To compare the approaches of linear inversion and quasi-linear inversion, LSRTM is applied to one supergather with quasi-linear inversion to produce the migration image shown in the Figure 2.8. This image is of comparable quality and approximately the same computation cost as Figure 2.4(b). In Figure 2.9, it can be seen that the quasi-linear inversion converges faster and it can reduce the data residual to a lower level compared to linear inversion. The reason is that the linear modeling operator is similar to diffraction stack modeling, where only diffractions and reflections are generated if the background velocity is smooth enough to only create direct waves (Mulder and Plessix, 2004a). In contrast, the non-linear modeling operator can predict all the arrivals in the input dataset. In fact, the input dataset is generated by the same modeling subroutine. Since the background velocity is not 100% accurate, the quasi-linear inversion cannot converge to zero data residual. In terms of reducing crosstalk noise, the linear inversion is expected to be more effective. For quasi-linear inversion, when the data residual approaches the lower limit after certain iterations, the step length calculated by the quadratic line search will be very small. In that case, further iterations receive very small weights and barely contribute to reducing crosstalk noise.