Taking heterogeneity into account

Finding the layer traveltime derivatives needed by equation 12 is generally straightforward in the case of 1-D media because both traveltime and offset can be conveniently expressed as functions of horizontal phase slownesses (Koren and Ravve, 2017; Sripanich and Fomel, 2016). However, in this study, we modify the layer traveltime $t_k$ (equation 4) by adding the two sources of lateral heterogeneity: non-flat reflectors and lateral velocity variations.