Chris H Harrison’s research while affiliated with Centre for Maritime Research and Experimentation (CMRE) and other places

The requirement by modern navies to predict sonar performance in shallow water, whether for use in research, planning or operations, led to an initiative for the validation of reverberation models in the form of two Reverberation Modeling Workshops at the University of Texas at Austin in November 2006 and May 2008 [J. S. Perkins and E. I. Thorsos, Update on the reverberation modeling workshops, J. Acoust. Soc. Am. 126 (2009) 2208]. The problem considered here (Problem XI, from the 2006 workshop) requires the computation of reverberation versus time in a Pekeris waveguide with Lambert scattering from the seabed. Results from eigenray, normal mode and (hybrid) continuum methods are presented and compared for the time window 0.05s to 1000s after pulse transmission. Approximate analytical solutions are used to provide insight into the expected behavior of the reverberation and establish regimes of validity of numerical models. In situations where the regimes of validity of different methods coincide, the solutions of models applying these methods overlap. The overlapping solutions agree with each other within ±0.3dB. Their purpose is to provide a baseline against which future model improvements can be assessed and quantified.

In an earlier paper [Harrison (2013). J. Acoust. Soc. Am. 133, 3777–3789] the computationally efficient energy flux approach to modeling sound propagation was modified to include focusing, ray convergence, and caustic-like behavior. The derivation started with the coherent normal mode sum but retained only terms that interfered on a scale of a ray cycle distance. Here, by starting with the adiabatic mode sum, the formulation is extended to a slowly varying range-dependent environment and applied to the target-echo and reverberation model, Artemis. Some examples are given.

The energy flux formulation of waveguide propagation is closely related to the incoherent mode sum, and its simplicity has led to development of efficient computational algorithms for reverberation and target echo strength, but it lacks the effects of convergence or modal interference. By starting with the coherent mode sum and rejecting the most rapid interference but retaining beats on a scale of a ray cycle distance it is shown that convergence can be included in a hybrid formulation requiring minimal extra computation. Three solutions are offered by evaluating the modal intensity cross terms using Taylor expansions. In the most efficient approach the double summation of the cross terms is reduced to a single numerical sum by solving the other summation analytically. The other two solutions are a local range average and a local depth average. Favorable comparisons are made between these three solutions and the wave model Orca with, and without, spatial averaging in an upward refracting duct. As a by-product, it is shown that the running range average is very close to the mode solution excluding its fringes, given a relation between averaging window size and effective number of modes which, in turn, is related to the waveguide invariant.

Predicting transmission loss in the ocean often strongly depends on the bottom loss. Bottom loss can be estimated using ocean noise and vertical array beam-forming [Harrison and Simons, J. Acoust. Soc. Am. 112, 1377-1389 (2002)]. With finite length arrays, the bottom loss estimate using this method can be smoothed due to beam widths. This paper describes how the noise coherence function can be synthetically expanded, which is similar to extending the length of an array. A full wave ocean noise model is used to demonstrate, in simulation, how this leads to improvements in the resolution of bottom loss estimates.

Weston's ray invariant or "characteristic time" in a range-dependent environment is exactly equivalent to the Wentzel-Kramers-Brillouin phase integral for ducted normal modes. By considering a ray element it is shown that the ray invariant can also be written in terms of ray cycle distance and cycle time. This leads to a useful formula for group velocity in terms of cycle distance and mode number. Drawing a distinction between the ray and wave interpretation, the Airy phase (i.e., the existence of a group velocity minimum) can be included in this approach. Favorable comparisons are made with group velocities derived from a normal mode model. The relationship is valid for variable sound speed and variable bathymetry, and this is demonstrated numerically. The formula is applicable to active sonar, multipath pulse shape, target signatures, reverberation, tomography, and underwater communications.

