“…The misfit function in the conventional FWI relies on the absolute waveform matching between synthetic data and observed data, and cycle skipping issue can easily occur if there is a significant phase and/or amplitude difference. Studies of seeking more convex function include the wave-equation traveltime based misfit function (Luo and Schuster, 1991;Luo et al, 2016), the envelope-based misfit function (Wu et al, 2014;Chi et al, 2014), the instantaneous-phase-based misfit function (Bozdag et al, 2011;Jiao et al, 2015), the correlation-based misfit function (Van Leeuwen and Mulder, 2010;Luo and Sava, 2011;Chi et al, 2015;Choi and Alkhalifah, 2016), the deconvolution-based misfit function (Luo and Sava, 2011;Warner and Guasch, 2016), the dynamic-time-warping-based misfit function (Ma and Hale, 2013), the Huber-norm misfit function (Guitton and Symes, 2003;Ha et al, 2009), and the optimal transport approach (Métivier et al, 2016a,b;Yang et al, 2017Yang et al, , 2018, etc. These misfit functions are generally more convex with respect to model perturbations, and therefore less prone to the cycle skipping issue.…”