Separating traveltimes and amplitudes in waveform inversion

One difficulty in full waveform inversion is the requirement for an accurate initial model, which if not satisfied, can result in cycle skipping and convergence to local minima. Similarly, in least-squares migration, errors in the background model can lead to an incoherent, defocused image. These difficulties can be attributed in part to the fact that the data residual, the difference between simulated and observed data, contains error in both the smooth background model that affects traveltimes, as well as the rough reflectivity model that affects amplitudes. These two types of error are not treated equally in either full waveform inversion or in least-squares migration. To address this issue, we use an approximation of the data residual to separate traveltime and amplitude errors, and we show that the use of this approximation results in more accurate inversions for velocity in full waveform inversion, and better focused images in least-squares migration.