Synthetic seismic intensity for historic earthquakes in the North China Plain: implications for the regional seismic hazard

Abstract

Multiple approaches are used to study the potential seismic hazard in the North China Craton (NCC, or North China Plain), where approximately 15 % of the Chinese population resides and under which active faults are located. In this study, we develop a new modified Mercalli intensity (MMI) attenuation relationship for the NCC using intensity data from 10 instrumentally recorded events. We then utilize this relationship to infer the magnitude and epicentral location of historic events based on the method proposed by Bakun and Wentworth (Bull Seismol Soc Am 87(6):1502–1521, 1997). In addition, a modified stochastic finite fault model is employed to simulate the strong ground motions caused by these historic events. The simulated peak ground accelerations and velocities are then converted into regional MMI distributions through empirical relationships, and these synthetic MMI maps are compared to field observations. The resultant MMI attenuation versus distance models of the 1976 M _w 7.6 Tangshan event and the 1679 M 8.0 Sanhe-Pinggu event are consistent with the empirical attenuation relationships, and the location and size of the meizoseismal area (>VIII) are consistent with observations. The successful modeling of these historic events indicates that a stochastic finite fault model constrained by the regional MMI attenuation relationship can be used to evaluate a wide range of scenarios based on modern computational simulations. These findings may also provide useful information for the estimation and mitigation of potential seismic hazards in this region.

Appendix

1.1 Methods

We use the method of Bakun and Wentworth (1997) to analyze the intensities assignments using a previously derived attenuation relationship. For each earthquake, we calculate the intensity magnitude, M _I, and the rms[M _I] over a grid of trial epicenter locations. The following attenuation relationships are used in this study to determine the historical earthquake magnitudes and locations:

$$M_{i} = {{\left( {{\text{In}}_{i} - 1.72 + 0.000447*\varDelta_{i} + 2.72*\log_{10} \varDelta_{i} } \right)} \mathord{\left/ {\vphantom {{\left( {{\text{In}}_{i} - 1.72 + 0.000447*\varDelta_{i} + 2.72*\log_{10} \varDelta_{i} } \right)} {1.38}}} \right. \kern-0pt} {1.38}}\quad {\text{and}}$$

(5)

$$M_{I} = {\text{mean}}\left( {M_{i} } \right)\quad \left( {i = 1,2, \cdots ,n} \right),$$

(6)

where In_i and Δ _i are the intensity value and the distance (km) between the intensity (MMI) observation location and the epicenter at site i, respectively, M _i is the magnitude estimated from Eq. (2), and M _I is the mean magnitude at the trial epicenter. The rms is defined as follows:

$${\text{rms}}(M_{I} - M_{i} ) = \sqrt {\frac{{\sum\nolimits_{i} {W_{i}^{2} \times \left( {M_{I} - M_{i} } \right)_{i}^{2} } }}{{\sum\nolimits_{i} {W_{i}^{2} } }}\quad {\text{and}}}$$

(7)

$${\text{rms}}\left[ {M_{I} } \right] = {\text{rms}}(M_{I} - M_{i} ) - {\text{rms}}_{0} (M_{I} - M_{i} ),$$

(8)

where ${\text{rms}}_{0} (M_{I} - M_{i} )$ is the minimum ${\text{rms}}(M_{I} - M_{i} )$ over the grid of trial epicenters and W _i is Bakun and Wentwoth’s (1997) distance weighting function, defined as follows:

$$W_{i} = \left\{ {\begin{array}{*{20}c} {a + \cos \left( {\frac{{\varDelta_{i} }}{b} \times \frac{\pi }{2}} \right)\quad \varDelta_{i} < b} \\ {a \quad \quad \varDelta_{i} > b} \\ \end{array} ,} \right.$$

(9)

where a is the “water level” and b is the cutoff distance in km. Bakun and Wentworth (1997) noted that the “water level” and cutoff distance chosen for the weighting function are arbitrary. However, our calculation indicates that if the b value is above 400 km, a better closure of rms[M _I] contours is obtained. The contours of rms[M _I] bound the epicentral region and are associated with different levels of confidence of the epicenter location. M _I values at tectonically active trial epicenters within the appropriate confidence level contours give the best estimates of magnitude for those epicenters.

1.2 Case studies

The strategy suggested above was tested for two pre-1900 earthquakes, the 1668 Tancheng earthquake and the 1679 Sanhe-Pinggu earthquake, and two instrumental earthquakes, the 1966 Longyao earthquake and the 1969 Bohai earthquake.

1.2.1 The 1668 Tancheng earthquake

This earthquake occurred on 25 July 1668 and is generally considered the largest recorded earthquake in China. The magnitude is estimated to be 8.5, and the estimated epicenter is 35.3°N and 118.6°E. We chose 118 intensity values to bound the epicentral region and to calculate the magnitude. Figure 6 shows a map of the rms[M _I] and M _I (b = 480 km). In Fig. 6, the innermost, middle, and outermost contours of rms[M _I] correspond to the 50, 80, and 95 % confidence levels for the location, respectively, and M _I is 8.8.

Fig. 6

Map of contours of rms[M _I] as colored areas and M _I as dashed lines for 1668 Tancheng earthquake. Total number of intensity assignment sites we used is 118, and round dots are part of them. The triangle is the estimated epicenter (118.6°E, 35.3°N), located within the 50 % confidence region, where M _I is 8.8

1.2.2 The 1679 Sanhe-Pinggu earthquake

This earthquake occurred on 2 September 1679; the intensity value was XI in the meizoseismal area. The magnitude is estimated to be 8.0, and the estimated epicenter is 40.0°N and 117.0°E, as reported by another study. Figure 7 shows a map of the rms[M _I] and M _I (b = 1,000 km). The estimated epicenter (117.0°E, 40.0°N) is located within the 90 % confidence region, where M _I is 7.8.

Fig. 7

Map of contours of rms[M _I] as colored areas and M _I as dashed lines for 1679 Sanhe-Pinggu earthquake. Total number of intensity assignment sites we used is 225, and round dots are part of them. The triangle is the estimated epicenter (117.0°E, 40.0°N), located within the 90 % confidence region, where M _I is 7.8

1.2.3 The 1966 Longyao earthquake

This earthquake occurred on 8 March 1966. The surface magnitude was 6.8, and the instrumental epicenter was 37.4°N and 114.9°E. Figure 8 shows a map of the rms[M _I] and M _I (b = 480 km). The epicenter is located within the 67 % confidence region, where M _I is 7.1.

Fig. 8

Map of contours of rms[M _I] as colored areas and M _I as dashed lines for 1966 Longyao earthquake. Total number of intensity assignments sites we used is 130, and round dots are part of them. The triangle is the instrumental epicenter (114.9°E, 37.4°N), located within the 67 % confidence region, where M _I is 7.1

1.2.4 The 1969 Bohai earthquake

This earthquake occurred on 18 July 1969. The instrument-observed magnitude was 7.4, and the instrumental epicenter was 38.2°N and 119.4°E, inside the Bohai Sea; the intensity value of the meizoseismal area is unknown. Figure 9 shows a map of the rms[M _I] and M _I (b = 400 km). The epicenter is located within the 80 % confidence region, where M _I is 6.9.

Fig. 9

Map of contours of rms[M _I] as colored areas and M _I as dashed lines for 1969 Bohai earthquake. Total number of intensity assignments sites we used is 125, and round dots are part of them. The triangle is the instrumental epicenter (119.4°E, 38.2°N), located within the 90 % confidence region, where M _I is 6.9