Sequential Bayesian geoacoustic inversion for mobile and compact source-receiver configuration
(Color online) MREA/BP07 environment. (a) The transect AB (dashed) is of 15-km length and is identical to the transect of the Yellow Shark 94 experiment. The thin dots indicate the location of single-beam and multibeam echosoundings.25 The corresponding bathymetry extrapolation is overlaid in color. Three CTD measurement locations, made on April 23, 2007, are indicated by the crosses. The active acoustic run 2 took place in the black box. (b) Zoom on the run 2 position. The acoustic source is deployed from the R/V Leonardo (cross). The ocean-acoustic array (OAA) is deployed from a rubber boat (RHIB) and drifts slowly toward R/V Leonardo during 1 h (solid track), close to the AB transect (dashed line). Gray contour lines indicate the estimated thickness of the upper sediment layer deduced from seismic survey. The top right plot shows the dynamic horizontal positioning of R/V Leonardo around its prescribed coordinates (partially functioning on that day).
In-water geometry and CTD measurements for MREA/BP07 run 2. The small dots show the OAA receivers position deduced from DGPS and pressure sensor data every minute. The source (S) remains at the prescribed depth of 89.5 m. The overlaid seismic profile is extracted from the boomer.26 The plot shows the matched filter receiver outputs on the OAA for the 4th transmitted MF-LFM of sequence 30 (intermediate gray circle).
(Color online) MREA/BP07 run 2 received signals. (a) Received time series on the four hydrophone array (normalized). (b) Zoom on a 1-min time series received at the 25-m deep hydrophone and its associated spectrum (bottom). (c) Evolution of the log-envelope matched filter output (in dB) of the MF-LFM signal at the 25-m deep hydrophone.
(Color online) (a) Acoustic propagation in terms of propagating rays obtained with bellhop propagation code31 for the run 2 source (S)-receiver (R) geometry. The source-receiver range corresponds to the transmitted sequence 10. The water-clay interface is represented by the black horizontal line. Three families of rays are distinguished: no bottom interaction (dotted, square), bottom interaction (dashed, triangle), and subbottom interaction (solid, circle). (b) Corresponding arrival times, with the same legend.
(Color online) 1D-marginal PPDs (line plots) and 2D-joint marginal PPDs (color images) of the geometric and geoacoustic parameters for (a) the LF- MT of sequence 31, using MFP-based likelihood function, and (b) the first transmitted MF-LFM of sequence 31, using MBMF-based likelihood function, MREA/BP07 run 2.
(a) Time-averaged RMS error on model parameters from synthetic LF-MT data, normalized by their respective process noise covariance, averaged on 10 realizations of an EKF (black), EnKF-500 (white), and EnKF-1000 (gray), low and high SNR simulation data in solid and dashed contours, respectively. (b) Corresponding percentage of model parameter estimates that lies within the 95% confidence interval. The value of 95% is indicated by the dashed line.
(Color online) Sequential tracking by EKF, EnKF-500, and EnKF-1000 filtering of 60 successive LF-MT data, MREA/BP07 run 2. The EnKF-1000 95% confidence intervals are shown in dashed lines. Global optimization results for a subsample of pings are shown in black circles, for comparison. Axis limits correspond to search bounds.
(Color online) Top hydrophone depth tracking, MREA/BP07 run 2, obtained with the different process noise covariance tuning (EnKF-1000), from the lowest to the highest values (A–E). The PT sensor data is in thick gray.
Sequential MT and LFM filtering results, with EnKF-1000 filtered MT signals (dashed line) and EKF-filtered LFM signals (solid line), for low frequency band (gray) and medium frequency band (black), MREA/BP07 run2.
(Color online) Comparison of MREA/BP07 run 2 MF-LFM tracking results with ground-truth data. (a) Seismic measurement locations (crossed mark) along seven acoustic transects defined by the time-evolving RHIB position during the run 2. (b) Corresponding SBES interpolated measurements of water column depth. (c) Corresponding seismic measurements of sediment thickness. (d) Range-averaged water column depth for each of these seven acoustic transects (gray, circles), MF-LFM tracking results (black). (e) Range-averaged sediment thickness for each of these seven acoustic transects (gray, circles), MF-LFM tracking results (black). (f) Top hydrophone depth given by the PT sensor (gray), MF-LFM tracking results (black).
(Color online) (a) Evolution of the matched-filter envelope of the MREA/BP07 run 2 MF-LFM signals (gray) and replica corresponding to the filtered results (black) on the 25-m deep hydrophone, first ping of every five transmitted sequence (1-56, bottom to top). The alignment between data and associated replica is given by the optimization algorithm. (b) Evolution of the normalized 2-D marginal PPD for the sediment thickness and compressional wave speed given by the EnKF-1000 applied to the MF-MT data (pings 1, 11, 21, 31, 41, and 51). The integral of the 2-D PPD over each surface is equal to one.
Extended Kalman filter algorithm in a prediction/correction form. The discrete time variable is reduced to the index k for the sake of clarity.
Initial parameter value and process noise standard deviation for the state-space model involved in the filtering of actual data for the multitone transmission (one signal per minute).
Process noise covariance matrices for LF-MT EnKF-1000 tracking and corresponding performances. The matrix Rww is a diagonal matrix constructed with the square of standard deviations given in Table II. RMS error precision is reproducible.
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