Physics of Seismic and Tidal Attenuation

地球材料的弹性和内摩擦理论对于地震学、材料科学以及地球和行星潮汐的研究都是非常重要的。我们认为，尽管其长期和广泛的使用，传统的粘弹性模型是不够的，有两个原因。首先，该模型是基于假设的数学概念，如蠕变函数，品质因数（Q），随时间变化的模量，和对应原理，缺乏第一原理物理定律的解释。第二，这个模型不够普遍，而且非均匀地球内部的非弹性并不总是归结为Q的影响。例如，在含有孔隙流体（沉积岩中地震衰减的主要原因）的岩石中，总是存在次级P波。这些二次波有助于所有可观察到的现象，例如波速色散、层状介质中的反射振幅或实验室测量中的应变/应力相位滞后。然而，二次波模式不包括在粘弹性模型中，粘弹性模型仅考虑主模式的Q因子。**为了克服这种缺乏理论理解的物理衰减，我们将给出一个一般的和严格的宏观理论框架，波的传播和衰减的各个方面，而不依赖于粘弹性模量。该方法将建立在理论连续介质力学，热力学和微扰理论的方法。作为端元的情况下，该理论将包含模型的牛顿流体，毕奥的孔隙弹性，和整个传统的粘弹性。该方法还将提供上述端元情况之间的概括和过渡。** 该理论将应用于勘探和全球地震学中的广泛问题，例如：1）岩石的现场和实验室实验模型，2）用重油饱和的岩石模型，3）非均匀多孔岩石的等效介质，4）月球和地球地幔内的热弹性衰减模型，5）陆地和月球潮汐模型，6）统一的非线性流变定律，解释了在宽频率范围内观测到的Q因子的标度律; 7）爆炸源附近的非线性波传播。由于使用了物理学中公认的方法，解决这些问题的信心程度很高。** 新的理论框架应该为解释地震和潮汐耗散的许多观测开辟新的途径，并为现代地震学中的一些关键问题提供新的见解。它还将产生重大的实际影响，为工业中使用的地震波传播和反演的许多数值算法做出贡献。

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.**