Full waveform inversion (FWI) aims at finding a model that produces data through simulation that fit the observed one. This model is often discretized consistently over the model space and adheres to our physical assumption of the medium, which may require multi parameter description. Though high-resolution analysis and complex physics are often desired and possibly only required in the reservoir region, we end up treating the reservoir as part of the complete model space, thus complicating our ability to emphasize its analysis. Thus, we propose an optimization scheme that splits our model space to the model above some datum level, probably just above the reservoir, and the data at the datum level representing the model below. The algorithm updates both wavepath and scattering components of the velocity model using the upper model extensions and the redatumed data from below the datum level. We describe a procedure that slowly builds the data at datum, meanwhile effectively introduces updates to the overburden model from the shallow (below datum) part to the deep. Our numerical test on the Marmousi model shows that our approach builds a credible velocity, and therefore retrieves virtual data with the expected dynamic features.


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