Steven Finette

Acoustic propagation through an internal wave field in a shallow water waveguide

This paper addresses the problem of predicting and interpreting acoustic wave field properties in a stochastic ocean waveguide, for which the sound-speed variability within the water column is treated explicitly as a random process. It is assumed that the sound-speed distribution is composed of three components: a deterministic, time-independent profile and two stochastic components induced by internal wave activity. One random contribution represents a spatially diffuse Garrett–Munk field whose spectrum is constrained by the shallow water waveguide, while the second corresponds to spatially localized soliton packets. A high-angle elastic parabolic equation method is applied to compute single frequency realizations of the pressure field using this three-component representation of the sound-speed distribution. Ensemble-averaged transmission loss and scintillation index measures for the full pressure field and its modal components are estimated for different source depths and for both flat and sloping bott...

Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Two numerical techniques are proposed to construct a polynomial chaos (PC) representation of an arbitrary second-order random vector. In the first approach, a PC representation is constructed by matching a target joint probability density function (pdf) based on sequential conditioning (a sequence of conditional probability relations) in conjunction with the Rosenblatt transformation. In the second approach, the PC representation is obtained by having recourse to the Rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target Spearmans rank correlation coefficient (SRCC) matrix. Both techniques are applied to model an experimental spatio-temporal data set, exhibiting strong non-stationary and non-Gaussian features. The data consists of a set of oceanographic temperature records obtained from a shallow-water acoustics transmission experiment [1]. The measurement data, observed over a finite denumerable subset of the indexing set of the random process, is treated as a collection of observed samples of a second-order random vector that can be treated as a finite-dimensional approximation of the original random field. A set of properly ordered conditional pdfs, that uniquely characterizes the target joint pdf, in the first approach and a set of target marginal pdfs and a target SRCC matrix, in the second approach, are estimated from available experimental data. Digital realizations sampled from the constructed PC representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy. The relative advantages and disadvantages of the two proposed techniques are also highlighted.

Acoustic propagation through anisotropic internal wave fields: Transmission loss, cross-range coherence, and horizontal refraction

Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is interpreted as a nonstationary oceanographic waveguide within the water column, preferentially funneling acoustic energy between the thermocline depressions.

A stochastic representation of environmental uncertainty and its coupling to acoustic wave propagation in ocean waveguides

It is argued that a quantitative measure of incomplete environmental knowledge or information (i.e., environmental uncertainty) should be included in any simulation-based predictions linked to acoustic wave propagation. A method is then proposed to incorporate environmental uncertainty directly into the computation of acoustic wave propagation in ocean waveguides. In this regard, polynomial chaos expansions are chosen to represent uncertainty in both the environment and acoustic field. The sound-speed distribution and acoustic field are therefore generalized to stochastic processes, where uncertainty in the field is interpreted in terms of its statistical moments. Starting from the narrow angle parabolic approximation, a set of coupled differential equations is derived in which the coupling term links incomplete environmental information to the corresponding uncertainty in the acoustic field. Propagation of both the field and its uncertainty in an isospeed waveguide is considered as an example, where the ...

Embedding uncertainty into ocean acoustic propagation models (L)

A probabilistic formalism is proposed for the direct inclusion of environmental uncertainty into an acoustic model that describes propagation in an ocean waveguide. Incomplete environmental knowledge is characterized by a spectral representation of uncertainty using expansions of random processes in terms of orthogonal random polynomials. A brief summary of the method is presented and a set of coupled differential equations describing the propagation of both the acoustic field and its associated uncertainty is derived for the case where the uncertain environment is attributed to a lack of complete information concerning the waveguide’s sound speed distribution.

Acoustic field variability induced by time evolving internal wave fields

A space- and time-dependent internal wave model was developed for a shallow water area on the New Jersey continental shelf and combined with a propagation algorithm to perform numerical simulations of acoustic field variability. This data-constrained environmental model links the oceanographic field, dominated by internal waves, to the random sound speed distribution that drives acoustic field fluctuations in this region. Working with a suite of environmental measurements along a 42-km track, a parameter set was developed that characterized the influence of the internal wave field on sound speed perturbations in the water column. The acoustic propagation environment was reconstructed from this set in conjunction with bottom parameters extracted by use of acoustic inversion techniques. The resulting space- and time-varying sound speed field was synthesized from an internal wave field composed of both a spatially diffuse (linear) contribution and a spatially localized (nonlinear) component, the latter consisting of solitary waves propagating with the internal tide. Acoustic simulation results at 224 and 400 Hz were obtained from a solution to an elastic parabolic equation and are presented as examples of propagation through this evolving environment. Modal decomposition of the acoustic field received at a vertical line array was used to clarify the effects of both internal wave contributions to the complex structure of the received signals.

