Doppler Passive Fathometry.

Passive fathometry is a technique whereby broadband ambient ocean noise received on an array of hydrophones is averaged and cross-correlated to produce a sub-bottom profile [Siderius, Harrison, and Porter (2006). J. Acoust.

The ocean noise coherence matrix and its rank.

An expression for the cross-spectral density matrix of ocean noise naturally separates into a Toeplitz part and a Hankel part [Harrison (2017). J. Acoust.

Separation of measured noise coherence matrix into Toeplitz and Hankel parts.

The cross-spectral density of ocean ambient noise is usually estimated from the product of the complex hydrophone signals, each of which already corresponds to the summed responses of sources from all angles. The true coherence is the integral over all angles of the angle-dependent product. The influence of this distinction on necessary time integration in geoacoustic inversion and passive fathometry is explored, and a meaningful separation of the cross-spectral density matrix into Toeplitz and Hankel parts is proposed.

Efficient modeling of range-dependent ray convergence effects in propagation and reverberation.

In an earlier paper [Harrison (2013). J. Acoust.

Ray convergence in a flux-like propagation formulation.

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.

Synthetic array processing of ocean ambient noise for higher resolution seabed bottom loss estimation.

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.

A relation between multipath group velocity, mode number, and ray cycle distance.

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.

Bayesian geoacoustic inversion using wind-driven ambient noise.

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.

Target time smearing with short transmissions and multipath propagation.

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.

The relation between the waveguide invariant, multipath impulse response, and ray cycles.

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.

An approximate form of the Rayleigh reflection loss and its phase: application to reverberation calculation.

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.

Fixed time versus fixed range reverberation calculation: analytical solution.

Reverberation is commonly calculated by estimating the propagation loss to and from an elementary area, defined by transmitted pulse length and beam width, and treating the resulting backscatter from the area as a function of its range. In reality reverberation is strictly a function of time and contributions for a given time come from many ranges. Closed-form solutions are given for reverberation calculated both at fixed range and at fixed time isovelocity water and some variants of Lambert's law and linear reflection loss with an abrupt critical angle.

Anomalous signed passive fathometer impulse response when using adaptive beam forming (L).

The impulse response of the seabed can be extracted from sea surface ambient noise by cross-correlating the time series from an upward and a downward steered beam. When the steering for each beam is standard minimum variance adaptive beam forming it has been found that the impulse response for significant echoes appears to have the same amplitude but opposite sign. A mathematical explanation is offered for this strange phenomenon.

Passive fathometer processing.

Ocean acoustic noise can be processed efficiently to extract Green's function information between two receivers. By using noise array-processing techniques, it has been demonstrated that a passive array can be used as a fathometer [Siderius, et al., J.

Bottom profiling by correlating beam-steered noise sequences.

It has already been established that by cross-correlating ambient noise time series received on the upward and downward steered beams of a drifting vertical array one can obtain a subbottom layer profile. Strictly, the time differential of the cross correlation is the impulse response of the seabed. Here it is shown theoretically and by simulation that completely uncorrelated surface noise results in a layer profile with predictable amplitudes proportional to those of an equivalent echo sounder at the same depth as the array.

Geoacoustic inversion using multipath pulse shape.

Experimental data, measured in a shallow water region of the Mediterranean Sea, are used to show that the variation of received intensity with time is well described by existing expressions [Harrison and Nielsen, J. Acoust. Soc.

Multipath pulse shapes in shallow water: theory and simulation.

In shallow water propagation the steeper ray angles are weakened most by boundary losses. Regarding the sound intensity as a continuous function of angle it can be converted into a function of travel time to reveal the multipath pulse shape received from a remote source (one-way path) or a target (two-way path). The closed-form isovelocity pulse shape is extended here to the case of upward or downward refraction.