## 4 Discussion
### Advantages and Constraints of Our Estimation Methodology
However, our work suggests a conceptual procedure for the combined geoacoustic inversion of both the position and intensity of the caustics, matching the experimental data with wide-band synthetic-source-gather modeling. The normalized weight function, which was produced by our geoacoustic inversion procedure, had a well-defined single maximum, implying that the estimates obtained are unique. This implication is subject to the assumptions embedded in our modeling, namely the presence of a generally increasing velocity gradient below the seafloor that formed a single caustic in the recorded data. Moreover, the investigation of the normalized weight function allowed us to assess the uncertainties associated with our estimates. Our suggested measure of uncertainty, the 95% level of the normalized weight function, implied accuracies of \(\pm\)5 to \(\pm\)27.5 m s\({}^{-1}\) (0.3 to 1.8 %) for the seafloor sound speed \(c_{0}\) estimations and up to \(\pm\)0.075 s\({}^{-1}\) (\(\sim\)9%) for the velocity gradient \(K\) estimations (Figure 11). These accuracies are comparable to those that were obtained in laboratory and in situ direct-measurement approaches. For our study site, at the base of the southeastern Mediterranean Sea continental margin, the estimated \(c_{0}\) values seemed to increase from 1495 to 1625 m s\({}^{-1}\) with the increase in bottom depth \(H_{1}\) from 1000 to 1350 m. The estimated \(K\) values varied between 0.75 to 0.85 and showed a slight increase with bottom depth (Table 1, Figure 12). These trends may be associated with the presumed decreasing sedimentation rates and increasing clay content away from the margin. Notably, the spatial distribution of the estimated values (Figure 12) demonstrates the consistency of the parameters and their variations between the different seismic lines. This consistency supports our estimation approach and our estimates of uncertainty. To examine the validity of our geoacoustic inversion results, a depth-migration velocity analysis procedure was performed for the seismic line ISEM-2073 (Figure 1), using Emerson-Paradigm Coherency Inversion analysis [71] (Figure S1 in supplementary information). This commercially standard, reflection-travel-time-analysis procedure was applied in a layer-cake manner in order to create a laterally varying, piecewise-constant-layered velocity model of the sedimentary overburden across the study area. Cross-plotting the modeled velocities vs. the depth of the modeled layers between the seafloor and the top salt reveals a general increase in the velocity with depth. Fitting these data with a linear trend estimates the velocity at the seafloor, \(c_{0}\), as 1539 m s\({}^{-1}\) and the gradient, \(K\), as 0.84 s\({}^{-1}\) with a correlation factor \(r^{2}\) = 0.93 (Figure 13). Thus, although a layered model was assumed, the results of this reflection-travel-time-based velocity analysis are consistent with the estimations presented in this paper based on the analysis of the travel times of the head waves of bending rays. [PERSON] et al. [12] estimated, in the laboratory, the sound speed of silty-clay sediments from six 1-3.5 m-long cores, which were obtained from the South Sea of Korea (\(\sim\)50 m bottom depth) using the pulse transmission technique (frequency of 1 MHz). They reported sound-speed estimates ranging from 1503 to 1604 m s\({}^{-1}\), and the measurement accuracy was approximately 1%. The results of sound-speed estimations using other approaches by [PERSON] et al. [20] (SAMS) and [PERSON] [19] (ISSAMS) showed similar accuracies, but their estimates were performed in areas with a sandy bottom. Thus, the absolute values of their estimates are not directly comparable with our estimates. [PERSON] and [PERSON] [10] performed laboratory measurements of sediment properties in cores from the Bering Sea, North Sea, Mediterranean Sea, equatorial Pacific, and other areas. They presented measurements from three general environments: a continental terrace (shelf and slope), an abyssal hill, and an abyssal plain.