Tarun K. Chandrayadula

Coupled mode transport theory for sound transmission through an ocean with random sound speed perturbations: Coherence in deep water environments

Second moments of mode amplitudes at fixed frequency as a function of separations in mode number, time, and horizontal distance are investigated using mode-based transport equations and Monte Carlo simulation. These second moments are used to study full-field acoustic coherence, including depth separations. Calculations for low-order modes between 50 and 250 Hz are presented using a deep-water Philippine Sea environment. Comparisons between Monte Carlo simulations and transport theory for time and depth coherence at frequencies of 75 and 250 Hz and for ranges up to 500 km show good agreement. The theory is used to examine the accuracy of the adiabatic and quadratic lag approximations, and the range and frequency scaling of coherence. It is found that while temporal coherence has a dominant adiabatic component, horizontal and vertical coherence have more equal contributions from coupling and adiabatic effects. In addition, the quadratic lag approximation is shown to be most accurate at higher frequencies and longer ranges. Last the range and frequency scalings are found to be sensitive to the functional form of the exponential decay of coherence with lag, but temporal and horizontal coherence show scalings that fall quite close to the well-known inverse frequency and inverse square root range laws.

Observations and transport theory analysis of low frequency, acoustic mode propagation in the Eastern North Pacific Ocean.

Second order mode statistics as a function of range and source depth are presented from the Long Range Ocean Acoustic Propagation EXperiment (LOAPEX). During LOAPEX, low frequency broadband signals were transmitted from a ship-suspended source to a mode-resolving vertical line array. Over a one-month period, the ship occupied seven stations from 50 km to 3200 km distance from the receiver. At each station broadband transmissions were performed at a near-axial depth of 800 m and an off-axial depth of 350 m. Center frequencies at these two depths were 75 Hz and 68 Hz, respectively. Estimates of observed mean mode energy, cross mode coherence, and temporal coherence are compared with predictions from modal transport theory, utilizing the Garrett-Munk internal wave spectrum. In estimating the acoustic observables, there were challenges including low signal to noise ratio, corrections for source motion, and small sample sizes. The experimental observations agree with theoretical predictions within experimental uncertainty.

Interpolation methods for vertical linear array element localization

Array element localization is crucial for applications such as ocean acoustic tomography. Loss of navigation data makes it difficult to compensate for array motion when implementing operations such as mode filtering or beamforming. This paper presents a method for estimating missing array navigation data using an empirical orthogonal function (EOF) model. The method can be applied to estimate the location of some vertical array elements based on the location of the other elements. It assumes that second order statistics can be estimated from a set of navigation measurements for the full array. The paper applies the EOF-based method to estimate missing navigation data for the long range ocean acoustic propagation experiment (LOAPEX). The results are evaluated by examining how the errors in mooring motion estimation affect mode processing. In particular the paper analyzes the degradation in array gain and the errors in time of arrival for the low order modes. The error statistics indicate that use of the EOF method has a negligible effect on mode processing.

Reduced rank models for travel time estimation of low order mode pulses

Mode travel time estimation in the presence of internal waves (IWs) is a challenging problem. IWs perturb the sound speed, which results in travel time wander and mode scattering. A standard approach to travel time estimation is to pulse compress the broadband signal, pick the peak of the compressed time series, and average the peak time over multiple receptions to reduce variance. The peak-picking approach implicitly assumes there is a single strong arrival and does not perform well when there are multiple arrivals due to scattering. This article presents a statistical model for the scattered mode arrivals and uses the model to design improved travel time estimators. The model is based on an Empirical Orthogonal Function (EOF) analysis of the mode time series. Range-dependent simulations and data from the Long-range Ocean Acoustic Propagation Experiment (LOAPEX) indicate that the modes are represented by a small number of EOFs. The reduced-rank EOF model is used to construct a travel time estimator based on the Matched Subspace Detector (MSD). Analysis of simulation and experimental data show that the MSDs are more robust to IW scattering than peak picking. The simulation analysis also highlights how IWs affect the mode excitation by the source.

Signal processing techniques for low‐order acoustic modes

Internal waves introduce substantial fluctuations in the lowest mode signals recorded during long‐range tomography experiments. Lacking a complete random model for the mode signals, tomographers typically resort to averaging the mode signals across receptions to mitigate internal wave effects. Chandrayadula et al. used the 2004 Long Range Ocean Acoustic Propagation EXperiment (LOAPEX) signals and parabolic equation (PE) simulations modeling the LOAPEX environment to derive range‐dependent statistics such as temporal mean, temporal covariance, and intermodal correlation of the lower mode signals [Chandrayadula et al., J. Acoust. Soc. Am. 120, 3062 (2006)]. This talk proposes several statistical signal processing techniques such as likelihood ratio detectors, minimum entropy deconvolution methods, and empirical orthogonal function detectors that are based on the derived statistics, to mitigate internal wave effects. The proposed methods are tested on both the LOAPEX signals and PE simulated mode signals and...

