## 2 The Experimental Data
### The Geacoustic Inversion Procedure  
The ray travel-time branches, which were extracted from the experimental source gather (Figure 5), were numerically compared to the modeled ray travel-time branches. The comparison was made both for the vertical (travel time) and horizontal (offset) axes of the travel-time branches. In practice, the travel time branches were defined by five points: two points for the top-salt reflection (SB1 and SB2), and three points at the edges of the two travel-time branches of the bending rays (BR1, BR2, BR3) (red squares, Figure 7b). The top-salt reflection points SB1 and SB2 were chosen at the constant offsets of 1000 and 5500 m, respectively. The bending refraction points were chosen as follows: BR1 was located at the cross-point of the bending refraction and the seafloor reflection, BR2 was a turning point (cusp) of the refraction travel-time curve, and BR3 was located at the end of the HLA at the distance of 7350 m from the source. This procedure was then repeated for each unique  
Figure 6: A schematic representation of rays propagating through our model with a linear velocity gradient in the sub-bottom layer down to the top salt, and a winter-oceanic-sound-velocity profile. (**a**) The sound-speed profile in the water and bottom that is used in the model. (**b**) A set of modeled rays (black curves), propagating through a multilayered medium that represents the velocity profile in (**a**). Blue dotted arrows schematically represent, for a comparison, the outline of a head wave propagating through a constant-velocity water model at the critical angle of incidence \(\theta_{c}\) and the critical distance \(R_{c}\). \(L\) is the length of the horizontal line array of hydrophones. Red dashed curves represent rays reflected from the top-salt interface. triplet of \(c_{0}\), \(K\), and \(H_{2}\) across ranges of each of these parameters with step sizes of 5 m s\({}^{-1}\), 0.05 s\({}^{-1}\), and 50 m, respectively. In each case, the deviation of the modeled travel-time marker points from the modeled ones was evaluated by computing the error function  
\[E(c_{0},K,H_{2})=\frac{1}{N}\sum_{n=1}^{N}\sqrt{\big{(}X_{exp\_n}-X_{\text{mod\_n }}\big{)}^{2}+\big{(}T_{\text{exp\_n}}-T_{\text{mod\_n}}\big{)}^{2}}, \tag{5}\]  
where \(N\) is the number of analyzed experimental points, \(X_{\text{exp\_n}}\), \(X_{\text{mod\_n}}\) are normalized experimental and modeled offsets, and \(T_{\text{exp\_n}}\), \(T_{\text{mod\_n}}\) are normalized experimental and modeled two-way reduced arrival time, of each of the marker points. In order to balance the impact of the horizontal and vertical components of the arrivals, both experimental and modeled arrival times and the offsets are normalized such that their maximum is 1. In our case, the offsets were normalized by 7350 m (the maximum offset of the HLA used), and the reduced arrival times were normalized by 4.2 s (the maximum offset of 7350 m divided by the roughly assumed average sound speed in the sub-seafloor medium of 1750 m s\({}^{-1}\); Figure 7b). Once the computation was complete, the normalized weight function was computed as  
\[F(c_{0},K,H_{2})=\frac{\mid E-\text{max}(E)\mid}{\text{max}(\mid E-\text{max}( E)\mid)}, \tag{6}\]  
where \(E=E(c_{0},K,H_{2})\) (Figure 8a-c). The best fit between the normalized experimental and the simulated ray travel times and distances corresponds to the maximum of the weight function, constraining the combined estimate of the geoacoustic parameters \(c_{0}\)-\(K\)-\(H_{2}\). Figure 7: (**a**) The normalized weight function \(F_{norm}\) vs. varying \(c_{0}\) and \(K\) with \(H_{2 best}=1000\) m. The white area represents arrival of the bending refracted rays beyond the bounds of the HLA used. The weight function has a single prominent maximum at \(c_{0}=1525\) m s\({}^{-1}\) and \(K=0.75\) s\({}^{-1}\). (**b**) The arrival times simulated for three combinations of \(c_{0}\), \(K\), and \(H_{2}(bottom\) right), overlaid with the experimentally chosen arrival times from source gather #2290.