基于因素分布模型的微震定位精度敏感性分析

Sensitivity analysis of microseismic positioning accuracy based on distribution models of influencing factors

根据微震定位方程,基于误差最小原理,构造微震定位精度敏感性评价的输入输出数学模型,选取震源点到各检波器之间距离测量误差、微震波波速标定误差和信号到时拾取误差3个影响因素作为分析因子。从信息熵的角度,分析因素分布密度函数,并通过泛函变分求得相应表达式。采用正交法设计16组方案,根据分布函数求取因素各水平值,进行全局敏感性分析。研究结果表明:3个因子取值在给定区间内均符合均匀分布;无论是对内场震源点还是外场震源点,微震波波速误差,是对定位结果影响最大的因素,各因子对定位精度影响的主次顺序为:Ve,Te,De;对于内场震源点,3个因素对定位精度均有高度显著影响。但对于外场震源点,可能由于因素之间的交互作用或者试验误差影响,仅微震波波速标定误差对定位精度有高度显著影响。相关研究可为微震监测的准确定位等提供针对性指导。

Based on microseismic positioning equation and minimum error principle, an input and output mathematical model for evaluating sensitivity of microseismic positioning accuracy was constructed. Distance error between microseismic sources and sensors, seismic wave velocity error and trigger times error were selected as analysis factors. Factor distribution fanction was discussed by using information entropy, and the corresponding expression was obtained by functional variation. Scheme of 16 groups was designed by using orthogonal method. Level value of each factor was given according to the factor distribution function. And the global sensitivity analysis was performed. The results show that three factors accord with uniform distribution in a given interval; for both the internal and external field sources, seismic wave velocity error is the most influential factor that affects the positioning results, and the significant order from big to small of influence on positioning accuracy is Ve, Te and De. For internal field source, all three factors have some significant influence on positioning accuracy; while for the external field source, only the seismic wave velocity error has some significant influence on positioning accuracy, which may probably be affected by the interaction between the factors or experimental errors. The research conclusions may offer specific guidance for the accurate location analysis of microseismic monitoring in the similar projects.