Fréchet kernels based on a fractional viscoacoustic wave equation

Incorporating the seismic attenuation into the waveform inversion framework could not only improve the accuracy of the velocity model but also provide an additional Q model. Recently, we proposed a viscoacoustic wave equation assisted by the fractional Laplacian operators to accurately model the wave propagation in heterogeneous attenuating media with computational efficiency. The explicit presence of Q as a coefficient in this equation suggests the potential to conveniently develop its full waveform inversion scheme. In this study, we utilize the adjoint-state method to formulate the computation of the Fréchet kernels with respect to both velocity and attenuation based on this wave equation. These kernels will play a fundamental role in the viscoacoustic multiparameter waveform inversion.