3D Least-Squares Reverse Time Migration Using Wavefield Decomposition via Hilbert transform

In this study, we suggest least-squares reverse-time migration (LSRTM) with wavefield decomposition method. Conventional imaging condition is comprised with the wavefields traveling upward and downward for source and receiver sides, respectively. Robust imaging condition can be obtained by separating those wavefields with respect to the vertical direction, however, it usually requires extremely heavy cost in computation in the 3D application due to Fourier transforms on both time and vertical axes. Wavefield decomposition by an analytic signal, i.e. complex signal, is an alternative method which is implemented by Hilbert transform. Since the analytic signal has only positive frequency component, wavefield decomposition can be more efficiently done by 1D Fourier transform only on the vertical axis. Taking the wavefields traveling opposite direction into account by decomposition for source and receiver sides, respectively, suppresses low wavenumber backscattered noise which is an intrinsic problem of two-way reverse-time migration (RTM) while LSRTM increases spatial resolution and frequency spectrum of the image. Thus, combining this wavefield decomposition method with existing LSRTM yields a robust depth imaging method.