Modified viscoelastic wavefield simulations in the time domain using the new fractional Laplacians

Accurately characterizing seismic attenuation effects on wave propagations is crucially important for structure interpretation and reservoir evaluation. The conventional fractional viscoelastic wave equation is not satisfactory on accuracy for small Q values. To solve this issue, we derive a novel fractional viscoelastic wave equation by combining an accurate relationship between angular frequency and complex wavenumber. The dissipation- and dispersion-dominated wave equations are also derived to simulate the amplitude-dissipation and phase-dispersion characteristics. The truncated Taylor-series expansion (TE) algorithm is developed to approximate the mixed-domain operators. After that, the generalized pseudospectral approach can be directly used to solve the new wave equation. In addition, an accurate viscoelastic wave equation constructed by the fractional time derivatives is used to calculate reference solutions to evaluate the accuracy of the new expression. Modelling results indicate that the newly proposed viscoelastic wave equation using the new fractional Laplacians is more accurate than the conventional one, especially in a small Q medium (i.e. QP = QS = 5). Furthermore, we also examine the accuracy of the TE approximation with a series of Q values. A homogeneous model and the modified BP2004 viscoelastic model are used to investigate the accuracy of viscoelastic wave propagations using the TE algorithm. All modelling results fully demonstrate the performance of the newly proposed viscoelastic wave equation and numerical algorithm.