Multichannel deconvolution of an acoustic transient in an oceanic waveguide

The temporal signature and source location of an acoustic pulse propagating in an oceanic waveguide is estimated from passively sensed multichannel data on a vertical hydrophone array. A theoretical solution for this inverse source problem is presented that incorporates both a broadband generalization of matched‐field processing to estimate the source location, and a Bayesian based deconvolution algorithm operating on multichannel array data to extract the source signature. The algorithms are implemented on a massively parallel computer architecture. The theory was tested on experimental data using a chirp signal recorded on a vertical hydrophone array located approximately one convergence zone from the source. Results indicate that deconvolving the Green’s function using multichannel data is important for stabilizing the inversion in the presence of environmental mismatch. The additional information about the source time series, obtained over slightly different propagation channels, limits the solution s...

A stochastic response surface formulation of acoustic propagation through an uncertain ocean waveguide environment

Stochastic basis expansions are applied to formulate and solve the problem of including uncertainty in numerical models of acoustic wave propagation within ocean waveguides. As an example, a constrained least-squares approach is used to estimate the intensity of an acoustic field whose waveguide environment has uncertainty in both source depth and sound speed. The mean intensity, a second moment of the field, and its probability distribution are computed and compared with independent Monte-Carlo computations of these quantities. Very good agreement is obtained, indicating the potential of stochastic basis expansions for describing multiple sources of uncertainty and their effect on acoustic propagation.

ACOUSTIC PROPAGATION IN AN UNCERTAIN WAVEGUIDE ENVIRONMENT USING STOCHASTIC BASIS EXPANSIONS

A generalization of acoustic propagation in an uncertain ocean waveguide environment is described using a probabilistic formulation in terms of stochastic basis expansions. The problem is studied in the context of wave propagation in random media, where environmental uncertainty and its interaction with the acoustic field are described by stochastic, rather than deterministic parameters and fields. This representation, constructed explicitly in terms of Karhunen-Loeve (KL) and polynomial chaos (PC) expansions, leads to coupled differential equations for the expansion coefficients from which the stochastic acoustic field can be obtained as a random process. The equations are solved in the narrow-angle parabolic approximation using a split-step method to compute moments of the random acoustic field at any point in the waveguide. Results are compared with Monte-Carlo computations of the acoustic field in the same environment to study the convergence of the truncated stochastic basis expansion representing the acoustic field. The rate of convergence of the truncated chaos expansion was found to be dependent on the particular moment computed. For the first and second moments corresponding to the mean field and the field intensity, convergence was achieved rapidly, only requiring low order expansions. Another second moment, the acoustic spatial coherence, converged more slowly due to the relative phase information that, in this formulation, is described by polynomial approximation. While stochastic basis expansions show promise for the development of compact representations of the acoustic field in the presence of environmental uncertainty, accelerated convergence schemes will be needed to allow for practical applications.

Stochastic basis expansions applied to acoustic propagation in an uncertain, range, and depth‐dependent, multi‐layered waveguide.

We study the utility of stochastic basis expansions in acoustic propagation through a multi‐layered ocean waveguide in the presence of environmental uncertainty. Environmental uncertainty means that the parameters that describe the waveguide are treated probabilistically. Specifically, in the differential equation governing propagation, the uncertainty appears in the sound speed profile as an explicit dependence on a set of random variables. This implies that the acoustic field itself is a random field. Stochastic basis expansions are attractive because of their often exponential convergence. We use a complete set of multivariate orthogonal polynomials to compute the acoustic field’s statistics. The field propagates by a wide‐angle parabolic equation through a rectangular waveguide comprised of three layers separated by two horizontal interfaces. A pressure release surface and hard bottom bound the waveguide. The water’s sound speed is a constant perturbed by a small, random range, and depth‐dependent ter...