Evolution of second‐order statistics of low‐order acoustic modes

Low‐mode signals measured during long range tomography experiments, such as the Acoustic Thermometry of Ocean Climate (ATOC) and the North Pacific Acoustic Laboratory experiments, have a random arrival structure due to internal waves. At megameter ranges, the narrow‐band mode amplitude is predicted to be Gaussian and uncorrelated with other modes [Dozier and Tappert, J. Acoust. Soc. Am. 63, 353–365 (1978)]. Wage et al. measured the centroid, frequency coherence, time spread, and time coherence for the broadband ATOC mode signals received at ranges exceeding 3000 km [Wage et al., J. Acoust. Soc. Am. 117, 1565–1581 (2005)]. The 2004 Long Range Acoustic Propagation EXperiment (LOAPEX) provided an opportunity to observe how the mode statistics evolves with range. This talk investigates the mean, temporal covariance, and intermodal correlation of the low modes at ranges between 50 and 3200 km using LOAPEX data. Broadband parabolic equation simulations were performed to model internal wave effects on the low‐mo...

Monterey Bay ambient noise profiles using underwater gliders

In 2012, during two separate week-long deployments, underwater gliders outfitted with external hydrophones profiled the upper 100 m of Monterey Bay. The environment contains various noises made by marine mammals, ships, winds, and earthquakes. Unlike hydrophone receivers moored to a fixed location, moving gliders measure noise variability across a wide terrain. However, underwater mobile systems have limitations such as instrument and flow noise, that are undesired. In order to estimate the system noise level, the hydrophones on the gliders had different gain settings on each deployment. The first deployment used a 0 dB gain during which the ambient noise recordings were dominated by the glider. The second used two hydrophones, one with a 0 dB gain and the other with 20 dB. Apart from system sounds, the higher-gain hydrophone also recorded far-away sources such as whales and ships. The noise recordings are used to estimate the spectrograms across depth and record time. The spectrograms are integrated with...

Wavefront statistics from measurements made in the Philippine Sea and comparisons to path integral theory

Between April 2010 and April 2011, acoustic transmissions were carried out by six sources moored near the sound channel axis and, which were deployed across a 200-300 km radius in the Philippine Sea. The acoustic sources transmitted broadband chirp signals that spanned frequency bands ranging from 140-200~Hz to 200-300~Hz. The transmissions were recorded by a water column spanning Distributed Vertical Line Array (DVLA) that was placed roughly at the center of the area covered by the sources. The transmission ranges from the different sources to the DVLA varied from 125~km to 450~km. The Philippine Sea is an oceanographically diverse environment, which apart from internal waves also contains energetic eddies and internal tides. The acoustic data recorded by the spatially diverse array is hence an opportunity to quantify the degree of anisotropy in the acoustic propagation. This presentation first discusses the wavefront resolution capabilities of the DVLA. The receptions are then used to estimate narrowban...

Statistics of mode amplitudes in an ocean with random sound speed perturbations: Temporal coherence.

A transport equation has been derived to describe the range evolution of the single frequency cross mode coherence matrix including time separations. The theory assumes 2‐D propagation in the depth range plane, small angle, weak multiple forward scattering, and the Markov approximation, and it has been shown to accurately predict the observable of mean intensity for both deep and shallow water (i.e., strongly lossy) situations. This paper will present results for the acoustic observable time coherence and will address the issues of accuracy of the temporal coherence approximations, relative contributions from coupling and adiabatic effects, scaling with range and frequency, and the functional form of the coherence with regards to lag.

Robust observables for mode tomography.

Deep water tomographic inversions should include the low modes to improve estimates of the axial sound speed. Unfortunately, the low‐mode signals are strongly affected by internal wave fluctuations, making it very challenging to estimate their arrival times. This talk describes the use of matched subspace detectors (MSDs) to measure mode travel times for ranges up to 400 km. The MSD approach was first proposed by Scharf and Friedlander [IEEE Trans. Signal Process. 42, 2146–2157 (1994)] as a way to detect signals that lie within a particular subspace. In this work the subspace for each mode is defined by analyzing simulations of mode propagation through independent realizations of the internal wave field. Simulations show that the MSD‐based travel time estimation approach yields higher accuracy and less variance than other methods such as peak‐picking. The end result is improved inversions for sound speed near the sound channel axis. In addition to the simulation study, mode signals from the 2004 Long Rang...