Tianrun Chen

Mean and variance of the forward field propagated through three-dimensional random internal waves in a continental-shelf waveguide

The mean and variance of the acoustic field forward propagated through a stratified ocean waveguide containing three-dimensional (3-D) random internal waves is modeled using an analytic normal mode formulation. The formulation accounts for the accumulated effects of multiple forward scattering. These lead to redistribution of both coherent and incoherent modal energies, including attenuation and dispersion. The inhomogeneous medium’s scatter function density is modeled using the Rayleigh-Born approximation to Green’s theorem to account for random fluctuations in both density and compressibility caused by internal waves. The generalized waveguide extinction theorem is applied to determine attenuation due to scattering from internal wave inhomogeneities. Simulations for typical continental-shelf environments show that when internal wave height exceeds the acoustic wavelength, the acoustic field becomes so randomized that the expected total intensity is dominated by the field variance beyond moderate ranges....

Empirical dependence of acoustic transmission scintillation statistics on bandwidth, frequency, and range in New Jersey continental shelf

The scintillation statistics of broadband acoustic transmissions are determined as a function of signal bandwidth B, center frequency f(c), and range with experimental data in the New Jersey continental shelf. The received signal intensity is shown to follow the Gamma distribution implying that the central limit theorem has led to a fully saturated field from independent multimodal propagation contributions. The Gamma distribution depends on the mean intensity and the number of independent statistical fluctuations or coherent cells micro of the received signal. The latter is calculated for the matched filter, the Parseval sum, and the bandpassed center frequency, all of which are standard ocean acoustic receivers. The number of fluctuations mu of the received signal is found to be an order of magnitude smaller than the time-bandwidth product TB of the transmitted signal, and to increase monotonically with relative bandwidth Bfc. A computationally efficient numerical approach is developed to predict the mean intensity and the corresponding broadband transmission loss of a fluctuating, range-dependent ocean waveguide by range and depth averaging the output of a time-harmonic stochastic propagation model. This model enables efficient and accurate estimation of transmission loss over wide areas, which has become essential in wide-area sonar imaging applications.

Temporal coherence after multiple forward scattering through random three-dimensional inhomogeneities in an ocean waveguide

An analytical expression is derived for the temporal coherence of an acoustic field after multiple forward scattering through random three-dimensional (3D) inhomogeneities in an ocean waveguide. This expression makes it possible to predict the coherence time scale of field fluctuations in ocean-acoustic measurements from knowledge of the oceanography. It is used to explain the time scale of acoustic field fluctuations observed at megameter ranges in various deep ocean-acoustic transmission experiments. It is shown that this time scale is nonlinearly related to the much longer coherence time scale of deep ocean internal waves through a multiple forward scattering process. It is also shown that 3D scattering effects become pronounced when the acoustic Fresnel width exceeds the cross-range coherence length of the deep ocean internal waves, which lead to frequency and range-dependent power losses in the forward field that may help to explain historic long range measurements.

Range‐dependent 3D scattering and reverberation in the continental shelf environment from biology, geology and oceanography

Several unified scattering and reverberation models were developed in support of the ONR Acoustic Clutter Program. They include a range‐dependent model based on the parabolic equation that can be used to efficiently model scattering from a random spatial distribution of random targets that obey the sonar equation in the waveguide and a similar but range‐independent waveguide model based on normal modes for scattering from extended objects. Both these models are bistatic and fully 3D, and the latter model also accounts for modal coupling between propagation and scattering caused by extended objects in the waveguide. These models are applied to examine both coherent and diffuse scattering measured after beamforming and match‐filtering on an array from schools of fish, plankton, volume inhomogeneities in the sea bottom, roughness on the seafloor, extended seafloor and sub‐bottom features such as river channels and reflective strata, and internal and surface waves. We provide a review of the dominant sources ...

