无需测速的微震源反演数学模型研究

MATHEMATICAL MODELING OF MICRO-SEISMIC SOURCE INVERSION IN MINES WITHOUT VELOCIMETRY

微震源反演数学模型、反演算法等对象是微震源定位误差的重要来源。针对P波速度易衰减、首波到时数据拾取误差较大的情况,基于到时差模型(ATD)和P波到时方程组,建立到时差比值法反演数学模型(ATDRM),从目标函数中消除了P波速度和发震时刻等参数;同时,引入范数概念,得到改进的L1、L2、L3、L4范数模型,设计一系列反演模型对比实验和反演算法对比实验综合分析研究这些模型的优越性。工程数据显示:ATDRM模型的定位效果整体比经典ATD模型更好,ATDRM-L1模型震源误差可减少13.437 0 m;反演模型的定位误差受反演算法影响较大,单形替换法相比遗传算法(GA)、非线性最小二乘法(NLSM)、模拟退火算法(SA)等方法定位精度更高,稳定性更好;在应用单形替换法求解模型时,反演误差会随着范数参数N的增加(L1→L4)呈现先下降再上升的现象;ATDRM模型及其范式形式对提高微震源定位精度有一定价值。

The micro-seismic source inversion mathematical model,inversion algorithm and other objects are important sources of micro-seismic source localization errors.To address the situation that the P-wave velocity is easily altenuated and the first wave arrival data pickup error is large,the inversion mathematical model of arrival time difference method(ATDRM)is established based on the arrival time difference model(ATD)and the set of P-wave arrival time equations,and the peirame-ters of P-wave velocity and seismic moment are eliminated from the objective function;meanwhile,the concept of parametric number is introduced to obtain the improved parametric models of L1,L2,L3 and L4,and a series of inversion A series of model comparison experiments and inversion algorithm comparison experiments are designed to comprehensively analyze the superiority of these models.The engineering data show that the overall localization effect of the ATDRM model is better than that of the classical ATD model,and the source error of the ATDRM-L1 model can be reduced by 13.4370 m.The localization error of the inversion model is influenced by the inversion algorithm,and the monomorphic replacement method has higher localization accuracy and better stability than the genetic algorithm(GA),nonlinear least squares method(NLSM),simulated annealing algorithm(SA)and other methods.The inversion error decreases and then increases with the increase of the parametric parameter N(LI→L4)when the monomorphic substitution method is applied to solve the model;the ATDRM model and its parametric form are valuable for improving the localization accuracy of micro-seismic sources.