An Approximate Constant-Q Viscoacoustic Full Waveform Inversion Method Based on Gradient Preconditioning

Abstract In viscoelastic media, velocity and quality factor (Q) exhibit crosstalk in full waveform inversion (FWI), where the gradient vector of Q is dominated by velocity, thereby impairing the accuracy of final inversion results. While sequential inversion of these two parameters can yield more accurate outcomes, it compromises the computational efficiency of FWI. Concurrently, in viscoacoustic FWI, relying solely on conventional wavefield energy values for simultaneous gradient illumination of the two parameters significantly degrades the precision of inversion results. Research has shown that the pseudo-Hessian operator, functioning as a preconditioner, enables separate gradient energy optimization for the gradients of different parameters, mitigates crosstalk between parameters, and achieves more balanced convergence across all parameters. In this study, the gradient formulation for viscoacoustic FWI under the approximate constant-Q model is first derived. Furthermore, to address the crosstalk issue between velocity and Q in viscoacoustic FWI and enhance inversion accuracy, a pseudo-Hessian matrix gradient preconditioning operator for approximate constant-Q viscoacoustic FWI is developed, leading to the establishment of an approximate constant-Q viscoacoustic full waveform inversion method based on gradient preconditioning. Model and field tests validate that this method effectively resolves the crosstalk between velocity and Q in viscoacoustic FWI and improves the accuracy of inversion results.