SUMMARY

Thermoelastic attenuation is similar to wave-induced fluid-flow attenuation (mesoscopic loss) due to conversion of the fast P wave to the slow (Biot) P mode. In the thermoelastic case, the P- and S-wave energies are lost because of thermal diffusion. The thermal mode is diffusive at low frequencies and wave-like at high frequencies, in the same manner as the Biot slow mode. Therefore, at low frequencies, that is, neglecting the inertial terms, a mathematical analogy can be established between the diffusion equations in poroelasticity and thermoelasticity. We study thermoelastic dissipation for spherical and cylindrical cavities (or pores) in 2-D and 3-D, respectively, and a finely layered system, where, in the latter case, only the Grüneisen ratio is allowed to vary. The results show typical quality-factor relaxation curves similar to Zener peaks. There is no dissipation when the radius of the pores tends to zero and the layers have the same properties. Although idealized, these canonical solutions are useful to study the physics of thermoelasticity and test numerical algorithm codes that simulate thermoelastic dissipation.

中文翻译：

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波浪引起的热弹性衰减的典范解析解

概要

由于快速P波转换为慢速（Biot）P模式，热弹性衰减类似于波引起的流体流量衰减（介观损耗）。在热弹性情况下，由于热扩散，P和S波能量会损失。与毕奥慢速模式相同，热模式在低频扩散，在高频呈波状。因此，在低频下，即忽略惯性项，可以在孔隙弹性和热弹性的扩散方程之间建立数学类比。我们分别研究了二维和三维中球形和圆柱形腔（或孔）的热弹性耗散，以及细小分层的系统，在这种情况下，仅允许Grüneisen比率发生变化。结果显示典型的品质因数松弛曲线类似于齐纳峰。当孔的半径趋于零并且各层具有相同的特性时，没有耗散。尽管是理想的，但这些规范的解决方案对于研究热弹性物理学和测试模拟热弹性耗散的数值算法代码很有用。