Fast estimation of fault rupture length and direction based on FinDer method

The distribution direction and rupture length of large earthquake faults will affect the prediction of the city intensity in the earthquake early warning system and the subsequent outputs in the intensity rapid reporting system, such as the intensity of cities and towns, spatial distribution maps of intensity, etc. For large earthquake catastrophes, the accurate fault location will effectively improve the comprehensive processing ability of the earthquake early warning system and the intensity rapid reporting system for major earthquakes. In 2012, Bose proposed the finite fault identification rupture detector （short for FinDer）, which used image recognition and template matching techniques to calculate the rupture length and direction of large earthquakes （M_W＞6.0） in real time. In 2015, the FinDer method was used in the ShakeAlert system in California, USA. In 2018, Bose expanded the warning range of fault parameters and proposed the second-generation algorithm, namely FinDer 2. For earthquakes with M＞2.0, the peak ground acceleration （PGA） threshold was set based on the earthquake magnitudes in FinDer 2.

When a station data records exceed the set PGA threshold, the station is determined as a near-source station. By identifying the distribution range of near-source stations, the near-field area with strong ground motion is obtained, which is then matched with a pre-made template with fault direction and length. Here, the length and direction of the fault are calculated using the template with the highest matching degree.

The FinDer method has been running online in California for nearly ten years, and hence it provides a good demonstration for the discrimination of major earthquake faults in the earthquake early warning system, and provides a foundation for the construction of the large earthquake early warning system in the National Seismic Intensity Rapid Reporting and Early Warning project. What is more, through the construction of the national project, the current monitoring station network provides a favorable data support for the implementation of the FinDer method. In order to adapt to local site conditions and improve the calculation efficiency of the direction and length of fault rupture of major earthquakes, this study optimized the two steps: station property discrimination and template matching, and the details are as follows:

1） Select earthquakes with magnitude M4.0 or above that occurred in China from January 2022 to July 2023, as well as the 1999 M_L7.3 Chi-Chi and 2008 M_S8.0 Wenchuan earthquakes, and recount the initial thresholds corresponding to different magnitudes.

2） Perform an interpolation calculation on the distribution range of the near-source stations to determine the boundary of the surface rupture area of the fault: ① calculate the PGA value of each interpolation point every second; ② compare PGA of the interpolation points with the initial triggering threshold and determine the classification of the interpolation points; ③ determine the edge of rupture projection on the surface through the envelope of the near-source stations and the near-source interpolation points.

3） Select the minimum enclosing rectangle of the fault surface rupture edge as the optimal template and select the length and direction of the long side of the rectangle as the length and direction of the surface projection of the fault rupture so as to quickly obtain the length and direction of the fault rupture.

Taking the Chi-Chi M_L7.3 earthquake in Taiwan region in 1999 as an example, the real-time calculation process by FinDer method is introduced in detail. Then, the improved FinDer method is verified by six earthquakes of M4.5−8.0 in Chinese mainland. The verification results show that:

1） By selecting an appropriate PGA threshold, the calculated length of the fault will be around a reasonable theoretical value. For earthquakes with larger magnitude, especially those with M＞7.0, the calculation results are consistent with the field investigation results. For earthquakes with 4.5＜M＜5.5, the length and direction of rupture is calculated in an extremely short time, with a relatively short rupture length. Although the FinDer method can calculate direction, its accuracy is not high.

2） The calculation of fault direction and length is related to the distribution of the station network. When there are near-source stations around the fault, there are better constraints on the calculation of fault length. When the near-source stations around the fault are densely distributed, the accuracy of fault direction will be improved.

3） Based on the existing network conditions, the fault rupture calculations are generally completed within one minute after the first station is triggered, meeting the timeliness requirements of the earthquake early warning system. However, when a single earthquake causes multiple faults to rupture simultaneously, the FinDer method can only calculate the comprehensive rupture length and direction of multiple faults, but cannot calculate the rupture length and direction of multiple faults.