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Seismic wave scattering dispersion and attenuation can be significant in cracked reservoirs. Many scattering models have been proposed, and the fractal (self-similar) features of the medium need to be further incorporated and analysed. We solve the P -wave scattering caused by fluid-saturated aligned cracks of finite thickness embedded in fractal media. The model is based on crack displacement discontinuities by using the Foldy approximation and representation theorem. The frequency dependence of velocity and attenuation are analysed as a function of the incidence angle and the crack and fluid properties. The results show that the crack density, thickness and radius can have a significant influence on the wave properties, as well as the fluid bulk modulus and saturation. The model requires three parameters to describe self-similar cracked media, and can be relevant in seismology, oil exploration and non-destructive testing of materials. [ABSTRACT FROM AUTHOR]

We analyse the reflection coefficient of an inhomogeneous plane wave incident on the thermally insulated surface of a thermo-poroelastic medium. The theory, which includes the classic Lord-Shulman (LS) and Green-Lindsay (GL) theories as well as a generalization of the LS model, predicts three inhomogeneous longitudinal waves and one transverse wave, described by potential functions specified by the propagation direction and inhomogeneity angle. The GL model can give a stronger P1-wave thermal attenuation and consequently a stronger velocity dispersion than the LS model. We investigate the influence of inhomogeneity angle, type of incident wave, frequency and surface boundary conditions. The generalized LS model exhibits increased P1-wave thermal attenuation with increasing Maxwell–Vernotte–Cattaneo relaxation time and consequently predicts more interference energy, irrespective if the surface is open or sealed. The inhomogeneity angle affects the energy partitions particularly near the grazing incidence, with a significant interference energy, which must be taken into account to satisfy the energy conservation. The thermal dispersion occurs at frequencies around the thermal relaxation peak, which moves to low frequencies when the conductivity increases. [ABSTRACT FROM AUTHOR]

Thermoelasticity extends the classical elastic theory by coupling the fields of particle displacement and temperature. The classical theory of thermoelasticity, based on a parabolic-type heat-conduction equation, is characteristic of an unphysical behaviour of thermoelastic waves with discontinuities and infinite velocities as a function of frequency. A better physical system of equations incorporates a relaxation term into the heat equation; the equations predict three propagation modes, namely, a fast P wave (E wave), a slow thermal P wave (T wave), and a shear wave (S wave). We formulate a second-order tensor Green's function based on the Fourier transform of the thermodynamic equations. It is the displacement–temperature solution to a point (elastic or heat) source. The snapshots, obtained with the derived second-order tensor Green's function, show that the elastic and thermal P modes are dispersive and lossy, which is confirmed by a plane-wave analysis. These modes have similar characteristics of the fast and slow P waves of poroelasticity. Particularly, the thermal mode is diffusive at low thermal conductivities and becomes wave-like for high thermal conductivities. [ABSTRACT FROM AUTHOR]