In terms of the parameter selection, we choose a relaxation strategy for , which is increasing exponentially. In this way, we relax the strength of the L1 constraint gradually to make the inversion converge. is a constant which depends on the scale of the data. We can set a proper to make sure around of the energy is passed through the shrinkage step in Algorithm 1, in order to improve the stability of the algorithm. Regarding the weights on the dominant direction and its perpendicular direction of gradients, it depends on the accuracy of the estimated dip field and the bias of the subsurface structures. Usually, is a safe choice. In this paper, we use for both examples, which puts more weight on the dominant spatial direction of the velocity gradient, because the structures of the Marmousi model are quite tilted and biased.
Regarding the calculation efficiency of JMI, JMI is more cost-effective than FWI. First, it doesn't require a good initial model to start with due to its linearization; Second, it is implemented in the frequency domain and no finite-difference-based method is used, therefore the horizontal and vertical grid size do not have to satisfy a frequency dispersion condition, but are defined by the spatial Nyquist criterion. For instance, in the JMI example, the frequency range is upto Hz and the chosen horizontal and vertical grid size is m and m, respectively.