Comparison between least-squares reverse time migration and full-waveform inversion

Lei Yang, Daniel O. Trad, Wenyong Pan

The inverse problem in exploration geophysics usually consists of two parts: seismic imaging and velocity model constructing. In this paper, we compare the algorithms for least-squares reverse time migration (LSRTM) and full-waveform inversion (FWI) and use numerical examples to understand the differences. LSRTM uses Born approximation as the modelling method because it requires the adjoint of migration (linear inversion), while FWI uses finite-difference modelling because it does not require an adjoint-pair operator (non-linear inversion). Linearized Born modelling can update model perturbations by a linear conjugate gradient method, but may have severe inaccuracies and inversion noise if the initial model is poor. Both, FWI and LSRTM depend on the initial model largely, but FWI has a mechanism to improve the velocities and LSRTM does not. Conversely, FWI suffers from cycle skipping while LSRTM does not. For LSRTM, the long wavelength components of the gradient are considered to be noise, while for FWI they are considered to be signal. In this work we try to use a FWI algorithm to solve for reflectivity instead of using standard LSRTM.