Cross-correlation analysis and time delay estimation of a homologous micro-seismic signal based on the Hilbert–Huang transform

Abstract

A micro-seismic signal's transient features are non-stationary. The traditional weighted generalized cross-correlation (GCC) algorithm is based on the cross-power spectrum density. This algorithm diminishes the performance of the time delay estimation for homologous micro-seismic signals. This paper analyzed the influence of calculation error on the cross-power spectrum density of a non-stationary signal and proposed a new cross-correlation analysis and time delay estimation method for homologous micro-seismic signals based on the Hilbert–Huang transform (HHT). First, the original signals are decomposed into intrinsic mode function (IMF) components using empirical mode decomposition (EMD) for de-noising. Subsequently, the IMF components and the original signals are analyzed using a cross-correlation analysis. The IMF components are subsequently remodeled at different scales using the Hilbert transform. The marginal spectrum density is obtained via a time integration of the remodeled components. The cross-marginal spectrum density of the two signals can also be obtained. Finally, the cross-marginal spectrum density is used in the weighted GCC algorithm for time delay estimation instead of the cross-power spectrum density. The time delay estimation is determined by searching for the weighted GCC function peak. The experiments demonstrated the superior time delay estimation performance of the new method for non-stationary transient signals. Therefore, a new time delay estimation method for non-stationary random signals is presented in this paper.