Microseismic P-Wave Travel Time Computation and 3D Localization Based on a 3D High-Order Fast Marching Method

The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.