Comparison of waveform inversion, part 2: phase approach

In this paper, we take advantage of the natural separation into amplitude and phase of a logarithmic-based approach to full-wavefield inversion and concentrate on deriving purely kinematic approaches for both conventional and logarithmic-based methods. We compare the resulting algorithms theoretically and empirically. To maintain consistency between this and the previous paper in this series, we continue with the same symbolism and notation and apply our new algorithms to the same three data sets. We show that both of these new techniques, although different in implementation style, share the same computational methodology. We also show that reverse-time back-propagation of the residuals for our new kinematic methods continues to be the basis for calculation of the steepest-descent vector. We conclude that the logarithmic phase-based method is more practical than its conventionally based counterpart, but, in spite of the fact that the conventional algorithm appears unstable, differences are not great.