Poro-elastic wave equations are one of the fundamental problems in seismic wave exploration and applied mathematics. In the past few decades, elastic wave theory and numerical method of porous media have developed rapidly. However, the mathematical stability of such wave equations have not been fully studied, which may lead to numerical divergence in the wave propagation simulation in complex porous media. In this paper, we focus on the stability of the wave equation derived from Tuncay’s model and volume averaging method. By analyzing the stability of the first-order hyperbolic relaxation system, the mathematical stability of the wave equation is proved for the first time. Compared with existing poro-elastic wave equations (such as Biot’s theory), the advantage of newly derived equations is that it is not necessary to assume uniform distribution of pores. Such wave equations can spontaneously incorporate complex microscale pore/fracture structures into large-scale media, which is critical for unconventional oil and gas exploration. The process of proof and numerical examples shows that the wave equations are mathematically stable. These results can be applied to numerical simulation of wave field in reservoirs with pore/fracture networks, which is of great significance for unconventional oil and gas exploration.

孔隙弹性波方程是地震波勘探和应用数学的基本问题之一。在过去的几十年中，弹性波理论和多孔介质的数值方法发展迅速。但是，此类波动方程的数学稳定性尚未得到充分研究，这可能导致复杂多孔介质中波动模拟中的数值差异。在本文中，我们关注从Tuncay模型和体积平均方法得出的波动方程的稳定性。通过分析一阶双曲松弛系统的稳定性，首次证明了波动方程的数学稳定性。与现有的孔隙弹性波动方程（例如毕奥特理论）相比，新推导的方程式的优点在于，不必假设孔的均匀分布。这样的波动方程可以自发地将复杂的微尺度孔隙/裂缝结构整合到大规模介质中，这对于非常规油气勘探至关重要。证明过程和数值示例表明，波动方程在数学上是稳定的。这些结果可用于带孔/裂隙网络的油藏波场数值模拟，对非常规油气勘探具有重要意义。证明过程和数值示例表明，波动方程在数学上是稳定的。这些结果可用于带孔/裂隙网络的油藏波场数值模拟，对非常规油气勘探具有重要意义。证明过程和数值示例表明，波动方程在数学上是稳定的。这些结果可用于带孔/裂隙网络的油藏波场数值模拟，对非常规油气勘探具有重要意义。