Data-driven Suppression of Short-Period Multiples from Laterally Varying Thin-Layered Overburden Structures

Marchenko multiple elimination methods remove all orders of overburden-generated internal multiples in a data-driven way. In the presence of thin beds, however, these methods have been shown to underperform. This is because the underlying inverse problem requires the information about short-period internal multiple (SPIM) imprint on the inverse transmission to be correctly constrained. This has been addressed in 1.5D media with energy conservation and minimum-phase reconstruction. Extending the applications to two dimensions and, hence, making the step toward field data were believed to be hampered by the need for a multidimensional minimum-phase reconstruction which is (1) not unique and (2) no algorithm has been found to perform this in practice on band-limited data. Here, we address both of these problems with an approach that includes solving the Marchenko equation with a trivial constraint, evaluating the energy conservation condition of its solutions to find the spatially dependent error syndrome, using the 1.5D minimum-phase reconstruction for each shot gather to find the spatially dependent constraint, and finally using that inside another run of the Marchenko equation solver to find a much-improved result. We find that the method works because in 2D media the expression of SPIMs in the inverse transmission coda is approximately 1.5D. We then investigate a class of models and synthetic data sets to verify where the 1.5D approximation starts breaking down. Our analysis indicates that this approach could perform very well in settings with moderate lateral variations, which also is where the (short-period) internal multiples are most difficult to differentiate from primary reflections.