Fig. 1. Time-lapse FWI schemes: a) parallel, b) sequential, c) central-difference, d) double-difference, and e) joint inversion methods.

The parallel workflow (Fig. 1a) is equivalent to run FWI separately for each survey, presumably the starting model and all the parameters of each FWI are the same. The sequential workflow (Fig. 1b) is similar like the parallel workflow except the monitor FWI takes the final FWI model of the baseline survey as a starting model. As the inversion is performed independently, these methods do not require the acquisition geometries to be the same. Bearing the pain of non-uniqueness of FWI solutions, they require a significant amount of manual interpretation and quality control. The joint inversion (Fig. 1e) (Maharramov et al., 2016) can penalize the model difference to stabilize the FWI regularization. We feel it is difficult to isolate the 4D changes to be only around the reservoirs. Zhou and Lumley (2019) proposed a central-difference method (Fig. 1c). We perform time-lapse FWI using the double-difference workflow (Fig. 1d) (Bian et al., 2017; Watanabe et al., 2004; Zhang and Huang, 2013), where we can mask the monitor model to be only different from the baseline at the reservoirs. The starting model of the double-difference FWI is the final model of the baselines FWI, and the input data of this workflow is the waveform difference between the monitor and baseline surveys. The waveform difference generated by the elastic property changes between time-lapse surveys can be regarded as the scatter waves. Even though the starting model, which is the baseline model in this scheme, may have its own error, the scatter waves can be migrated to isolated areas around the reservoirs, rather than to distribute the energy to the whole area. Real and synthetic data examples will be demonstrated in the talk.