Karl C. Focke

Broadband sound propagation in shallow water and geoacoustic inversion

Part of an experiment to test a measurement package in a shallow water region in the Gulf of Mexico was designed to gather broadband acoustic data suitable for inversion to estimate seabed geoacoustic parameters. Continuous wave tow acoustic signals at multiple frequencies and broadband impulsive source signals were recorded on a horizontal line array in a high-noise environment. Simulated annealing with a normal mode forward propagation model is utilized to invert for a geoacoustic representation of the seabed. Several inversions are made from different data samples of two light bulb implosions, the measured sound speed profiles at the HLA and at the positions of the light bulb deployments, and for two different cost functions. The different cost functions, measured sound speed profiles, and measured time series result in different inverted geoacoustic profiles from which transmission loss is generated for comparison with measurements. On the basis of physical consistency and from the comparison of the transmission loss and time series, a best estimate geoacoustic profile is selected and compared to those obtained from previously reported inversions. Uncertainties in the sound speed profile are shown to affect the uncertainties of the estimated seabed parameters.

New measurements of compressional wave attenuation in deep ocean sediments

In many situations of low frequency acoustic propagation in the ocean, the acoustic properties of the bottom are an important factor. One quantity of which few measurements have been made or reported is the compressional wave attenuation profile. This paper reports attenuation measurements based upon measurements from explosive sources which encountered the ocean bottom several times. It was found that compressional wave attenuation coefficients at 100 m depth are approximately 0.015 dB/m‐kHz in terrigenous turbidite sediments and 0.03 dB/m‐kHz in calcareous sediments. These values are as low as, and lower than, the smallest previously reported estimates.

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.

The role of the seabottom attenuation profile in shallow water acoustic propagation

The effect of the seabottom upon acoustic propagation in the frequency range from 20 to 2000 Hz in shallow water is analyzed. In particular, the role of depth and frequency variations of attenuation is considered. The point of view that attenuation in the seabottom varies linearly with frequency and changes with depth is taken. Normal mode calculations which demonstrate the interplay between depth variations of attenuation and the frequency dependence of propagation loss and mode attenuation coefficients are presented. It is shown that, if in the course of data analysis, attenuation were erroneously constrained to be constant with depth, then a nonlinear estimate for frequency dependence of attenuation could result. Calculations based upon attenuation profiles from the geophysical literature are compared with reported propagation loss data from the acoustics literature.

Caustics in range‐averaged ocean sound channels

The caustics present after range averaging are illustrated by depth plots of range‐averaged ray calculations and also of energy flux calculations. Although well understood, these infinities prevent the range‐averaging method from giving a well‐behaved summary of the propagation, and so three approaches to the true level are presented here. One solution is to assume some source directivity; in particular, a variation with the square of the grazing angle not only corresponds to the physically meaningful dipole radiation from a near‐surface source with its image, but removes all trace of the caustics. Second, a local wave approach patches together a solution, replacing the infinity by a peak shape calculated from an Airy function convolution. This predicts a broad pedestal shape at both source and conjugate depth, with a small sharp peak riding on it, although usually for the source depth only. Third, a full wave approach for the whole water column is represented by range averaging of parabolic equation fiel...

The predictibility of broadband sound propagation in shallow water and geoacoustic inversion

Part of an experiment to test a measurement package in a shallow water region in the Gulf of Mexico was designed to gather broadband acoustic data suitable for inversion to estimate seabed geoacoustic parameters. Continuous wave tow acoustic signals at multiple frequencies and broadband impulsive source signals were recorded on a horizontal line array in a high-noise environment. Simulated annealing with a normal mode forward propagation model is utilized to invert for a geoacoustic representation of the seabed. Several inversions are made from different data samples of two light bulb implosions, the measured sound speed profiles at the HLA and at the positions of the light bulb deployments, and for two different cost functions. The different cost functions, measured sound speed profiles, and measured time series result in different inverted geoacoustic profiles from which transmission loss is generated for comparison with measurements. On the basis of physical consistency and from the comparison of the transmission loss and time series, a best estimate geoacoustic profile is selected and compared to those obtained from previously reported inversions. Uncertainties in the sound speed profile are shown to affect the uncertainties of the estimated seabed parameters.

An Analysis of Deep Ocean Sound Attenuation at Very Low Frequencies

The attenuation coefficient of low‐frequency, deep ocean acoustic waves is computed for various assumptions regarding the depth profile and the frequency dependence of the scatterers. The calculations are made for a realistic velocity profile by means of a perturbation technique proposed by Guthrie [Ph. D. dissertation, The University of Auckland (1975)]. It is shown that excellent agreement with experimental data is obtained when the attenuation function is independent of frequency and decreases exponentially with depth with a characteristic depth of 200 to 500 m. A surface value of 0.11 dB/km gives good agreement with the data. At frequencies below 50 Hz the attenuation in the water column is comparable to the attenuation in the sediments for the lowest order normal modes.

Inversion of shallow water ocean acoustic data using a complex plane‐wave reflection coefficient approach

A previously reported method of inversion in range‐dependent environments using a complex plane‐wave approach [Stotts et al., J. Acoust. Soc. Am. 109, 2334 (2001)] has been applied to data analysis. The method separates the propagation in the water column from the interaction with the seabed by first calculating and then storing the eigenray characteristics associated with the assumed known waveguide geometry. The inversion is then performed by calculating the plane‐wave reflection coefficients at the predetermined angles and constructing the modeled field of the entire propagation for each perturbation of the seabed parameters. Results of applications of this model to data taken off the coast of Florida during the spring of 2001, will be presented. Consistent inversion results obtained from other models along with an examination of received time series, as well as sound speed profiles collected over the region, will also be discussed in the context of range‐dependent inversion analysis. Comparisons of th...