Viscoelastic wave propagation: Spectral-element simulation with a novel GSLS-type wave equation

SUMMARY Seismic waves undergo attenuation and dispersion as they propagate through the Earth. These effects are caused by mechanisms such as partial melting in the crust and mantle, and the presence of water in the mantle. Neglecting attenuation effects may result in phase distortion and amplitude anomalies when imaging the Earth’s interior structure. Here, we introduce a novel wave equation for modeling viscoelastic wave propagation in frequency-independent Q media. The proposed viscoelastic wave equation offers several advantages over previous methods: (1) the quality factor Q is explicitly integrated into the wave equation, simplifying the derivation of sensitivity kernels for Q full waveform inversion; (2) the wave equation can be directly solved using the spectral element method, which is computationally more efficient than methods requiring Fourier transforms; and (3) the relaxation time (weighting function) of the wave equation depends only on the selected frequency range, independent on the specific Q values. The accuracy of the proposed wave equation is validated through comparisons with analytical solutions and results from the Generalized Standard Linear Solid (GSLS) method. Furthermore, the method is rigorously tested on two benchmark earth models to assess its capability in handling topographic variations and complex structural configurations in heterogeneous attenuative media. Given its accuracy and reduced computational costs, this new wave equation is expected to be highly beneficial for seismic reverse time depth imaging and viscoelastic full waveform inversion applications.