Accelerating full-waveform inversion with attenuation compensation

The calculation of the gradient in full-waveform inversion (FWI) usually involves crosscorrelating the forward-propagated source wavefield and the back-propagated data residual wavefield at each time step. In the real earth, propagating waves are typically attenuated due to the viscoelasticity, which results in an attenuated gradient for FWI. Replacing the attenuated true gradient with a Q-compensated gradient can accelerate the convergence rate of the inversion process. We have used a phase-dispersion and an amplitude-loss decoupled constant-Q wave equation to formulate a viscoacoustic FWI. We used this wave equation to generate a Q-compensated gradient, which recovers amplitudes while preserving the correct kinematics. We construct an exact adjoint operator in a discretized form using the low-rank wave extrapolation technique, and we implement the gradient compensation by reversing the sign of the amplitude-loss term in the forward and adjoint operators. This leads to a Q-dependent gradient preconditioning method. Using numerical tests with synthetic data, we demonstrate that the proposed viscoacoustic FWI using a constant-Q wave equation is capable of producing high-quality velocity models, and our Q-compensated gradient accelerates its convergence rate.