Least-squares reverse time migration in the presence of velocity errors

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We utilize an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further explore this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and less migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared with conventional LSRTM when the bulk velocity errors are as large as 10%.