Attenuation Sensitivity Kernel Analysis in Viscoelastic Full-Waveform Inversion Based on the Generalized Standard Linear Solid Rheology

Obtaining accurate subsurface Q (quality factor) models using full-waveform inversion (FWI) methods remains a challenging task. The forward modeling problem of viscoelastic wave propagation can be solved by superimposing N rheological bodies of Maxwell or Zener type with generalized standard linear solid rheology. However, different approaches were proposed to calculate the attenuation sensitivity kernels in viscoelastic FWI. This study reviews and compares previous theories for constructing the viscoelastic sensitivity kernels. Furthermore, we derive the viscoelastic sensitivity kernels directly following the adjoint-state (or Lagrangian multiplier) method. Compared to previous approaches, we reveal that the Q sensitivity kernels can be calculated with adjoint memory strain variables. In the numerical experiments, different methods are used to calculate the viscoelastic sensitivity kernels for comparison. We have found that when simultaneously inverting for velocity and Q models, these methods can provide inversion results of comparable quality. However, in the event of inaccurate velocity structures, the Q sensitivity kernels calculated with memory strain variables can resolve the Q anomalies more clearly, while suffering from fewer parameter trade-offs.