We develop a numerical algorithm for simulation of wave propagation in anisotropic thermoelastic media, established with a generalized Fourier law of heat conduction. The wavefield is computed by using a grid method based on the Fourier differential operator and a first-order explicit Crank-Nicolson algorithm to compute the spatial derivatives and discretize the time variable (time stepping), respectively. The model predicts four propagation modes, namely, a fast compressional or (elastic) P wave, a slow thermal P diffusion/wave (the T wave), having similar characteristics to the fast and slow P waves of poroelasticity, respectively, and two shear waves, one of them coupled to the P wave and therefore affected by the heat flow. The thermal mode is diffusive for low values of the thermal conductivity and wave-like (it behaves as a wave) for high values of this property. As in the isotropic case, three velocities define the wavefront of the fast P wave, i.e, the isothermal velocity in the uncoupled case, the adiabatic velocity at low frequencies, and a higher velocity at high frequencies. The heat (thermal) wave shows an anisotropic behavior if the thermal conductivity is anisotropic, but an elastic source does not induce anisotropy in this wave if the thermal properties are isotropic.

我们开发了一种数值算法，用于模拟各向异性热弹性介质中的波传播，该算法是根据热传导的广义傅立叶定律建立的。波场的计算采用基于傅立叶微分算子的网格法和一阶显式 Crank-Nicolson 算法分别计算空间导数和离散时间变量（时间步进）。该模型预测四种传播模式，即快速压缩或（弹性）P 波、慢速热 P 扩散/波（T 波），分别与孔隙弹性的快速和慢速 P 波具有相似的特征，以及两种剪切模式波，其中之一与 P 波耦合，因此受到热流的影响。对于低热导率值，热模式是扩散的；对于高热导率值，热模式是波状的（它表现为波）。与各向同性情况一样，三个速度定义了快速 P 波的波前，即非耦合情况下的等温速度、低频下的绝热速度和高频下的较高速度。如果热导率是各向异性的，则热（热）波表现出各向异性行为，但如果热属性是各向同性的，则弹性源不会在该波中引起各向异性。