mgun Cho

The relation between the waveguide invariant and array invariant

The waveguide invariant β is based on the dependence of group speed on phase speed and summarizes the robust interference phenomenon in the range-frequency plane. Over the last decade the elegant approach has been utilized for various applications including passive source ranging. Separately, the array invariant approach [Lee and Makris, J. Acoust. Soc. Am. 119, 336-351 (2006)] has been proposed for a robust source-range estimator from beam-time intensity data using either a horizontal or vertical array. In this paper, it is shown that the array invariant can be derived from the waveguide invariant theory assuming β=1.

Array invariant-based source localization in shallow water using a sparse vertical array

The array invariant proposed for robust source localization in shallow water exploits the beam-time migration of broadband signals. The approach requires minimal knowledge of the environment, but involves plane wave beamforming using a short-aperture vertical array in stratified acoustic waveguides. In this paper, the array invariant approach is extended to a large-aperture vertical array that is sparse with significant variation of the sound speed across the aperture for conventional beamforming. The extension is feasible because the array invariant in shallow water utilizes surface/bottom-reflected arrivals that behave like those in ideal waveguides. Robust source-range estimation is demonstrated using data from a 16-element, 56-m long vertical array at various ranges (1.5-3.5 km) from a broadband source (0.5-2 kHz) in approximately 100-m deep shallow water.

Robust source-range estimation using the array/waveguide invariant and a vertical array

The array invariant based on beam-time migration has been proposed for source-range estimation using a horizontal or vertical array (VA), with no need for forward model computations. The approach has been demonstrated successfully with experimental data in shallow water using a horizontal towed array. Recently, the array invariant has been shown to be a special case of the waveguide invariant theory. In this paper, the unified array/waveguide invariant approach to source-range estimation is applied to a short-aperture VA in a fluctuating ocean environment over a one-day period. Specifically, the mean range estimates using a 12-m long VA in ∼100 m deep water are <8% relative error for a source (2-3 kHz) at 6-km range, demonstrating the robustness of this approach.

Impact of array tilt on source-range estimation in shallow water using the array invariant

The array invariant proposed for robust source-range estimation in shallow water is based on the dispersion characteristics in ideal waveguides for broadband signals. With minimal knowledge of the environment, the approach involves plane-wave beamforming using a vertical array, utilizing multiple arrivals (i.e., eigenrays) separated in beam angle and travel time. In the presence of array tilt, however, the beam angle estimates are shifted, which potentially affects the range estimation based on the array invariant. Conversely, the array tilt could be estimated for a known source range. In this paper, the sensitivity to array tilt is analyzed theoretically and examined using simulations and data. It is found that even a small tilt angle (e.g., <2°) of a 1.2 -m long vertical array near the surface, if not compensated for, can result in a relative range error of 20% or more, for a high-frequency source (7-19 kHz) at 3-km range in approximately 100 -m deep shallow water. Moreover, the power spectrum of the time-evolving array tilt estimated for 9 min shows a dominant period of 5.6 s, which is consistent with the surface wave period concurrently measured from a waverider buoy.

Cascade of blind deconvolution and array invariant for robust source-range estimation

The array invariant proposed for robust source localization in shallow water is based on the dispersion characteristics in ideal waveguides. It involves conventional plane-wave beamforming using a vertical array, exploiting multiple arrivals separated in beam angle and travel time, i.e., beam-time migration. The approach typically requires either a short pulse emitted by a source or the Greens function that can be estimated from a probe signal to resolve distinct multipath arrivals. In this letter, the array invariant method is extended to unknown source waveforms by extracting the Greens function via blind deconvolution. The cascade of blind deconvolution and array invariant for robust source-range estimation is demonstrated using a 16-element, 56-m long vertical array at various ranges (1.5-3.5 km) from a towed source broadcasting broadband communication waveforms (0.5-2 kHz) in approximately 100-m deep shallow water.

Seasonal variation of speed and width from kinematic parameters of mode-1 nonlinear internal waves in the northeastern East China Sea

To better understand the statistical and theoretical characteristics of nonlinear internal waves (NLIWs) in the broad continental shelf of the northeastern East China Sea (ECS), historical hydrographic data collected over 50 years between 1962 and 2011 are analyzed to calculate monthly climatology. Based on KdV and extended KdV models under the two-layer approximation (i.e., mode-1 NLIWs), the monthly climatology for propagating speed and characteristic width is constructed, ranging from 0.8 to 1.2 m s−1 and from O(102) to O(103) m, respectively. The result is consistent with a few previous in situ observations in the region. When NLIWs originating in the southeastern slope area approach the shallower regime (northwestward propagation), they propagate more slowly with neither break nor extinction, but with a shorter width, since both the Iribarren and Ostrovsky numbers are small (Ir ≪ 0.45 and Os ≪ 1, respectively). Limitations of the two-layered KdV-type models are discussed (e.g., an importance of mode-2 waves) in the context of occasional extension of the low-salinity Changjiang Discharged Water onto the area, which implies distinct effects on the kinematic parameters of NLIWs in the ECS.

