Update Reverse Time Migration Images by Least Squares in Acoustic and Elastic Media

The primary objective of reverse time migration (RTM) is to image the spatial positions of subsurface reflective interfaces using reflected seismic data. As a linearized inversion scheme, least-squares RTM (LSRTM) is capable of producing higher quality images compared to RTM. However, current LSRTM utilizes scattered seismic data to image the relative perturbations in medium parameters rather than the reflective interface positions. Consequently, existing LSRTM methods, whether in acoustic and elastic cases, do not iteratively update the RTM images. To address this limitation, we introduce a linearized scalar reflectivity function of acoustic impedance as the imaging target and propose a reflected wave LSRTM method designed to iteratively update acoustic RTM images. For elastic media, we synthesize prior research and employ the least-squares inversion to derive vector reflection demigration operators, enabling the iterative update of elastic RTM images. As a result, we clarify the relationship between conventional RTM and proposed LSRTM methods in both acoustic and elastic media. Numerical examples and field data test demonstrate that the proposed LSRTM methods can effectively iteratively update RTM images and provide high-quality imaging results.