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该文针对矿井不良地质异常体的反射波超前探测问题,建立了典型矿井介质模型,通过对一阶速度-应力方程进行时间2阶、空间4阶有限差分求解,得到了高阶交错网格有限差分格式,推导了完全匹配层和自由边界方程,并对稳定性条件进行了分析,实现了矿井介质模型的高阶交错网格有限差分数值模拟。结果表明:高阶交错网格有限差分数值模拟,能清晰描述矿井介质模型中弹性波传播规律,能为矿井反射波超前探测数据处理与解释提供理论依据。
In this paper, a typical mine medium model is established for the advanced detection of reflected waves in adverse geological anomalies in mines. By solving the first-order velocity-stress equations with finite difference time 2 and space 4, Differential format, the perfect matching layer and the free boundary equation are deduced, and the stability conditions are analyzed. The finite difference numerical simulation of high-order staggered-grid mesh model is realized. The results show that the finite difference numerical simulation of high-order staggered grids can clearly describe the elastic wave propagation law in the mine media model and provide a theoretical basis for the processing and interpretation of the advanced detection data of mine reflected waves.