The magnitude of the Sanhe-Pinggu earthquake based on the multi-rupture method

The 1679 Sanhe-Pinggu earthquake is the largest earthquake ever recorded in the history of the Beijing-Tianjin-Hebei region, causing severe damage. But the surface rupture length and related deformation characteristics from a series of studies do not match the defined M_W8.0. Therefore, this article, building upon previous research, simulates the strong ground motion of the Sanhe-Pinggu earthquake using the multi-rupture and multi-focal set method, aiming to study its magnitude and ultimately determine the true magnitude of the Sanhe-Pinggu earthquake.　　The method employed in this paper is the NNSIM （non-negative source-specific impulse modeling） random finite fault method, drawing inspiration from traditional random finite fault methods. It divides the main fault into N sub-faults that can be considered as point sources. Under the influence of rupture delay and propagation delay, the simulation results for each sub-fault are superimposed to obtain the seismic effects of the entire fault. The paper also provides a detailed explanation of the role of time window functions in the low-frequency domain. In this approach, we use this method to make the low-frequency component of the simulated seismic effects closer to the actual records, thereby enhancing the reliability of the simulation results across the entire frequency spectrum.　　 The Sanhe-Pinggu earthquake occurred on the Xiaodian fault. Building upon previous research, we selected the middle section of the Xiadian Fault as the study area, with a total length of approximately 80 km and a width of 25 km. We divided the magnitude range from M_W7.5 to M_W8.0 into six magnitude levels with an increment of 0.1, and each magnitude level was simulated using multiple source and multiple rupture scenarios.Considering that the Sanhe-Pinggu earthquake is a historically significant event in the North China region, we incorporated two fault asperities in our simulation. According to our setup criteria and the distribution of slip for each rupture mode, we calculated corresponding stress drop distributions, rupture velocity distributions, rise time distributions, and different source functions, which can generate complex earthquake source models. Our calculations revealed that there are primarily two rupture points along the fault, one at around 20 km and the other at around 60 km, with the rupture at 20 km being more intense. The initial rupture times for the fault are concentrated between 0.02 s and 0.05 s, with a maximum duration of up to 22 s. The resulting seismic moment is approximately 7×10²⁵ N·m, and the maximum stress drop occurs near 8 MPa. These four distributions represent the seismic source parameters required for the NNSIM simulation method used in this study. Based on these seismic source parameters, we conducted simulations of strong ground motions under multiple rupture scenarios.　　 In order to determine the magnitude of the Sanhe-Pinggu earthquake, we first converted the historical intensity curves Ⅸ, Ⅹ, and Ⅺ into peak ground acceleration （PGA） and peak ground velocity （PGV） values according to GB/T 17742−2020 （Chinese Seismic Intensity Scale）. Specifically, intensity Ⅸ corresponds to 402 cm/s², intensity Ⅹ corresponds to 831 cm/s², and intensity Ⅺ corresponds to 1730 cm/s². Each intensity curve was sampled at approximately 50 points. Based on the principle that the maximum fault asperity is located southwest of the macroscopic epicenter, we constrained the position of the maximum fault asperity to be in the southwest of the macroscopic epicenter. Through calculations in the seismic source setup section, we identified a total of 180 rupture scenarios that satisfied this constraint. We then used the NNSIM method to compute the acceleration, velocity, PGA, and PGV values at comparison reference points. By evaluating the differences between the simulated and converted PGA and PGV values, we defined two parameters, R and S, to reflect the disparities between the acceleration, velocity, PGA, and PGV at reference points and historical intensity values.From these differences, it was determined that the simulated PGA and PGV values for M_W7.8 exhibited the smallest discrepancies with historical intensity values, followed by M_W7.9, while M_W8.0 showed relatively larger discrepancies. 　　 For the purpose of conducting a detailed comparative analysis of the spatial distribution of simulated ground motion for earthquakes with magnitudes M_W7.8, M_W7.9, and M_W8.0, we utilized 180 different rupture scenarios corresponding to these three magnitudes. We simulated strong ground motions for each of these scenarios and plotted intensity curves corresponding to intensities Ⅸ, Ⅹ, and Ⅺ.From the four intensity curves for M_W7.8, it can be observed that the Ⅸ and Ⅹ intensity curves closely matched historical intensity curves. However, the M_W7.8 scenarios almost did not generate Ⅺ intensity, indicating that within the seismogenic area, M_W7.8 is insufficient to produce ground motions with a PGA exceeding 1730 cm/s². For the M_W7.9 earthquake, the Ⅸ and Ⅹ intensity ranges exceeded the corresponding historical intensity circles, while the spatial range of the Ⅺ intensity circle closely resembled that of the historical intensity circle, but it was slightly shifted to the south.In the case of the M_W8.0 earthquake, the intensity ranges for all three intensities were much larger than the historical intensity circles. The Ⅺ and Ⅹ intensities were similar in size to historical Ⅹ and Ⅸ intensities, but the Ⅸ intensity extended far beyond the historical Ⅸ intensity range. This suggests that the rupture generated by the M_W8.0 earthquake is significantly more powerful than what historical records indicate. In conclusion, the magnitude of the Sanhe-Pinggu earthquake should be less than M_W8.0, greater than M_W7.8, and close to M_W7.9. It is likely to be an earthquake with a magnitude around M_W7.8＋ ＋ or even M_W7.9−.