This study investigates the performance of a passive time-reversal mirror (TRM) combined with acoustic ray theory in localizing underwater sound sources with high frequencies (3–7 kHz). The TRM was installed on a floating buoy and comprised four hydrophones. The ray-tracing code BELLHOP was used to determine the transfer function between a sound source and a field point. The transfer function in the frequency domain obtained from BELLHOP was transformed into the time domain. The pressure field was then obtained by taking the convolution of the transfer function in the time domain with the time-reversed signals that were received by the hydrophones in the TRM. The location with the maximum pressure value was designated as the location of the source. The performance of the proposed methodology for source localization was tested in a towing tank and in the ocean. The aforementioned tests revealed that even when the distances between a source and the TRM were up to 1600 m, the distance deviations between estimated and actual source locations were mostly less than 2 m. Errors originated mainly from inaccurate depth estimation, and the literature indicates that they can be reduced by increasing the number of TRM elements and their apertures.

A phase gradient (PG)-based algorithm is proposed in this study to determine coastal bathymetry from X-band radar images. Although local wavenumbers with the same spatial resolution of the wave field can be obtained from the wave field using the PG method, only a single wavenumber result can be extracted from each location theoretically. Due to the influence of unavoidable noise on the wave field image, single wavenumber estimation often shows high uncertainty. This study combines a bandpass filter and directional pass filter to produce different nearly monocomponent wave fields from X-band radar images and then estimates more wavenumbers from these wave fields using the PG method. However, the distributions of wavenumbers in higher-frequency bins still show high variance because the strength of wave signals is weak. We confirmed that the uncertain wavenumber–frequency pairs can be improved using the Kalman filter and are more consistent with the dispersion relation curve. To decrease the influence of inaccurate wavenumbers, we also use the strength of the wave signals as the weights for the least-squares fit. Although the depth errors from shallow-water areas are still unavoidable, we can remove the inaccurate depth estimation from shallow-water areas according to the coefficients of determination of the fitting. In summary, the algorithm proposed in this study can obtain a bathymetry map with high spatial resolution. In contrast to the depth result estimated using a single wavenumber of each frequency bin, we confirm that more wavenumbers from each of the frequency bins are helpful in fitting the dispersion relation curve and obtaining a more reliable depth result.