Temporal coherence of the acoustic field forward propagated through a continental shelf with random internal waves

An analytical model derived from normal mode theory for the accumulated effects of range-dependent multiple forward scattering is applied to estimate the temporal coherence of the acoustic field forward propagated through a continental-shelf waveguide containing random three-dimensional internal waves. The modeled coherence time scale of narrow band low-frequency acoustic field fluctuations after propagating through a continental-shelf waveguide is shown to decay with a power-law of range to the -1/2 beyond roughly 1 km, decrease with increasing internal wave energy, to be consistent with measured acoustic coherence time scales. The model should provide a useful prediction of the acoustic coherence time scale as a function of internal wave energy in continental-shelf environments. The acoustic coherence time scale is an important parameter in remote sensing applications because it determines (i) the time window within which standard coherent processing such as matched filtering may be conducted, and (ii) the number of statistically independent fluctuations in a given measurement period that determines the variance reduction possible by stationary averaging.

General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides

A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.

Mean, variance, and temporal coherence of the 3D field forward propagated through random internal waves in deep‐ocean waveguides

An analytical expression for the temporal coherence of an acoustic signal propagated through a 3D random internal‐wave field in a deep‐ocean waveguide is derived. The modeled coherence time scale of the acoustic fluctuations at 3000‐km range is on the order of 10 min and matches the ATOC experimental measurement. It is found that the 3D scattering effects on the forward field become pronounced when the Fresnel width exceeds the cross‐range coherence length of the internal‐wave field. The depth‐integrated intensity losses due to internal waves first increase then decrease as frequency decreases from 75 to 10 Hz. These results are derived by applying a general modal solution for the statistical moments of an acoustic field propagating through 3D random inhomogeneities [Ratilal and Makris, ‘‘Mean and covariance of the forward field propagated through a stratified ocean waveguide with three‐dimensional random inhomogeneities,’’ J. Acoust. Soc. Am. 118, 3532–3559 (2005)] to the acoustic propagation through a r...

Optimal passive source localization in a fluctuating ocean waveguide based on an analytic model for the mean field and covariance

The ocean acts as an enormously complex channel for signal transmission. It is characterized by temporal fluctuations and spatial variabilities that often lead to significant randomization of the measured field. Signal processing techniques must be derived from fundamental physical models to attain statistical optimality in such an environment. Here we present such an analysis with a new analytic model [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)] for the mean field and its covariance after propagation through a fluctuating ocean waveguide based on the first principles of waveguide scattering theory. The model is advantageous because it includes the primary physical effects of attenuation, dispersion, and coupling of modal energy due to multiple forward scattering in a convenient and intuitive form that is well suited to analytic manipulations. An example will be presented for passive source localization in range and depth in a fluctuating ocean waveguide by nonlinear matched field inversion....

Estimating internal wave statistics from underwater acoustic transmission scintillation measurements on the New Jersey shelf with a 3‐D stochastic model

The acoustic intensity expected after transmission through random inhomogeneities in an ocean waveguide is analytically expressed in terms of modal dispersion, attenuation, and energy redistribution in a 3‐D multiple forward scattering formulation [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)]. This approach is used to model forward scattering through a random internal wavefield. Scattering from the density and compressibility inhomogeneities caused by the internal waves is approximated with the Rayleigh–Born series. The model is used to estimate the rms internal‐wave height from low‐to‐mid‐frequency underwater acoustic transmission scintillations measured during the Main Acoustic Clutter experiment of 2003 in the New Jersey Strataform area. Estimated internal wave height standard deviations matched those obtained from independent temperature and CTD measurements and suggest that the internal wave field was not temporally stationary.

Assessing fish populations and enhancing biological detection in continental shelf environments with range‐dependent scattering and reverberation models

Fish populations in continental shelf environments can be continuously imaged over thousands of square kilometers using acoustic waveguide remote sensing techniques [Makris et al., Science, Feb. (2006)]. A calibrated range‐dependent scattering and reverberation model [Ratilal et al., J. Acoust. Soc. Am. 114, 2302 (2003)] based on the parabolic equation has been applied to assess population densities of fish by inverting long‐range acoustic data collected on the New Jersey continental shelf. This model is now applied to predict the types of fish species and zooplankton that are detectable in a general range‐dependent continental shelf environment, including the resolution and accuracy that can be expected in estimating fish population densities and for differentiating fish species. We consider different geometries of the source and receiving array to enhance biological detection and reduce background reverberation in highly range‐dependent environments. Using multiple source frequencies, the possibility of...