138 Seismic Imaging Figure 5.10 Snapshots (from the same source, the same time and at the same scale); top left: in the initial model (Figure 5.4, top); top right: in the inverted model (Figure 5.6, bottom); bottom right: in the exact model (Figure 5.3, top) and bottom left: differences between the snapshots on the right. Figure 5.11 Least-squares migration results (30 iterations), expressed in vp perturbations (in m/s) and computed in the model from Figure 5.6, top). Most of the energy in the shot gather for the shot position at x = 32 m is contained in the first arrival (Figure 5.9, left). As the initial model for the first meter is relatively correct, the initial residuals are related to the first reflection at 1 m depth as well as deeper reflections (Figure 5.9, middle). After inversion, the misfit is largely reduced. Note that in the imaging algorithm, the shallowest part is not updated, indicating that the largest final residuals are associated to the first event (Figure 5.9, right). It is interesting to analyse the snapshots in the initial, exact and inverted models (Figure 5.10). This is a representation of the wave field for a given propagation time, here t = 22.9 ms. The snapshot for the exact model is not available on real data. After minimization, there is an excellent match between the up-going waves. The down-going waves differ (Figure 5.10, bottom left) as they are not recorded at the surface: the model is not constrained below the deepest reflectors. Least-squares migration (LSM) is a linearized version of FWI. It only deals with reflected waves and ignores transmitted waves, refracted waves, multiples, etc.
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