# Travel-Time Inversion Method of Converted Shear Waves Using RayInvr Algorithm
## 4 Crustal S-Wave Velocity Inversion
### Inversion Results and Analysis  
The final inversion model shows (Figure 11a,c) that the upper crust and lower crust have a Vs. of 3.0-3.7 km/s and 3.7-4.4 km/s, respectively. On the upper slope (at profile distance of 0-183 km), the Vp/Vs of the upper crust and lower crust are 1.71-1.75 and 1.72-1.75, respectively. Beneath the lower slope (at profile distance of 183-289 km), the upper crustal Vp/Vs is 1.75-1.79, and lower crustal Vp/Vs is 1.75-1.80. The high-velocity lower crust is also observed in our model that has a Vs. of 4.0-4.4 km/s, and a Vp/Vs of 1.72-1.78. The final inversion model has a similar trend in the lateral velocities and Vp/Vs ratios with the forward model, due to the small difference with \(\Delta\)Vs of 0.1 km/s and \(\Delta\)Vp/Vs of 0.03 between the two models (Figure 12). The inversion model reveals more details in the crustal structures. For example, the high Vp/Vs ratios of the crust below two buried volcanos [19] may be related to magma conduits (Figure 11c). Therefore, the inversion results obtained by the RayInvr inversion algorithm are reliable and detailed for crustal structures.  
Figure 9: Inversion results for crustal S-wave velocity along profile NS5. The initial crustal S-wave velocity models of (**a**,**d**,**g**,**j**,**m**) in column 1 are originated from starting Vp/Vs ratios of 1.71, 1.73, 1.75, 1.78, and 1.81, respectively. Column 2 (**b**,**e**,**h**,**k**,**n**) shows the final results from inversion obtained from the different initial models in column 1 (**a**,**d**,**g**,**j**,**m**). Column 3 (**c**,**f**,**i**,**l**,**o**) shows apparent crustal Vp/Vs models from the division of the P-wave velocity model by the final S-wave velocity models in column 2 (**b**,**e**,**h**,**k**,**n**).  
Figure 11: (**a**) The final inversion result for crustal S-wave velocity model. (**b**) Ray coverage density distribution, and the dimensions of counting grid are 1 \(\times\) 0.25 km. (**c**) Apparent crustal Vp/Vs model that calculated by dividing the P-wave model by the inverted S-wave model (**a**). V1, V2 represent the buried volcanos [19].  
Figure 10: Variation in the number of tracing phases and travel-time residuals (RMS) during the inversion process under the initial models with the Vp/Vs ratios of 1.71 (**a**), 1.75 (**b**), 1.78 (**c**), 1.81 (**d**). Red dots indicate inversion is terminated at this time.  
Figure 11b shows that the model has a good ray coverage with the ray coverage of most areas exceeding 20-40 hits. To better determine the resolution of the inversion model, we imposed a checkerboard pattern on the model [28]. This grid pattern had a width of 15-25 km in the upper crust, 20-40 km in the lower crust, and the vertical dimension was constrained by the model interface. Furthermore, we added S-wave velocity perturbations of \(\pm\) 0.2 km/s that were equal in amplitude but opposite in terms of the sign at adjacent nodes (Figure 13a). The output model is shown in Figure 13b. The checkerboard test confirmed the good resolutions of the lower crust, especially in the upper crust.  
Figure 12: The difference between the forward and inversion results for crustal S-wave velocity (**a**), Vp/Vs ratios (**b**). \(\Delta\)Vs and \(\Delta\)Vp/Vs are the difference between inversion and forward results.  
Figure 13: (**a**) Synthetic S-wave velocity perturbation using a checkerboard test. (**b**) Calculated S-wave velocity perturbation for the checkerboard test. The horizontal size of the anomalous block was 15-25 km in the upper crust, 20-40 km in the lower crust, the vertical size was bounded by interface.