Nuts and bolts of least squares Kirchhoff migration

Daniel O. Trad

Least squares migration (LSMIG) has been an important research topic in the academia for about two decades, but only recently it has attracted interest from the industry. The main reason is that from a practical point of view its ratio of benefit/cost has not been sufficient for its use in seismic exploration. Another problem is that these benefits are mixed with effects from the filtering techniques used to regularize the inversion, which are computationally much cheaper. In this report, I discuss some challenges with least squares Kirchhoff depth migration. This algorithm, although less precise than the more popular least squares reverse time migration, has the advantage of being fast enough to be applied in a production environment, and flexible enough to be applied without data regularization. This last characteristic makes it a good candidate to understand benefits in terms of footprint acquisition and aliasing. In addition, its limitations in terms of modelling/imaging accuracy make more evident some problems that exist but are often ignored when using reverse time migration with synthetic data. This work focuses on some implementation issues that are not often mentioned in other papers. First I discuss the effects of amplitude weights by testing on a flat synthetic reflector I compare spectra, amplitude preservation and convergence when using different weights and imaging condition. Second I apply LSMIG to the Marmousi data set, and compare the previously discussed effects. Also, I show the impact of traveltime tables on the convergence and the predictions. Finally, I explore some connections with seismic data interpolation, and show examples of data prediction using time and depth migration.