# Travel-Time Inversion Method of Converted Shear Waves Using RayInvr Algorithm
## 4 Crustal S-Wave Velocity Inversion  
We only used the corrected PSS phases for the crustal S-wave velocity inversion, while the S-wave velocity of the sediments, constrained by the PPS phases, stays fixed during inversion. The RayInv inversion was a process used to invert and update the velocity at individual nodes of the crust, the geometry of the model interfaces was kept consistent with the P-wave model, and the interface depths were kept constant. \(\mathrm{Vp/Vs}\) ratios were very sensitive to the perturbation of the S-wave velocity model, which can supervise the instabilities during the inversion. The crustal \(\mathrm{Vp/Vs}\) calculated from dividing the P-wave velocity model by the inverted S-wave velocity model was monitored during the inversion to ensure that the \(\mathrm{Vp/Vs}\) ratios remained reasonable.  
The damping factor (DF) will affect the convergence rate of the RMS. A small damping factor makes convergence faster, and the inversion result gradually approached  
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline
**Stations** & **Phases** & **Uncertainties (ms)** & **RMSb (ms)** & **RMSa (ms)** & **Conversion Interface** \\ \hline OBS01 & PSSuc & 80 & 82 & 86 & \({}^{1}\) S1 \\ OBS02 & PSSuc & 180 & 182 & 183 & \({}^{1}\) S1 \\ OBS03 & PSSuc & 160 & 189 & 189 & \({}^{1}\) S1 \\ OBS03 & PSSmb & 200 & 181 & 179 & Basement \\ OBS05 & PSSm & 180 & 150 & 141 & \({}^{1}\) S1 \\ PSSuc & 140 & 102 & 105 & \({}^{1}\) S1 \\ OBS07 & PPSic & 140 & 111 & 111 & \({}^{1}\) S1 \\ PSSm & 180 & 221 & 221 & \({}^{1}\) S1 \\ PSSuc & 160 & 239 & 241 & \({}^{1}\) S1 \\ OBS08 & PSSm & 200 & 141 & 144 & \({}^{1}\) S1 \\ OBS09 & PSSmb & 200 & 185 & 167 & Basement \\ PSSuc & 160 & 234 & 240 & \({}^{1}\) S1 \\ OBS10 & PSSmb & 160 & 197 & 198 & Basement \\ OBS11 & PSSuc & 160 & 256 & 262 & \({}^{1}\) S1 \\ OBS12 & PSSuc & 200 & 193 & 199 & \({}^{1}\) S1 \\ PSSlc & 200 & 205 & 214 & \({}^{1}\) S1 \\ \hline \hline \end{tabular} \({}^{\dagger}\)S1: sedimentary layers 1.  
\end{table}
Table 1: The total root-mean-square travel-time residuals before (RMSb) and after (RMSa) travel-times correction, picking uncertainties, conversion interface, for PSS mode arrival phases.  
Figure 8: Comparison of the ray paths before and after the PSS phases’ travel-time correction; The red dotted lines represent the original ray path, and the black solid lines represent the corrected ray path. The left-lower map shows a partial enlarged view of the 20-40 km in the model.  
the least-squares solution, whereas the slower convergence rate is performed with a large damping factor. The numerical experiments show that a large damping factor will reduce the efficiency of the RayInvr algorithm, resulting in the number of iterations being increased and the resolution being reduced [26]. Selecting an appropriate damping factor can not only improve the inversion efficiency, but also make the inversion stable and reliable. After a series of tests, DF = 3 was finally selected as the damping factor for the following inversion. The velocity nodes of inversion are the same as those of P-wave model. The average inversion grid is set to 14, 16.5 and 19 km in the upper crust, lower crust and high-velocity lower crust, respectively (Figure S3).