In this appendix, we provide a detailed derivation of the studied recursive formula (equation (12)) and discuss a possible extension to evaluate higher-order traveltime derivatives. We start from the case of two-layer media previously investigated by Blias (1981), Blyas et al. (1984), Gritsenko (1984), and Goldin (1986) and proceed to the case of three-layered media to show how the recursion can be established for multi-layer media.
![[pdf]](icons/pdf.png){kind=icon}