# Dispersion Curve Interpolation Based on Kriging Method
## 6 Conclusions  
In this study, we developed a process of dispersion curve interpolation based on kriging, and proved the applicability of the process through several different tests. This study provides a basis for subsequent temporal-spatial interpolation of dispersion curves. The mean RMSE of the predicted data is less than 0.1 and the max relative error is less than 10%. Moreover, the interpolation method provides new ways for the data supplementation of noise source imaging. Cross-validation is used to determine the best variogram in this study. According to the sensitivity analysis, \"distance\" and \"angle\" are determined to be 15,000 m and 265\({}^{\circ}\) in this study. If the method is used in a different data set, the parameters should be reset. Finally, the method is applied in the Changbai volcano, which complements the areas with low ray density and expands the original imaging area. The max expansion multiple can reach 2.4. The application of the method can reduce the cost of field work. Conceptualization, Y.T. and P.Z. ; methodology, H.Z., Y.T. and P.Z. ; software, H.Z. ; validation, H.Z. ; formal analysis, H.Z., Y.T. and P.Z. ; investigation, H.Z. ; resources, Y.T. and P.Z. ; data curation, H.Z. and Y.T. ; writing--original draft preparation, H.Z. ; writing--review and editing, P.Z. ; visualization, H.Z. ; funding acquisition, Y.T. All authors have read and agreed to the published version of the manuscript. This study was funded by the National Natural Science Foundation of China (grant No. 42274065), the National Key R&D Program of China (Grant No. 2022 YFF0801003), the Program for JLU Science and Technology Innovative Research Team (No. 2021 TD-05) and Fundamental Research Funds for the Central Universities in China. Not applicable. The Vs model of the Changbai volcano (Changbai model) is available at the [[https://doi.org/10.5281/zenodo.7509119](https://doi.org/10.5281/zenodo.7509119)]([https://doi.org/10.5281/zenodo.7509119](https://doi.org/10.5281/zenodo.7509119)) (accessed on 6 January 2023). We thank [PERSON] and [PERSON] of the Changbaishan Volcano Observatory for their help in the fieldwork. We thank [PERSON], [PERSON] and [PERSON] for their work in the Changbai volcano. We also appreciate [PERSON] for his help in this study. We thank the editor and four referees for their comments and efforts to improve the manuscript. The authors declare no conflict of interest. **Figure A2. ** Comparison of dispersion curve interpolation results (127.91\({}^{\circ}\) E, 41.94\({}^{\circ}\) N). The blue curve indicates the ordinary kriging results, while the black curve indicates those of universal kriging: (**a**) Comparison of the dispersion curves; and (**b**) deviation of the OK (blue) or UK (black) results. **Figure A3. ** Comparison of dispersion curve interpolation results (128.0\({}^{\circ}\) E, 42.0\({}^{\circ}\) N). The blue curve indicates the ordinary kriging results, while the black curve indicates those of universal kriging: (**a**) Comparison of the dispersion curves; and (**b**) deviation of the OK (blue) or UK (black) results. **Figure A4. ** Comparison of dispersion curve interpolation results (128.09\({}^{\circ}\) E, 41.88\({}^{\circ}\) N). The blue curve indicates the ordinary kriging results, while the black curve indicates those of universal kriging: (**a**) Comparison of the dispersion curves; and (**b**) deviation of the OK (blue) or UK (black) results. Figure 17: Comparison of dispersion curve interpolation results (128.18\({}^{\circ}\) E, 42.18\({}^{\circ}\) N). The blue curve indicates the ordinary kriging results, while the black curve indicates those of universal kriging: (**a**) Comparison of the dispersion curves; and (**b**) deviation of the OK (blue) or UK (black) results. Figure A9: Comparison of dispersion curve interpolation results (128.21\({}^{\circ}\) E, 42.24\({}^{\circ}\) N).