Identification of the meta-instability stage via synergy of fault displacement: An experimental study based on the digital image correlation method

•Detailed spatiotemporal evolution of fault displacement fields are obtained in experiment.•Two parameters quantifying the synergy of fault displacement are power functions of time.•The meta-instability stage can be proximately identified via the peak curvatures of the two parameters.

In stick–slip experiments modeling the occurrence of earthquakes, the meta-instability stage (MIS) is the process that occurs between the peak differential stress and the onset of sudden stress drop. The MIS is the final stage before a fault becomes unstable. Thus, identification of the MIS can help to assess the proximity of the fault to the earthquake critical time. A series of stick–slip experiments on a simulated strike-slip fault were conducted using a biaxial servo-controlled press machine. Digital images of the sample surface were obtained via a high speed camera and processed using a digital image correlation method for analysis of the fault displacement field. Two parameters, A and S, are defined based on fault displacement. A, the normalized length of local pre-slip areas identified by the strike-slip component of fault displacement, is the ratio of the total length of the local pre-slip areas to the length of the fault within the observed areas and quantifies the growth of local unstable areas along the fault. S, the normalized entropy of fault displacement directions, is derived from Shannon entropy and quantifies the disorder of fault displacement directions along the fault. Based on the fault displacement field of three stick–slip events under different loading rates, the experimental results show the following: (1) Both A and S can be expressed as power functions of the normalized time during the non-linearity stage and the MIS. The peak curvatures of A and S represent the onsets of the distinct increase of A and the distinct reduction of S, respectively. (2) During each stick–slip event, the fault evolves into the MIS soon after the curvatures of both A and S reach their peak values, which indicates that the MIS is a synergetic process from independent to cooperative behavior among various parts of a fault and can be approximately identified via the peak curvatures of A and S. A possible application of these experimental results to field conditions is provided. However, further validation is required via additional experiments and exercises.