Normal Information Diffusion Distribution and Its Application in Inferring the Optimal Probability Density Functions of the Event Coordinates From the Microseismic or Acoustic Emission Sources

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.