Preconditioning of full-waveform inversion in viscoacoustic media

Intrinsic absorption in the earth affects the amplitude and phase spectra of the seismic wavefields and records, and may degrade significantly the results of acoustic full-waveform inversion. Amplitude distortion affects the strength of the scatterers and decreases the resolution. Phase distortion may result in mislocated interfaces. We show that viscoacoustic gradient-based inversion algorithms (e.g., steepest descent or conjugate gradients) compensate for the effects of phase distortion, but not for the effects of amplitude distortion. To solve this problem at a reasonable numerical cost, we have designed two new forms of preconditioning derived from an analysis of the inverse Hessian operator. The first type of preconditioning is a frequency-dependent compensation for dispersion and attenuation, which involves two extra modeling steps with inverse absorption (amplification) at each iteration. The second type only corrects the strength of the recovered scatterers, and requires two extra modeling steps at the first iteration only. The new preconditioning methods have been incorporated into a finite-difference inversion scheme for viscoacoustic media. Numerical tests on noise-free synthetic data illustrate and support the theory.