Wave fields in real media : wave propagation in anisotropic, anelastic, porous and electromagnetic media

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Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians (2014, methodology): “Time-domain ap- proaches commonly use superposition of mechanical elements (e.g., Maxwell and standard linear solid [SLS] elements) to describe Q behavior, which are known as approximate constant-Q (ACQ) models (Liu et al., 1976; Emmerich and Korn, 1987; Carcione, 2007; Zhu et al., 2013).”
On the rheological models used for time‐domain methods of seismic wave propagation (2005, methodology): “Formulas (11) and (12) were presented by Carcione [2001]. Note that Liu et al. [1976], in generalizing the strain-stress relation for one ZB (equation 16 in their paper) to the relation for the GZB (equation 22 in their paper), introduced an error, which then has been repeated in the following paper”
An unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave propagation in poroelastic media (2008, background): “…WAVE EQUATION: BIOT MODEL AND VELOCITY-STRESS FORMULATION The differential, or “strong,” form of the poroelastic wave equaion can be written as e.g., Carcione, 2007 t 2us f t 2w · C: us PfI f t 2us w t 2w Pf K tw Pf M · us M · w , 1 here us uis i 1,D D denotes the space dimension ; w u f us and u…”