高阶有限差分法管波传播数值模拟

Tube Wave Propagation Numerical Simulation Based on High Order Finite-Difference Method

为正确认识流体充填钻孔中管波的传播规律,首先给出均匀各向同性介质中包含流体充填钻孔条件下的弹性波动力学方程和二阶速度-应力公式及差分格式的稳定性条件和边界条件;然后利用高阶交错网格有限差分法,结合典型模型,模拟了不同时刻管波的传播快照和复杂层状介质中管波的合成地震记录,并与实际管波地震记录进行了对比。结果表明:在地层分界面、溶洞的边界等波阻抗差异界面处,管波都会产生反射;反射管波的振幅、频率特征受界面两侧的岩石物理性质差异的影响;在理论合成记录中,反射管波与直达管波同相轴的交点与理论模型中地层分界面或异常体的边界一致。

Making use of the tube wave detection method to find geological disasters,such as karsts or corrosion cracks within a certain range around the borehole,is a new means of engineering geophysical survey.To better understand the tube wave propagation mechanism in fluid-filled boreholes,a staggered-grid finite-difference approach is applied to compute the wave propagation in homogeneous isotropic media including a fluid-filled borehole.Firstly,the wave motion equation was introduced,and the finite-difference solution was obtained with Taylor’s series expansion,and then,the stability and absorption boundary conditions were discussed.Using a homogenous isotropic model,the snapshots were calculated under the non-borehole conditions and borehole conditions respectively.Two models were designed for the seismology,one was a three-layered model containing a hole filled with soil,and another was a practical model designed according to field data.Numerical simulation results showed that tube wave reflections existed on the interface of different impedance,such as formation interfaces and karst boundaries;the difference of physical properties of strata had an influence on the amplitude and the frequency of reflection waves;and in the synthesis record,the intersection of reflection tube waves and direct tube waves is consistent with the actual boundaries of formation or anomalous bodies designed in the theoretical model.