## 4 Discussion
### Advantages and Constraints of Our Estimation Methodology  
The geoacoustic characterization of the seafloor at large water depths requires the use of several kilometer-scale acoustic arrays, the implementation of which is difficult and costly. Our utilization of commercial 2D multichannel seismic-profiling data offset the need for extensive designated acoustic measurement layouts, utilizing instead the standard seismic streamer as an HLA. As a rule, conventional marine seismic acquisition utilizes air-gun arrays as energy sources [66; 67]. These are normally tuned to provide sharp- and high-power, downward-propagating signals, which provide deep penetration into the seafloor and high signal-to-noise ratios of reflected and refracted phases over ranges of many kilometers. However, with their primary frequency content being in the tens of Hz, seismic-profiling data provide unusually low-frequency measurements with respect to common acoustic applications. Thus, our results are low-frequency estimates of the geoacoustic parameters. Indeed, the actual velocity at the seafloor, where water content in the sediments is high, is not expected to depend on the frequency, suggesting the general validity of our estimated values. In turn, the estimated gradient may represent the average trend of multiple velocity layers. Our geoacoustic estimation methodology is a practical extension of [PERSON]'s [35] simplistic analytic formulation for interpreting the sound-speed structure of the upper oceanic crust from data on the wide-angle reflections and the travel times of the head waves of bending rays from sonobuoy and ocean-bottom reflection experiments. Both approaches are based on the theoretical formulation of Nettleton [56]. However, our modeling was based on the precise numerical calculations of ray travel times, which were carried out here with BELLHOP [57] and MATLAB software. Moreover, we presented a conceptual integration of recursive modeling with an organized geoacoustic inversion, which provided a simultaneous estimation of both the seafloor velocity \(c_{0}\) and the sub-bottom velocity gradient \(K\). Importantly, this estimation correctly accounted for a realistic velocity profile in the water column, which may have a significant impact on the calculations at the higher angles of incidence, thereby improving the accuracy of the geoacoustic estimations. The estimations were further constrained by the modeling of a prominent reflection from the base of the sub-bottom constant-velocity-gradient layer, which is the top-salt reflection, constraining its sub-seafloor depth \(H_{2}\). Here we applied our methodology to a relatively simple case, considering only the vertical variation of the velocity structure and a constant-velocity gradient beneath the seafloor. Such an approximation is generally accepted to represent sediment compaction and is often confirmed by measurements of clay or silt clastic sediments [44]. In reality, the velocity gradient is not necessarily linear. However, building on a standard set of modeling tools, our procedure is directly expandable to allow for a more complex velocity structure. Such structures may be incorporated into the other sub-bottom trends, such as (1) exponential [42], (2) parabolic [40], (3) Faust law [68], (4) using slowness [46], (5) quadratic law, (6) instantaneous velocity [69], or (7) exponential asymptotically bounded velocity model [44]. Moreover, our procedure allows for the relatively simple integration of the lateral variability of the seafloor and the sub-seafloor structure. The results of the travel-time-based estimation were validated here through caustic amplitude modeling. An analytical expression (Equation (7)) for estimating velocity gradients based on the position of caustics was suggested, for instance, by [36; 70], and can be used for rough preliminary estimations.