Abstract
To obtain optimal probability density functions (PDFs) or cumulative density functions (CDFs) of the event coordinates from the microseismic or acoustic emission sources, the normal information diffusion (NID) method based on the “ $3\sigma $ ” truncated interval is introduced. Six sets of different data of the event coordinates from the locating sources are used to illustrate the goodness-of-fit of the NID method, log-logistic (3P) method, lognormal method, and normal method. The results show that the Kolmogorov-Smirnov (K-S) and chi-square test values of the NID distributions (NIDDs) are always less than those of the log-logistic (3P) distributions (LLD3s), lognormal distributions (LNDs), and normal distributions (NDs); the cumulative probability values of the NIDDs are equal to 1, while those of the LLD3s, LNDs, and NDs are less than 1; the curves of the NIDDs have multimodal feature and can reflect the fluctuation of the event coordinates’ data. The conclusion can be drawn that the NIDDs are the optimal PDFs or CDFs of the event coordinates from the microseismic or acoustic emission sources. In the locating methods of the microseismic or acoustic emission sources, it is suggested that the NID method can be further used to improve the locating accuracy.
Highlights
Microseismic monitoring technology is one of the most effective means to monitor and analyze the stability of largescale rock mass, slope, and tunnelling [1]–[7]
This paper introduces the normal information diffusion (NID) method based on the ‘‘3σ ’’ truncated interval to infer the optimal probability density functions (PDFs) among analytical solutions from the locating sources of sensor networks
Six sets of analytical solutions were used to illustrate the fitting advantages of the NID distributions (NIDDs) compared with the LLD3s, lognormal distributions (LNDs), and normal distributions (NDs)
Summary
Microseismic monitoring technology is one of the most effective means to monitor and analyze the stability of largescale rock mass, slope, and tunnelling [1]–[7]. In studying that how to determine the event coordinate position of a microseismic source or an acoustic emission source, Dong et al [11]–[13] proposed the three-dimensional analytical solutions for an unknown velocity system and probability density function (TDAS-UVS-PDF) method. Considering the above three issues, it is doubtful whether the LLD3 is the optimal probability distribution of the event coordinates from the microseismic or acoustic emission sources when using the TDAS-UVS-PDF method. This paper focuses on these three issues to obtain the optimal probability distributions of analytical solutions from microseismic or acoustic emission sources. The aim of this study was to obtain the optimal probability distributions of analytical solutions by investigating the goodness-of-fit of the NIDD, LLD3, LND, and ND methods using six sets of analytical solutions. Several conclusions are drawn from the results of this study
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