Array invariant-based calibration of array tilt using a source of opportunity

The array invariant, a robust approach to source-range estimation in shallow water, is based on the dispersion characteristics of broadband signals in ideal waveguides. It involves time-domain plane-wave beamforming using a vertical line array (VLA) to separate multiple coherent arrivals in beam angle and travel time. Typically, a probe signal (i.e., a cooperating source) is required to estimate the Greens function, but the array invariant has been recently extended to a ship of opportunity radiating random signals using a ray-based blind deconvolution [Byun, Kim, Cho, Song, and Byun, J. Acoust. Soc. Am. 142, EL286-EL291 (2017)]. Still, one major drawback is its sensitivity to the array tilt, shifting the beam angles and adversely affecting the array invariant parameter that determines the source range. In this paper, a simple optimization algorithm for simultaneous estimation of the array tilt and the source range is presented. The method is applied to a ship of opportunity (200-900 Hz) circling around a 56-m long VLA at a speed of 3 knots (1.5 m/s) at ranges of 1.8-3.6 km in approximately 100-m deep shallow water. It is found that the standard deviation of the relative range error significantly reduces to about 4%, from 14% with no compensation of the array tilt. The estimated tilt angle displayed as a function of the ships azimuth angle reveals that the VLA is tilted about 3° towards the northwest, suggesting that the array invariant can serve as a remote sensing technique for calibration of the array tilt using a source of opportunity.

Array invariant-based ranging of a source of opportunity

The feasibility of tracking a ship radiating random and anisotropic noise is investigated using ray-based blind deconvolution (RBD) and array invariant (AI) with a vertical array in shallow water. This work is motivated by a recent report [Byun, Verlinden, and Sabra, J. Acoust. Soc. Am. 141, 797-807 (2017)] that RBD can be applied to ships of opportunity to estimate the Greens function. Subsequently, the AI developed for robust source-range estimation in shallow water can be applied to the estimated Greens function via RBD, exploiting multipath arrivals separated in beam angle and travel time. In this letter, a combination of the RBD and AI is demonstrated to localize and track a ship of opportunity (200-900 Hz) to within a 5% standard deviation of the relative range error along a track at ranges of 1.8-3.4 km, using a 16-element, 56-m long vertical array in approximately 100-m deep shallow water.

Extension of the array invariant to deep-water environments

The array invariant utilizes multiple arrivals separated in beam angle and travel time for broadband signals, achieving robust source-range estimation without detailed knowledge of the environments in shallow water. This approach includes the waveguide invariant parameter β, which is close to one for surface/bottom-interacting shallow-water environments. In deep water, however, β significantly varies from large negative to positive values depending on the group of modes, while being sensitive to the sound speed variation within the water column. In this paper, two different approaches are investigated: 1) an extension of the array invariant by integrating multiple arrivals with varying β and 2) the use of dispersion relationship between several pairs of arrivals. These two approaches will be applied to a deep-water environment (4-km deep) using a 13-m aperture vertical array deployed to the sound channel axis (e.g., 330-m) from the Medium Frequency Noise experiment (MFN), where a high-frequency source (ab...

Iterative range estimation in a sloping-bottom shallow-water waveguide using the generalized array invariant

The array invariant theory was generalized by incorporating the waveguide invariant β, referred to as the generalized array invariant. In this paper, the generalized array invariant is extended to mildly range-dependent environments with a sloping bottom where the waveguide invariant is variable in range. Assuming knowledge of the bottom slope, the array invariant can be applied iteratively to estimate the source range starting with β = 1 (i.e., range-independent), which converges toward the correct source range by updating β at the previously estimated range. The iterative array invariant approach is demonstrated using a short-aperture vertical array (2.8-m) in a sloping-bottom shallow-water waveguide from the Random Array of Drifting Acoustic Receivers 2007 experiment, where a high-frequency source (2-3.5 kHz) close to the surface (6-m) was towed between 0.5 and 5 km in range with the water depth varying from 80 to 50 m.