Waveform inversion for shear velocity and attenuation via the spectral-element adjoint method

Intrinsic attenuation affects both amplitude and phase behavior of the seismic wavefield. Its three-dimensional distribution in the subsurface needs to be robustly estimated to make earth models accurate. Full Waveform Inversion (FWI) has become the technique of choice for recovering high-resolution velocity structure, but its ability to reliably recover attenuation variations remains challenging. Multistage and hierarchical approaches offer promise to control the delicate trade-off between resolving elastic and anelastic structure in inversions for the shear velocity V_S and quality factor Q_µ, in regimes with strong surface waves prone to cycle skipping. We present a procedure for their joint reconstruction via spectral-element adjoint-based full-waveform modeling. Starting from a checkerboard example, we develop a frequency and offset continuation strategy for onshore active-source acquisition. In the early stages of our algorithm, the inversion targets the refinement of the shear-wave speed model by gradually widening the frequency band and increasing the offset range. The shear quality factor is of major consideration only in the final stage of the inversion. Our procedure is robust, competitive, and practical.