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Numerical Example

The proposed method was applied to a modified 2D Marmousi model (Bourgeois et al., 1991). For simplicity, we neglect overburden geomechanical changes and assume no change in reflectivity, except within the reservoir (Figure 3(a)). Using a Born modeling algorithm, we simulated $ 15$ data sets representing different production stages (Figure 4). Each data set comprises $ 56$ randomly encoded shot records with unique shot positions and unique relative shot-timings (Figure 5). We estimated the dip-field and dip-contrast (Figures 3b and c) from the migrated baseline image. For data modeling and migration, we use a phase-encoding one-way wave-equation operator. For comparison, using the same number of shots and receivers and perfect repeatability, we modeled and migrated $ 15$ conventional data sets. The migrated and inverted images, together with the corresponding time-lapse images, are shown in Figures 6 to 8.