Michael B. Porter

Gaussian beam tracing for computing ocean acoustic fields

The method of Gaussian beam tracing has recently received a great deal of attention in the seismological community. In comparison to standard ray tracing, the method has the advantage of being free of certain ray‐tracing artifacts such as perfect shadows and infinitely high energy at caustics. It also obviates the need for eigenray computations. The technique is especially attractive for high‐frequency, range‐dependent problems where normal mode, FFP, or parabolic models are not practical alternatives. The Gaussian beam method associates with each ray a beam with a Gaussian intensity profile normal to the ray. The beamwidth and curvature are governed by an additional pair of differential equations, which are integrated along with the usual ray equations to compute the beam field in the vicinity of the central ray of the beam. We have adapted the beam‐tracing method to the typical ocean acoustic problem of a point source in a cylindrically symmetric waveguide with depth‐dependent sound speed. We present an...

A numerical method for ocean‐acoustic normal modes

The method of normal modes is frequently used to solve acoustic propagation problems in stratified oceans. The propagation numbers for the modes are the eigenvalues of the boundary value problem to determine the depth dependent normal modes. Errors in the numerical determination of these eigenvalues appear as phase shifts in the range dependence of the acoustic field. Such errors can severely degrade the accuracy of the normal mode representation, particularly at long ranges. In this paper we present a fast finite difference method to accurately determine these propagation numbers and the corresponding normal modes. It consists of a combination of well‐known numerical procedures such as Sturm sequences, the bisection method, Newton’s and Brent’s methods, Richardson extrapolation, and inverse iteration. We also introduce a modified Richardson extrapolation procedure that substantially increases the speed and accuracy of the computation.

A passive fathometer technique for imaging seabed layering using ambient noise

A passive acoustics method is presented that uses the ocean ambient noise field to determine water depth and seabed sub-bottom layering. Correlating the noise field measured by two sensors one can recover a function that closely resembles the two-point Green’s function representing the impulse response between the two sensors. Here, a technique is described that is based on noise correlations and produces what is effectively a passive fathometer that can also be used to identify sub-bottom layers. In principle, just one or two hydrophones are needed—given enough averaging time. However, by combining the cross correlations of all hydrophone pairs in a vertical array a stronger signature can be obtained and this greatly reduces averaging time. With a moving (e.g., drifting) vertical array, the resulting algorithm yields both a map of the bottom depth (passive fathometer) and the locations of significant reflectors in the ocean sub-bottom. In this paper, the technique is described and illustrated using numer...

Impact of ocean variability on coherent underwater acoustic communications during the Kauai experiment (KauaiEx)

During the July 2003 acoustic communications experiment conducted in 100m deep water off the western side of Kauai, Hawaii, a 10s binary phase shift keying signal with a symbol rate of 4kilosymbol∕s was transmitted every 30min for 27h from a bottom moored source at 12kHz center frequency to a 16 element vertical array spanning the water column at about 3km range. The communications signals are demodulated by time reversal multichannel combining followed by a single channel decision feedback equalizer using two subsets of array elements whose channel characteristics appear distinct: (1) top 10 and (2) bottom 4 elements. Due to rapid channel variations, continuous channel updates along with Doppler tracking are required prior to time reversal combining. This is especially true for the top 10 elements where the received acoustic field involves significant interaction with the dynamic ocean surface. The resulting communications performance in terms of output signal-to-noise ratio exhibits significant change o...

The problem of energy conservation in one-way models

It is shown that the standard stair-step representation of a sloping bottom may result in significant prediction errors. In fact, current parabolic equation implementations are not energy conserving. The problem is shown to derive from the approximate treatment of the interface conditions at vertical boundaries along the stair steps. Several improved interface conditions are proposed.

A numerical method for bottom interacting ocean acoustic normal modes

In this paper we present a finite‐difference method to numerically determine the normal modes for the sound propagation in a stratified ocean resting on a stratified elastic bottom. The compound matrix method is used for computing an impedance condition at the ocean–elastic bottom interface. The impedance condition is then incorporated as a boundary condition into the finite difference equations in the ocean, yielding an algebraic eigenvalue problem. For each fixed mesh size this eigenvalue problem is solved by a combination of efficient numerical methods. The Richardson mesh extrapolation procedure is then used to substantially increase the accuracy of the computation. Two applications are given to demonstrate the speed, accuracy, and efficiency of the method.

Effects of ocean thermocline variability on noncoherent underwater acoustic communications.

The performance of acoustic modems in the ocean is strongly affected by the ocean environment. A storm can drive up the ambient noise levels, eliminate a thermocline by wind mixing, and whip up violent waves and thereby break up the acoustic mirror formed by the ocean surface. The combined effects of these and other processes on modem performance are not well understood. The authors have been conducting experiments to study these environmental effects on various modulation schemes. Here the focus is on the role of the thermocline on a widely used modulation scheme (frequency-shift keying). Using data from a recent experiment conducted in 100-m-deep water off the coast of Kauai, HI, frequency-shift-key modulation performance is shown to be strongly affected by diurnal cycles in the thermocline. There is dramatic variation in performance (measured by bit error rates) between receivers in the surface duct and receivers in the thermocline. To interpret the performance variations in a quantitative way, a precise metric is introduced based on a signal-to-interference-noise ratio that encompasses both the ambient noise and intersymbol interference. Further, it will be shown that differences in the fading statistics for receivers in and out of the thermocline explain the differences in modem performance.

Localization of marine mammals near Hawaii using an acoustic propagation model

Humpback whale songs were recorded on six widely spaced receivers of the Pacific Missile Range Facility (PMRF) hydrophone network near Hawaii during March of 2001. These recordings were used to test a new approach to localizing the whales that exploits the time-difference of arrival (time lag) of their calls as measured between receiver pairs in the PMRF network. The usual technique for estimating source position uses the intersection of hyperbolic curves of constant time lag, but a drawback of this approach is its assumption of a constant wave speed and straight-line propagation to associate acoustic travel time with range. In contrast to hyperbolic fixing, the algorithm described here uses an acoustic propagation model to account for waveguide and multipath effects when estimating travel time from hypothesized source positions. A comparison between predicted and measured time lags forms an ambiguity surface, or visual representation of the most probable whale position in a horizontal plane around the array. This is an important benefit because it allows for automated peak extraction to provide a location estimate. Examples of whale localizations using real and simulated data in algorithms of increasing complexity are provided.

Matched-field processing for broad-band source localization

In the Hudson Canyon experiment, a sound source moved at a constant depth in 73 m of water while transmitting four tonals. The signal was received on a vertical array of hydrophones that spanned the water column. The data set from this experiment has become a standard test case for studying source tracking using matched field processing. As part of that process it was important to first determine a suitable environment model and demonstrate the feasibility of matched-field processing. In this paper, we provide the background on the original data processing that was done to accomplish this. Several interesting results emerged from that study. Frequency averaging was demonstrated to be extremely beneficial when used with the Bartlett processor. However, the popular Minimum Variance processor performed poorly. Finally we discuss a very simple approach to combining the energy coherently that provided significantly improved results.

Adjoint modeling for acoustic inversion

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used.