Location method of ill-conditioned microseismic source and its engineering application

Microseismic event location is one of the core parameters in microseismic monitoring, and the accuracy of localization will directly affect the effectiveness of engineering applications. However, limited by spatial factors, the geometry of the sensor installation will be close to linear, which makes the localization equation suffer from the pathological problem, and the localization accuracy is greatly reduced. To address this problem, the reasons for the pathological problem are analyzed from the perspective of the objective function residuals and coefficient matrix. The pathological problem is caused by the combined effect of the poorer sensor array and data errors, and its residual isosurface shows a conical distribution, and as the residual value decreases, the apex of the isosurface gradually extends to the far side, and the localization results do not converge. For this reason, an improved regularized Newton downhill localization algorithm is proposed. In this method, firstly, the Newtonian downhill method is improved so that the magnitudes of the seismic source parameters are the same, and the condition number of the coefficient matrix is reduced; then, the L-curve method is used to calculate the regularization factor for the pathological equations, and the coefficient matrix is improved; finally, the pathological equations are regularized, and the seismic source coordinates are obtained by the improved Newtonian downhill method. The results of engineering applications show that compared with the traditional algorithm based on automatic of P-arrival picking, the number of effective microseismic events calculated by the proposed localization algorithm is increased by 194.7%, and the localization accuracy is substantially improved. The proposed algorithm reduces the problem of low accuracy of S-arrival picking and allows localization using only P-wave arrival. The method reduces the quality requirements of the data and significantly improves the utilization of microseismic events and positioning accuracy.