Sensitivity kernel analysis for time-domain viscoelastic full-waveform inversion based on the GSLS model

Wenyong Pan, Kristopher A. Innanen

Viscoelastic full-waveform inversion (FWI) is promising to build high-resolution sub- surface velocity and quality factor Q models. Based on the generalized standard linear solid model, the attenuation effects on propagating waves can be simulated with the superposition of parallel relaxation mechanisms. However, discrepancies exist between the frameworks for constructing the sensitivity kernels in viscoelastic FWI: (I) Charara derived the sensitivity kernels for unrelaxed moduli and attenuation parameters with a perturbation approach based on Born approximation; (II) Tromp proposed to construct the Q sensitivity kernels by introducing additional adjoint source based on the Kolsky-Futterman model and frequency domain Born scattering integral; (III) Fichtner derived the sensitivity kernels for relaxation functions and Q following the adjoint-state method. The Q sensitivity kernels were constructed with the strain memory variables. This study revisits the theories of these frameworks for constructing the viscoelastic FWI sensitivity kernels. In the numerical modeling section, we calculate the sensitivity kernels within these different frameworks for comparison. Synthetic experiments are carried out to evaluate their inversion performances. We have found that the Q sensitivity kernels constructed with memory variables can resolve the Q anomalies better suffering from fewer trade-off artifacts and uncertainties in the presence of velocity errors.