Mirages in shallow water matched-field processing

Abstract

Broadband (50–200 Hz) matched field processing was performed on vertical line array data from a recent shallow water experiment. Although the actual water depth steadily decreased from 200 to 100 m over the source tow track, the replica vectors were calculated assuming a range-independent environment of 200 m depth. Rather than breaking up due to the increasingly severe environmental mismatch, the broadband matched field output peak in range and depth behaved in a consistent way; both the predicted range and depth of the source became increasingly greater than its true range and depth as the true water depth decreased. A simple analytical model was developed to predict the behavior of these MFP mirages. The good agreement between model predictions and actual results suggests that the model can be used to quantify the impact of unknown water depth changes (e.g., ocean swell on synthetic aperture studies) and to ‘‘calibrate’’ water depth in a region using the sinking mirages of surface ships of opportunity. By use of the concept of ‘‘effective depth’’ developed by D. E. Weston et al., the model also can be applied to studies of ocean bottom geoacoustic parameter mismatch. [Work supported by ONR, code 321.]

Geoacoustic and source tracking using particle filtering: Experimental results

“…In an ideal waveguide with pressure release boundaries, the ratio of MFP range estimate to true source range is equal to the ratio of flat bathymetry water depth to true water depth at source location, creating a mirage. 31 The same ratio is valid for source depth regardless of the frequency used. Since the actual environment used here is more complex with a sedimentary layer these relations are approximate.…”

“…At the beginning of the track the water depth at the source is more than the 216 m used in the range-independent profile, creating a side lobe at a shallower and closer point. 31 Likewise, toward the end of the track the water depth at the source is shallower and hence the worst case inversion predicts a source deeper and farther away than the true location.…”

“…When there is a mismatch between the assumed water depth and its actual value, the source appears at a different location which is known as the source mirage effect. 30,31 The bathymetry changes from initially flat ͑at 130 m͒ to a slopedbottom as the ship moves into shallower water finally reaching a water depth of 100 m. Ignoring this variation results in a mirage forming after t = 0 and slowly moving away from the true location. Figure 5 shows such a mismatched MFP estimator using a normalized Bartlett mismatch ͓Eq.…”

Bayesian model selection applied to self-noise geoacoustic inversion

“…7, 1D and 2D marginal probability plots indicate relatively homogeneous PPDs for most parameter pairs, except in the case of water depth D and source range R s , which shows a very strong positive correlation of the type commonly found in shallow-water acoustics. 21,30 This correlation is also apparent in the parameter covariance matrices, estimated via Eqs. ͑21͒ and ͑22͒ and plotted as correlation matrices i j in Figs.…”

“…As noted by Collins and Fishman, 29 algorithms that generate univariate parameter perturbations, such as SA and Gibbs sampling, are particularly susceptible to poor acceptance ratios when sampling strongly correlated parameter spaces. In ocean acoustics, such parameter correlations are frequently encountered, 30 and coordinate rotation, whereby the parameter covariance matrix C, or alternatively, a covariance matrix computed from field derivatives 29 is effectively orthogonalized, is a standard solution that will not be discussed here in detail. Following Dosso, 3 our Gibbs sampler originally included a covariance estimation phase conducted at Tϭ1 following which the parameter covariance was estimated from sampled vectors m as C m Ϸ͗mm † ͘Ϫ͗m͗͘m͘ † .…”