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Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord–Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case. [ABSTRACT FROM AUTHOR]

The rheological models of Lomnitz and Jeffreys have been widely used in earthquake seismology (to simulate a nearly constant Q medium) and to describe the creep and relaxation behavior of rocks as a function of time. Other similar models, such as those of Becker, Scott Blair and Kolsky, show similar properties, particularly the Scott Blair model describes a perfectly constant Q as a function of frequency. We first give a historical overview of the main scientists and the development and versions of the various models and priorities of discovery. Then, we clarify the relationship between the different versions of these models in terms of mathematical expressions of the complex modulus and calculate the phase velocity and quality factor Q as a function of frequency, illustrating the various special cases. In addition, we give useful hints for the numerical calculation of these moduli, which include special cases of the hypergeometric function. [ABSTRACT FROM AUTHOR]

The quality factor Q is a dimensionless measure of the energy loss per cycle of a wave field, and a proper understanding of this factor is important in a variety of fields, from seismology, geophysical prospecting to electrical science. Here, the focus is on viscoelasticity. When interpreting experimental values, several factors must be taken into account, in particular the shape of the medium (rods, bars or unbounded media) and the fact that the measurements are made on stationary or propagating modes. From a theoretical point of view, the expressions of Q may differ due to different definitions, the spatial dimension and the inhomogeneity of the wave, i.e. the fact that the vectors of propagation (or wavenumber) and attenuation do not point in the same direction. We show the difference between temporal and spatial Q, the relationships between compressional and shear Q, the dependence on frequency, the case of poro-viscoelasticity and anisotropy, the effect of inhomogeneous waves and various loss mechanisms, and consider the analogy between elastic and electromagnetic waves. We discuss physical theories describing relaxation peaks, bounds on Q and experiments showing the behaviour of Q as a function of frequency, saturation and pore pressure. Finally, we propose an application example where Q can be used to estimate porosity and saturation. [ABSTRACT FROM AUTHOR]