Physics of Seismic and Tidal Attenuation

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The theory of elasticity and internal friction in Earth's materials is most important for seismology, materials science, and studies of terrestrial and planetary tides. We argue that despite its long and broad use, the conventional viscoelastic model is insufficient for two reasons. First, this model is based on postulated mathematical concepts such as the creep function, quality factors (Q), time-dependent moduli, and the correspondence principle which lack explanations from first-principle physical laws. Second, this model is insufficiently general, and inelasticity within the heterogeneous Earth does not always reduce to an effect of a Q. For example, in rocks containing pore fluids (the primary cause of seismic attenuation in sedimentary rocks), secondary P-waves are always present. These secondary waves contribute to all observable phenomena, such as wave velocity dispersion, reflection amplitudes in layered media or strain/stress phase lags in laboratory measurements. Nevertheless, secondary wave modes are not included in the viscoelastic model, which only considers the Q factors for the primary modes.******To overcome this lack of theoretical understanding of the physics of attenuation, we will give a general and rigorous macroscopic theoretical framework for all aspects of wave propagation and attenuation without relying on the viscoelastic moduli. The approach will be based on established methods of theoretical continuum mechanics, thermodynamics, and perturbation theory. As end-member cases, the theory will contain the model of the Newtonian fluid, Biot's poroelasticity, and the entire conventional viscoelasticity. The approach will also provide generalizations and transitions between the end-member cases above. ******The theory will be applied to a broad range of problems in exploration and global seismology, such as: 1) models of field and laboratory experiments with rocks, 2) models of rock saturated with heavy oil, 3) equivalent media for heterogeneous porous rock, 4) models of thermoelastic attenuation within the Moon and the Earth's mantle, 5) models of terrestrial and lunar tides, 6) unified nonlinear rheologic law explaining the scaling law for the observed Q-factor for a broad range of frequencies, and 7) nonlinear wave propagation near an explosion source. Because of using methods that are well-established in physics, the degree of confidence in solving these problems is high. ******The new theoretical framework should open new avenues of interpreting many observations of seismic and tidal dissipation and provide new insights on a number of key problems in modern seismology. It will also have a significant practical impact, contributing to many numerical algorithms for seismic wave propagation and inversion used in the industry.**