Least-squares reverse time migration in viscoacoustic tilted transversely isotropic media

ABSTRACT Iterative optimization-based least-squares reverse time migration (LSRTM) has proven effective in reducing imaging artifacts, enhancing amplitudes, and improving imaging resolution. We use a pure viscoacoustic tilted transversely isotropic (TTI) wave equation with separate amplitude attenuation and phase dispersion terms to implement attenuation-compensated LSRTM. This viscoacoustic anisotropic wave equation enables attenuation compensation during gradient calculation, which in turn accelerates the convergence of LSRTM. However, incorporating an attenuation-compensation-based wavefield propagator into the gradient calculation significantly amplifies high-frequency noise, which can lead to numerical instability. To address this, we apply a window function to the plane wave solution of the amplitude-compensated wavefield extrapolation operator. This method allows us to derive an explicit and stable operator for simulating attenuation-compensated wavefields. In addition, we develop Born modeling and gradient update operators based on amplitude-attenuated and attenuation-compensated wavefield simulation operators, and we implement attenuation-compensated TTI LSRTM. Synthetic tests demonstrate that our attenuation-compensated TTI LSRTM effectively reduces imaging noise, enhances amplitudes, and improves imaging resolution.