Shane C. Walker

Estimation of modal group velocities with a single receiver for geoacoustic inversion in shallow water

Due to the expense associated with at-sea sensor deployments, a challenge in underwater acoustics has been to develop methods requiring a minimal number of sensors. This paper introduces an adaptive time-frequency signal processing method designed for application to a single source-receiver sensor pair. The method involves the application of conjugate time-frequency warping transforms to improve the SNR and resolution of the time-frequency distribution (TFD) of the measured field. Such refined knowledge of the TFD facilitates efforts to extract tomographic information about the propagation medium. Here the method is applied to the case of modal propagation in a shallow ocean range independent environment to extract a refined TFD. Given knowledge of the source-receiver separation, the refined TFD is used to extract the frequency dependent group velocities of the individual modal components. The extracted group velocities are then incorporated into a computationally light tomographic inversion method. Simulated and experimental results are discussed.

Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean

Ambient acoustic noise fields in the ocean are generally three dimensional in that they exhibit vertical and horizontal directivity. A model of spatially homogeneous noise is introduced in which the directionality is treated as separable, that is, the overall directionality of the field is the product of the individual directivities in the horizontal and vertical. A uni-modal von Mises circular distribution from directional statistics is taken to represent the noise in the horizontal, whilst the vertical component is consistent with a surface distribution of vertical dipoles. An analysis of the coherence and cross correlation of the noise at two horizontally aligned sensors is developed. The coherence function involves a single integral over finite limits, whilst the cross-correlation function, derived on the assumption that the noise has been pre-whitened, is given by an integral with limits that depend on the correlation delay time. Although the cross-correlation function does not exhibit delta functions that could be identified with the Greens function for propagation between the two sensors in the field, it does drop abruptly to zero at numerical time delays equal to the travel time between the sensors. Hence the noise could be used to recover the sound speed in the medium.

Active waveguide Green’s function estimation with application to time-reversal focusing without a probe source in a range-independent waveguide

A method is introduced for using a pair of vertical line transducer arrays (VLAs) to produce time-reversal (TR) foci at any location in a range-independent shallow-ocean waveguide without the need for a probe source. Modal theory suggests that the acoustic response sampled between a pair of VLAs separated by a range R can be repeatedly iterated to estimate the acoustic response at ranges that are integer multiples of R. When combined with the frequency-based variable-range-TR method, the process results in a virtual sampling of the acoustic response over long distances that can be applied to both passive and active shallow-ocean acoustic imaging. Here, the technique is applied to active time-reversal focusing. Array geometry effects are explored and simulation and experimental results are presented.

Application of the coherent-to-incoherent intensity ratio to estimation of ocean surface roughness from high-frequency, shallow-water propagation measurements

For acoustic propagation through a shallow ocean channel or waveguide, the coherence between different transmissions is controlled primarily by the roughness of the ocean surface and to a lesser degree by fluctuations in the volume. In this study, the coherent-to-incoherent intensity ratio (CTIR) is defined as a way to quantify the coherence between multipath transmissions and ocean surface rms wave height and wind speed. A theory that connects the CTIR and the coherent surface reflection coefficient is developed using both Kirchhoff and small-slope approximations as rough surface scattering models. The CTIRs have been evaluated over a period of several days using broad-band experimental results from shallow-water deployment of source and receiver arrays that span most of the water column. Estimates of wind speed and rms wave height obtained using these CTIR calculations are compared with environmental measurements to demonstrate the validity of the theory.

Measuring the effect of ambient noise directionality and split-beam processing on the convergence of the cross-correlation function

Measurements of ambient noise have been used to infer information about the ocean acoustic environment. In recent years the correlation of ambient noise has been shown to give estimates of the travel time of acoustic paths between the sensors recording the noise. A number of issues affect the results of the noise correlation. This paper presents the results of noise correlation of the two horizontally separated arrays of sensors in the 2010 ambient noise experiment. Using the experimental data, the effects on the convergence of the noise correlation are examined with respect to the size and shape of the arrays, the length of time used, and the directionality of the noise field.

Focal depth shifting of a time reversal mirror in a range-independent waveguide

A time reversal mirror refocuses back at the original probe source position. A goal has been to refocus at different positions without model based calculations. A method to refocus at different ranges has been developed earlier [Song et al., J. Acoust. Soc. Am. 103, 3224–3240 (1998)] using frequency shifting. Here we present a technique to refocus at different depths than the original probe source in a shallow ocean range‐independent waveguide. The requirement is to collect data from various ranges at a single depth, as from a moving broadband radiator, over a distance sufficient to construct the relevant frequency‐wavenumber structure of the waveguide. With this information, it is then possible to focus at arbitrary depth at any of the ranges that the probe source data were taken. Theory and laboratory measurements are presented.

Sensitivity kernel for surface scattering in a waveguide

Using the Born approximation, a linearized sensitivity kernel is derived to describe the relationship between a local change at the free surface and its effect on the acoustic propagation in the water column. The structure of the surface scattering kernel is investigated numerically and experimentally for the case of a waveguide at the ultrasonic scale. To better demonstrate the sensitivity of the multipath propagation to the introduction of a localized perturbation at the air-water interface, the kernel is formulated both in terms of point-to-point and beam-to-beam representations. Agreement between theory and experiment suggests applications to sensitivity analysis of the wavefield for sea surface perturbations.

Modal Doppler theory of an arbitrarily accelerating continuous-wave source applied to mode extraction in the oceanic waveguide.

A Doppler-based method for using a moving narrow-band source to extract the modes of acoustic propagation in a range-independent shallow ocean waveguide over a partial-water-column spanning vertical line array (VLA) is introduced. Because the modal components propagate at distinct frequencies in the case of uniform radial source motion, the modal depth functions may be isolated and extracted from a frequency decomposition of the field. Because Doppler broadening due to radial source accelerations degrades the effectiveness of the extraction method, the method incorporates a technique to compensate for Doppler broadening. As the basis for the compensation technique, a theory is introduced for describing the VLA field from an accelerating cw source. By connecting the range of the source at the time a signal feature is emitted (the retarded time) to the range of the source at the time the signal feature arrives at the receiver (the contemporary time), the theory incorporates the Doppler effects associated with the finite group velocities of the modal components. The mode extraction method and compensation technique are applied to simulation and ocean data.

A model for the spatial coherence of arbitrarily directive noise in the depth-stratified ocean

Though referred to as noise, the ambient ocean soundscape carries valuable information about the physical ocean environment. To study this information, Kuperman and Ingenito introduced a model for spatial coherence in a depth stratified ocean arising from the vertically directive diffuse acoustic noise produced by bubbles distributed throughout the surface. Here the model is adapted to incorporate horizontal directivity as well, making it possible to include additional noise contributions from directive features such as storms, biologics, shipping, and wave breaking. As an analytic approach, the model can serve as a computationally light complement to existing methods.

A model for spatial coherence from directive ambient noise in attenuating, dispersive media

As a complement to experimental efforts in seismics and acoustics to infer geo-acoustic properties of the propagation environment from the second order statistics of ambient noise measurements, a set of exact, explicit, closed form expressions for the cross-spectral density and spatial coherence of diffuse random wave fields is presented. Taken together, the expressions are well suited for modeling broadband, diffuse wave coherence in realistic scenarios involving directive, ambient noise from local (i.e., volume) and distant (i.e., plane wave) source features in an open, dispersive, attenuating medium.