Comparison of waveform inversion, part 3: amplitude approach

In the second paper of this three part series, we studied the case of conventional and logarithmic phase-only approaches to full-waveform inversion. Here, we concentrate on deriving amplitude-only approaches for both conventional- and logarithmic-based methods. We define two amplitude-only objective functions by simply assuming that the phase of the modelled wavefield is equal to that of the observed wavefield. We do this for both the conventional least-squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse-time propagation algorithm of the full conventional methodology. Although the residuals in this case are not really residual wavefields, they can both be considered and utilized in that sense. In contrast to the case for our phase-only algorithms, we show through numerical tests that the conventional amplitude-only inversion is better than the logarithmic method.