Seismic data inversion using an optimal least square reverse time migration

There are several methods of seismic migration and the main objective of those is to place the reflectors in their true positions. One way for seismic migration is the algorithms that directly apply imaging conditions; on the other hand, the inversion-based imaging method implemented through different strategies to obtain a better depth model that fits the observed data. One of these inversion methods named least square migration solves the inverse problem through direct migration and demigration. The least squares migration has the main advantage that it can gradually reduce errors caused by initial migration. In this paper, particularly the reverse time migration (RTM) is used as an operator of migration and demigration.  Therefore, two numerical schemes are developed to implement least-squares migration with the reverse time migration method.

Methodology and Approaches:

The Helmholtz equation is used to derive the forward modeling operators named reverse time migration (RTM) operator with the Born approximation that is donated as linear inversion. Thus, the linear least square reverse time migration (LSRTM) is the inversion procedure to obtain the final image. LSRTM uses the RTM results as the initial reflectivity model and Born modeling to simulate the seismic data. The reflectivity model is updated by calculating the differences between observed and calculated data through the conventional an adaptive gradient. After multiple iterations, the differences are minimized and this is taken to suggest that the final reflectivity model reflects the real subsurface interface.

The results indicate that the LSRTM through an adaptive gradient procedure can successfully produce the subsurface migrated image free of artifacts including the steep dip structures during a reasonable computational cost.