Conclusions

Full waveform inversion (FWI) and Joint migration inversion (JMI) with the directional total variation (TV) has been demonstrated to be a more effective method than the alternatives (i.e., FWI/JMI without regularization, with the conventional TV, or directional Laplacian smoothing). We design the directional TV based on the dip field calculated from an initial image. By considering the local structural directions of the spatial gradient and their weights according to the local dip, the proposed method achieves a better result compared to FWI/JMI without regularization or with conventional TV. Finally, it can be concluded that the impact of directional TV is larger for FWI than for JMI, because in JMI the velocity model only explains the propagation effects and, thereby, makes it less sensitive to the details in the velocity model.