Sources spatial localization algorithm and applications of rock failure acoustic emission

Accurate localization of acoustic emission(AE) sources and velocity tomographic imaging are essential for predicting rock deformation and failure in laboratory experiments. This paper proposes a novel multi-stencils fast marching method(MSFM) algorithm that accounts for anisotropy to compute the arrival times of seismic(or acoustic) waves in the source space. By matching the observed time difference matrix with the theoretical time difference matrix，this approach identifies the optimal source location. By integrating AE localization data，the algorithm achieves three-dimensional tomographic imaging of the anisotropic P-wave structure in rock samples. Furthermore，a coupled predictive method based on <italic>RA</italic>-<italic>AF</italic> value，<italic>Ib</italic> value，and AE multi-parameter critical slowing down is developed to forecast rock instability and failure. Additionally，an innovative wavelet coherence method is used to characterize damage evolution by analyzing the crack propagation modes of <italic>RA</italic>-<italic>AF</italic> parameters over time. Findings indicate that the new localization algorithm accurately identifies source locations within heterogeneous rock materials. The velocity tomography results reveal a sharp 5%–30% decrease in wave speed and a 5%–20% increase in anisotropy within the stress range of 95%–100% of peak stress. The stress peak range for AE multi-parameter prediction of rock instability is identified between 86% and 93%. These results and methods demonstrate substantial potential for enhancing failure localization and velocity imaging along nonlinear stress curves in complex geotechnical materials，providing insights into local changes associated with microcracks and failure.