Thermoelasticity is important in seismic propagation due to the effects related to wave attenuation and velocity dispersion. We have applied a novel finite-difference (FD) solver of the Lord-Shulman thermoelasticity equations to compute synthetic seismograms that include the effects of the thermal properties (expansion coefficient, thermal conductivity, and specific heat) compared with the classic forward-modeling codes. We use a time splitting method because the presence of a slow quasistatic mode (the thermal mode) makes the differential equations stiff and unstable for explicit time-stepping methods. The spatial derivatives are computed with a rotated staggered-grid FD method, and an unsplit convolutional perfectly matched layer is used to absorb the waves at the boundaries, with an optimal performance at the grazing incidence. The stability condition of the modeling algorithm is examined. The numerical experiments illustrate the effects of the thermoelasticity properties on the attenuation of the fast P-wave (or E-wave) and the slow thermal P-wave (or T-wave). These propagation modes have characteristics similar to the fast and slow P-waves of poroelasticity, respectively. The thermal expansion coefficient has a significant effect on the velocity dispersion and attenuation of the elastic waves, and the thermal conductivity affects the relaxation time of the thermal diffusion process, with the T mode becoming wave-like at high thermal conductivities and high frequencies.

中文翻译：

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基于Lord-Shulman理论的热弹性波模拟

由于与波衰减和速度色散有关的影响，热弹性在地震传播中很重要。我们已经应用了Lord-Shulman热弹性方程式的新型有限差分（FD）求解器来计算合成地震图，其中包括热性能（膨胀系数，热导率和比热）与经典正向建模代码相比的影响。我们使用时间分割方法，因为慢速准静态模式（热模式）的存在使微分方程对于显式时间步长方法变得僵硬和不稳定。使用旋转交错网格FD方法计算空间导数，并使用未拆分的卷积完美匹配层吸收边界处的波，并在掠入射时获得最佳性能。检查了建模算法的稳定性条件。数值实验说明了热弹性特性对快P波（或E波）和慢热P波（或T波）衰减的影响。这些传播模式的特性分别类似于多孔弹性的快P波和慢P波。热膨胀系数对弹性波的速度色散和衰减有显着影响，并且热导率影响热扩散过程的弛豫时间，在高热导率和高频下，T模式呈波状。数值实验说明了热弹性特性对快P波（或E波）和慢热P波（或T波）衰减的影响。这些传播模式的特性分别类似于多孔弹性的快P波和慢P波。热膨胀系数对弹性波的速度色散和衰减有显着影响，并且热导率影响热扩散过程的弛豫时间，在高热导率和高频下，T模式呈波状。数值实验说明了热弹性特性对快P波（或E波）和慢热P波（或T波）衰减的影响。这些传播模式的特性分别类似于多孔弹性的快P波和慢P波。热膨胀系数对弹性波的速度色散和衰减有显着影响，并且热导率影响热扩散过程的弛豫时间，在高热导率和高频下，T模式呈波状。