A Dimensional Analysis Method for Improved Load–Unload Response Ratio

The load–unload response ratio (LURR) method is proposed to measure the damage extent of source media and the criticality of earthquake. Before the occurrence of a large earthquake, anomalous increase in the time series of LURR within the certain temporal and spatial windows has often been observed. In this paper, a dimensional analysis technique is devised to evaluate quantitatively the magnitude and time of the ensuing large earthquake within the anomalous areas derived from the LURR method. Based on the π-theorem, two dimensionless quantities associated with the earthquake time and magnitude are derived from five parameters (i.e. the seismic energy (E S), the average seismic energy (E W), the maximum value of LURR’s seismogenic integral (I PP), the thickness of seismogenic zone (h), the time interval from I PP to earthquake (T 2), and the shear strain rate (\(\dot{\gamma }\))). The statistical relationships between the earthquakes and the two dimensionless quantities are derived by testing the seismic data of the 50 events of M4.5 ~ 8.1 occurred in China since 1976. In earthquake prediction, the LURR method is used to detect the areas with anomalous high LURR values, and then our dimensional analysis technique is applied to assess the optimal critical region, magnitude, and time of the ensuing event, when its seismogenic integral is peaked (I PP). As study examples, we applied this approach to study four large events, namely the 2012 M S5.3 Hami, 2015 M S5.8 Alashan, 2015 M S8.1 Nepal earthquakes, and the 2013 Songyuan earthquake swam. Results show that the predicted location, time, and magnitude correlate well with the actual events. This provides evidence that the dimensional analysis technique may be a useful tool to augment current predictive power of the traditional LURR approach.