基于快速行进迎风线性插值的微震定位算法研究

准确的微震定位方法是微震监测技术进行岩体稳定性分析的基础,而初至波走时计算方法是决定微震定位精度重要因素之一。引入一种由快速行进法(fast marching methods, FMM)与线性插值射线追踪法(LTI ray tracing)改进而来的线性插值算法,实现了在复杂岩体中相对准确的微震初至走时计算,并在均一速度模型和Marmousi模型中得到了验证。在此基础上,采用常微分方程数值算法中的单步高精度Runge-Kutta法,得到了震源点和传感器之间的射线路径,并在分层和带空洞的岩体模型中验证了其合理性。选取最小二乘法为目标函数,通过寻找目标函数值最小的方式来获得最优节点实现微震定位。在所建立的加入地下硐室的Marmousi岩体模型中,对于预设震源点的定位结果误差分别为1.41、1.00、2.83、1.41、1.41m,验证了所提方法在复杂岩体速度模型中能够实现较准确的微震定位,为进一步提高工程岩体的微震定位精度提供了新思路。

Research on microseismic location based on fast marching upwind linear interpolation method

An accurate microseismic (MS) source location method is the foundation of MS monitoring technology for stability analysis of rock mass, and the first-arrival travel time calculation method is one of the important factors determining the precision of MS source location. An improved linear interpolation algorithm based on the fast marching methods (FMM) and LTI ray tracing is introduced to obtain relatively accurate first-arrival travel time in complex rock masses. Moreover, this improved algorithm is verified by the uniform velocity model and the Marmousi model. On the basis of travel time calculation, Runge-Kutta method, a single-step high-precision method in the numerical algorithm of ordinary differential equations, is introduced to calculate the ray propagation path. Besides, its rationality is verified in the uniform, stratified and hollow rock mass model established by us. Finally, using the least-squares method as the objective function, the MS source location is achieved by obtaining the optimal node that makes the objective function taken the minimum value. In the Marmousi model with underground caverns established by us, the location errors for the pre-set source points are 1.41, 1.00, 2.83, 1.41 m and 1.41 m, respectively. It is verified that the method in this paper can achieve relatively accurate location in the complex rock mass and provide a new idea for improving the accuracy of microseismic location in the engineering rock mass.