel transforming these data to obtain the depth-dependent Green’s function versus horizontal wavenumber. In shallow water, the Green’s function contains prominent peaks at horizontal wavenumbers corresponding to the eigenvalues for any trapped and virtual modes excited in the waveguide. A geoacoustic model for the bottom is obtained by computing the theoretical Green’s function for various values of the bottom parameters and determining the parameter set which provides the best agreement with the experimental Green’s function, particularly in the positions and relative magnitudes of the modal peaks. Comparisons are also made between the measured and theoretically computed pressure field magnitudes. The technique is demonstrated using experimental data at 140 Hz and 220 Hz.

Modal mapping in shallow water using synthetic aperture horizontal arrays

An experimental technique is described for mapping the wavenumber spectrum of the normal mode field as a function of position in a shallow water waveguide with three-dimensional variation in its acoustic properties. These modal maps provide a characterization of the modal properties of the waveguide, can be used as input data to inversion techniques for inferring the 3D geoacoustic properties of the bottom, and improve our ability to localize and track source. The experimental configuration consists of a source radiating one or more pure tones to a field of freely drifting buoys, each containing a hydrophone, GPS navigation, and radio telemetry. A key component of the method is the establishment of a local differential GPS system between the source ship and each buoy, thereby enabling the determination of the positions of the buoys relative to the ship with submeter accuracy. In this manner, the drifting buoys create 2D synthetic aperture horizontal arrays along which the modal evolution of the waveguide can be observed in the spatial domain, or after beam forming, in the horizontal wavenumber domain. Typical results from two modal mapping experiments (MOMAX) are presented in which fixed and moving source configurations were used to transmit pure tones in the band 50-300 Hz to several buoys at ranges up to 10 km. MOMAX I was conducted in about 70 m of water off the New Jersey coast in March, 1997, while MOMAX II was carried out in 50-150 m water depths in the Gulf of Mexico in February, 1999. A striking feature of these data is the remarkable stability and regularity of the phase, although the magnitude displays a complex multimodal interference pattern.

A Review of Modal Inversion Methods for Inferring Geoacoustic Properties in Shallow Water

A review is presented of modal inversion techniques for determining the acoustic properties of the seabed in shallow water. Attention is focused on methods which utilize measurements of the modal eigenvalues at one or more frequencies as input data. Various inversion schemes for inferring the geoacoustic properties in a horizontally stratified waveguide are discussed. It is shown that these concepts can be extended to laterally varying waveguides as well, based on the notion, originating in adiabatic mode theory, that the local modes adapt to the local environment. Measurements of the modal trajectories in range can then be used to infer the range-dependent variation in geoacoustic properties. The results of the range-dependent inversion of experimental data obtained at 140 Hz in Nantucket Sound are presented.

A PERTURBATIVE INVERSE METHOD FOR THE DETERMINATION OF GEOACOUSTIC PARAMETERS IN SHALLOW WATER

An inverse method is described for obtaining the acoustic properties of a horizontally stratified bottom in shallow water from measurements of the magnitude and phase versus range of the pressure field due to a CW point source. These data are numerically Hankel transformed to obtain the depth-dependent Green’s function versus horizontal wavenumber. The Green’s function contains prominent peaks at horizontal wavenumbers corresponding to the eigenvalues for any trapped and virtual modes excited in the waveguide. The eigenvalues are then used as input data to a perturbative inverse scheme. The method is applied to the problem of determining the compressional wave speed as a function of depth and is demonstrated for experimental data. The results are compared with those obtained using an iteration of forward models method.

Determination of Sediment Sound Speed Profiles Using Caustic Range Information

A method for determining sediment sound speed profiles is described. It employs measurements, obtained at various receiver heights, of ranges to the caustic which is formed due to a positive gradient in the sediment. The bottom profile can then be obtained from equations, derived using the WKB approximation, which relate the parameters of the water-bottom profile to the caustic range and source/receiver heights. Using an existing result, the theory is presented for the case of an isovelocity ocean overlying a sediment half-space with a linear gradient and continuous sound speed at the water-bottom interface. A new theoretical result is derived for the linear gradient case with a discontinuity at the water-bottom interface. The method is illustrated using data at 220 Hz.

Effects of Sound Speed Fluctuations Due to Internal Waves in Shallow Water on Horizontal Wavenumber Estimation

There is considerable current interest in the influence of water-column variability on acoustic propagation and its effects on geoacoustic inversion. In general, the effect of sound speed fluctuations due to internal waves in the water column is to promote the coupling of energy between propagating acoustic modes. The effects of mode coupling include fluctuations in individual modal amplitudes and arrival times along with time spreading of the original pulses. In contrast to the broadband case, little research has been conducted on the effects of internal waves on cw modal-based inversion methods. These techniques require estimates of the propagating modal eigenvalues for a cw point source field as input data to the inversion algorithm. In much of the literature, wavenumber estimation is performed with the assumption that pressure is given by an adiabatic mode sum. Changes in modal content as a function of range are then attributed to local changes in the waveguide boundaries, specifically, the bottom. For a shallow-water waveguide including internal waves, the adiabatic assumption is violated and estimates of local wavenumber content is affected. This paper addresses the nature of the these affects on the wavenumber estimation problem. In particular, numerical studies of internal wave effects are conducted with respect to identification and bias of individual modes along with the ability to resolve closely spaced eigenvalues. Preliminary results for a weak internal wave field show that mode coupling leads to an enhancement of the wavenumber spectral estimates due to the energizing of weak modes that were previously not excited.

Multi-season acoustic tomography experiment in the Arctic

Acoustic properties of sea ice are important parameters which affect the propagation of sound both within the ice and in the water column under the ice. These properties are functions of space and time. The authors present details of a crosshole tomography experiment conducted in the Arctic to estimate two important acoustic parameters (compressional and shear wave speeds) of multi-year sea ice in three dimensions and to monitor their evolution with season. Some preliminary results of the data analysis are also presented.<<ETX>>

The Effect of Seasonal Temperature Fluctuations in the Water Column on Sediment Compressional Wave Speed Profiles in Shallow Water

In shallow water areas, the temperature of the water column undergoes large fluctuations during the course of a year. In the Gulf of Mexico, for example, temperature fluctuations of as much as twelve degrees Centigrade have been observed. These seasonal variations in water column temperature affect the pore water temperature of the bottom sediments which, in turn, affects the compressional wave speed profile. Using Biot theory, it is shown that the sediment compressional wave speed varies approximately linearly with pore water temperature and this effect is, to first order, independent of the porosity and sediment type. It is also shown that the velocity ratio (ratio of sound speeds in the water and the sediment at the sediment/water interface) is independent of the temperature but dependent on sediment type. These effects are demonstrated using two experimental measurements made at the same site in the Gulf of Mexico but during different seasons. In both cases, perturbative inversion techniques were used to infer the sound velocity profiles in the bottom. The differences between the two profiles fall within the error bounds predicted by linear inverse theory everywhere except the top 10 m of sediment, where the differences are attributed to the seasonal temperature fluctuation phenomenon. The experimental results suggest that the influence of the water column extends to greater depths than those predicted by theory.