A comparison of two reflectivity parametrizations in acoustic least-squares reverse time migration

In comparison with conventional reverse time migration (RTM), least-squares RTM (LSRTM) can improve imaging resolution and compensate irregular illumination caused by acquisition geometry and complex structures. Since proposed, as an advanced version of RTM, it has been applied a lot to improve resolution and balance amplitude in imaging. Generally, in LSRTM, there are two kinds of LSRTM reflectivity models: velocity perturbation related reflectivity model and normal-incidence reflection coefficient related reflectivity model. Each has its specific physical meaning and provides different inverted results. In this paper, we first give a brief review about the two different definitions. Then, we compare the differences of these two methods and build a mathematical relationship. In the definition related to reflection coefficient model, we rescale the defined reflectivity with background velocity. Also, in source wavefield reconstruction, we use an effective trick by moving file pointer to fetch data from disk to reduce the memory cost. Finally, we test these two LSRTM schemes using the Marmousi model. We observe that the two inverted reflectivities are different, although they both image the subsurface discontinuities well. We furthermore extract traces from the inversion results and compare them with the true reflectivity models, respectively, to verify the physical definitions of them.