Abstract:The size selection of the critical seismogenic region prior to an earthquake has great influence on seismic hazard evaluation.By adopting an appropriate critical region,we can reduce the occurrence of false alarms and enhance the critical sensitivity of the precursory anomalies.In this study,we examine the optimal critical region scale using the load/unload response ratio(LURR)and accelerating moment release(AMR)methods.These two methods are intuitively reasonable.Prior to the occurrence of large or great earthquakes,the AMR phenomenon is usually observed.A simple power-law time-to-failure equation derived from damage mechanics can be used to model the observed seismicity.This hypothesis is an outgrowth of efforts to characterize large earthquakes as a critical phenomenon.The LURR is a short-to-intermediate-term earthquake prediction method based on measuring the ratio between Benioff strains released during the time periods of loading and unloading,corresponding to the Coulomb Failure Stress change induced by Earth tides on optimally oriented faults.Prior to the occurrence of large earthquakes(M>6.0),anomalous increases in the time series of LURR within a time frame of months to years has often been observed. A circular region is usually adopted as the spatial window in the LURR and AMR practices,allowing us to link these two unrelated subjects to investigate the optimal critical region prior to a large earthquake.In this study,the optimal critical region scale for LURR evaluation is determined by computing the anomaly within various-sized regions centered at the epicenter of the incoming large event to reach the maximum LURR precursory anomalies.For the AMR method,the calculation of the optimal critical region includes the following steps:The Benioff strain of earthquakes within each circular region is fitted to a power-law time-to-failure function and to a straight line;we then compute a curvature parameter as the ratio of the residuals to the powerlaw fit to the residuals of the linear fit;and the critically seismogenic region is finally defined as the circular region that minimizes the curvature parameter.Retrospective testing on 36 M > 5 earthquakes occurring in North China during the last 40years show remarkable enhancement of the LURR precursory anomalies with the optimal critical regions.From these statistics,we found that the optimal critical regions derived from both methods are consistent with each other:The slopes of the linear relationship between the radii of the optimal critical regions and the magnitude of the detection earthquakes for LURR and AMR are 0.34and 0.36,respectively.The results show that by combining different earthquake prediction methods,we can quantitatively assess critical seismogenic region scale and therefore provide information and constrains about the approaching criticality of the system.