Q-compensated full waveform inversion using constant-Q wave equation

The gradient in time-domain full waveform inversion (FWI) is usually constructed by taking the cross-correlation of the forward propagated source wavefield and the back propagated data residual wavefield at each time step. In the real Earth, propagating waves can be attenuated due to the anelatic nature of subsurface media, 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 propose to use phase-dispersion and amplitudeloss decoupled constant-Q wave equation to formulate a viscoacoustic FWI, and use this wave equation to generate a Qcompensated gradient, which has the recovered amplitude while preserving the correct kinematics. We construct an exact adjoint operator in the discretized form using the lowrank wave extrapolation technique, and implement the gradient compensation by reversing the sign of the amplitude-loss term in both forward and adjoint operators. This leads to a Q-dependent gradient preconditioning method. Numerical tests with synthetic data demonstrate that the visco-acoustic FWI using constant- Q wave equation is capable of producing high-quality velocity models, and that the proposed Q-compensated gradient can accelerate its convergence rate.