This paper applies Bayesian inversion to bottom-loss data derived from wind-driven ambient noise measurements from a vertical line array to quantify the information content constraining seabed geoacoustic parameters. The inversion utilizes a previously proposed ray-based representation of the ambient noise field as a forward model for fast computations of bottom loss data for a layered seabed. This model considers the effect of the array's finite aperture in the estimation of bottom loss and is extended to include the wind speed as the driving mechanism for the ambient noise field. The strength of this field relative to other unwanted noise mechanisms defines a signal-to-noise ratio, which is included in the inversion as a frequency-dependent parameter. The wind speed is found to have a strong impact on the resolution of seabed geoacoustic parameters as quantified by marginal probability distributions from Bayesian inversion of simulated data. The inversion method is also applied to experimental data collected at a moored vertical array during the MAPEX 2000 experiment, and the results are compared to those from previous active-source inversions and to core measurements at a nearby site.

In active sonar the target echo level is often estimated with a propagation model that adds all multipath arrivals. If the (post-correlator) transmitted pulse is short compared to the multipath time spread then there is effectively an extra loss (which may be substantial) since only a few of the paths contribute to the target echo at any one instant. This well known "time-smearing" loss is treated in a self-consistent manner with previous calculations of reverberation [Harrison, J. Acoust. Soc. Am. 114, 2744-2756 (2003)] to estimate the target response and the signal-to-reverberation-ratio. Again isovelocity water, Lambert's law, and reflection loss proportional to angle are assumed. In this important short pulse regime the target response becomes independent of boundary reflection properties but proportional to transmitted pulse length. Thus the signal-to-reverberation-ratio becomes independent of pulse length. The effect on signal-to-ambient-noise is also investigated and the resulting formulas presented in a table.

The waveguide invariant, β, that manifests itself as interference fringes or "striations" in a plot of frequency vs source-receiver separation, is usually thought of as a modal phenomenon. This paper shows that striations can be explained simply through the variation of the eigenray arrival times with range, in short, the variation of the multipath impulse response. It is possible to calculate β for a number of sound speed profiles analytically and to find what β depends on, why it switches from one value to another, how it depends on source-receiver depth, how it depends on variable bathymetry, and how smooth the sound speed profile needs to be for clear fringes. The analytical findings are confirmed by calculating striation patterns numerically starting from eigenray travel times in various stratified environments. Most importantly the approach throws some light on what can be deduced from β alone and the likelihood and utility of striations in reverberation.

The requirement by modern navies to predict sonar performance in shallow water, whether for use in research, planning, or operations, led to an initiative for the validation of reverberation models in the form of two reverberation modeling Workshops at the University of Texas at Austin [J. S. Perkins and E. I. Thorsos, J. Acoust. Soc. Am. 126, 2208 (2009)]. The scenario considered here (Problem XI, from the first workshop) requires the computation of reverberation versus time in a Pekeris waveguide with Lambert scattering from the seabed. Simple analytical methods are presented that provide insight into the dominant propagation paths giving rise to the reverberation and hence establish regimes of validity for various computermodels making different approximations or assumptions. Results from eigenray, normal mode, and hybrid continuum methods are compared with each other and with the analytical solutions. Numerical predictions are shown to overlap to within a few tenths of a decibel in regions where the different assumptions made by the various models are valid. These overlapping solutions are proposed as ?benchmarks? in the sense of a baseline against which future model improvements can be assessed and quantified.

A useful approximation to the Rayleigh reflection coefficient for two half-spaces composed of water over sediment is derived. This exhibits dependence on angle that may deviate considerably from linear in the interval between grazing and critical. It shows that the non-linearity can be expressed as a separate function that multiplies the linear loss coefficient. This non-linearity term depends only on sediment density and does not depend on sediment sound speed or volume absorption. The non-linearity term tends to unity, i.e., the reflection loss becomes effectively linear, when the density ratio is about 1.27. The reflection phase in the same approximation leads to the well-known "effective depth" and "lateral shift." A class of closed-form reverberation (and signal-to-reverberation) expressions has already been developed [C. H. Harrison, J. Acoust. Soc. Am. 114, 2744-2756 (2003); C. H. Harrison, J. Comput. Acoust. 13, 317-340 (2005); C. H. Harrison, IEEE J. Ocean. Eng. 30, 660-675 (2005)]. The findings of this paper enable one to convert these reverberation expressions from simple linear loss to more general reflecting environments. Correction curves are calculated in terms of sediment density. These curves are applied to a test case taken from a recent ONR-funded Reverberation Workshop.