Time difference of arrival estimation of microseismic signals based on alpha-stable distribution

Microseismic signals are generally considered to follow the Gauss distribution. A comparison of the dynamic characteristics of sample variance and the symmetry of microseismic signals with the signals which follow alpha-stable distribution reveals that the microseismic signals have obvious pulse characteristics and that the probability density curve of the microseismic signal is approximately symmetric. Thus, the hypothesis that microseismic signals follow the symmetric alpha-stable distribution is proposed. On the premise of this hypothesis, the characteristic exponent alpha of the microseismic signals is obtained by utilizing the fractional low-order statistics, and then a new method of time difference of arrival (TDOA) estimation of microseismic signals based on fractional low-order covariance (FLOC) is proposed. Upon applying this method to the TDOA estimation of Ricker wavelet simulation signals and real microseismic signals, experimental results show that the FLOC method, which is based on the assumption of the symmetric alpha-stable distribution, leads to enhanced spatial resolution of the TDOA estimation relative to the generalized cross correlation (GCC) method, which is based on the assumption of the Gaussian distribution.