An application of the Marchenko internal multiple elimination scheme formulated as a least-squares problem

Abstract

Images produced by migration of seismic data related to complex geology are often contaminated by artifacts due to the presence of internal multiple reflections. These reflections are created when the seismic wave is reflected more than once in a source-receiver path and can be interpreted as the main coherent noise in seismic data. Several schemes have been developed to predict and subtract internal multiple reflections from measured data, such as the Marchenko multiple elimination (MME) scheme that eliminates the referred events without requiring a subsurface model or an adaptive subtraction approach. The MME scheme is data-driven, can remove or attenuate most of these internal multiples, and was originally based on the Neumann series solution of Marchenko’s projected equations. However, the Neumann series approximate solution is conditioned to a convergence criterion. We reformulate the MME as a least-squares problem (LSMME) in such a way that it can provide an alternative that avoids a convergence condition as required in the Neumann series approach. To demonstrate the LSMME scheme performance, we apply it to 2D numerical examples and compare the results with those obtained by the conventional MME scheme. In addition, we evaluate the successful application of our method through the generation of in-depth seismic images, by applying reverse time migration (RTM) to the original data set and to those obtained through MME and LSMME schemes. From the RTM results, we found that the application of both schemes on seismic data allows the construction of seismic images free of artifacts related to internal multiple events.