Seismic wave propagation within thinly layered anelastic reservoirs is modeled by direct application of Lagrangian continuum mechanics. Instead of postulating viscoelastic Q-factors or specific microscopic mechanisms, the anelastic properties of the layers are modeled by using generalized macroscopic internal variables. These variables represent averaged measures of various types of internal deformations of the rock, such as relative movements of grains, inclusions, pores and mobile dislocations, wave-induced pore-fluid flows (WIFFs), capillary and layer-boundary effects, or temperature variations. The continuum-mechanics model reveals the existence of body-force (Darcy-type) frictional effects, which are also absent in the viscoelastic model. To implement the attenuation effects observed in laboratory studies, the mechanical properties of the layers are represented by standard linear solid (Zener) rheologies approximating a mesoscopic-scale WIFF effect known as the drained/undrained transition. Optionally, the layer rheologies also include Biot’s poroelastic effects. All compressional- and shear-wave transmission, reflection, and mode-conversion amplitudes and waveforms for primary and secondary waves are modeled at variable angles of incidence. The modeled records exhibit the expected seismic-wave attenuation and dispersion phenomena but differ from the predictions of viscoelastic modeling. The key observation is that wave-propagation effects are sensitive not only to the Q-factors of the layers but also to properties not considered in conventional models: (1) elastic coupling between the internal variables, (2) body-force friction parameters analogous to fluid mobility, and (3) mechanical properties of contact zones between different rocks, such as the effective permeabilities of layer boundaries. Although challenging, these properties of layer boundaries need to be measured for earth’s media and included in the modeling of seismic waves. Another important general observation from this modeling is that the often observed broadband or near-constant seismic Q may result from superposition of the effects of multiple heterogeneities (layers) and material-property contrasts within the medium.

中文翻译：

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层状线性非弹性固体的宏观地震响应：粘弹性模型以外的波浪引起的内部变形

地震波在薄层非弹性储层中的传播是通过直接应用拉格朗日连续力学来模拟的。代替假设粘弹性Q-因素或特定的微观机制，通过使用广义的宏观内部变量对层的非弹性性质进行建模。这些变量代表各种岩石内部变形的平均量度，例如晶粒，包裹体，孔隙和移动位错的相对运动，波诱导的孔隙流（WIFF），毛细管和层边界效应或温度变化。 。连续力学模型揭示了体力（达西型）摩擦效应的存在，粘弹性模型中也没有这种效应。为了实现在实验室研究中观察到的衰减效应，各层的机械性能用近似于介观尺度的WIFF效应的标准线性固体（Zener）流变学来表示，这称为排水/不排水过渡。（可选）层流变学还包括Biot的多孔弹性效应。初级和次级波的所有压缩波和剪切波传输，反射以及模式转换幅度和波形均以可变的入射角建模。建模记录显示了预期的地震波衰减和色散现象，但与粘弹性建模的预测有所不同。关键观察结果是，波传播效应不仅对波的传播敏感。层的Q因子以及常规模型中未考虑的特性：（1）内部变量之间的弹性耦合;（2）类似于流体流动性的体力摩擦参数;（3）不同层之间的接触区的机械性能岩石，例如层边界的有效渗透率。尽管具有挑战性，但层边界的这些属性需要针对地球介质进行测量，并包括在地震波建模中。此模型的另一个重要的一般观察结果是，经常观察到的宽带Q或近恒定地震Q可能是由于介质中多个非均质性（层）和材料-属性对比的叠加而导致的。