Relation between Earth’s rotation and small earthquakes occurring before the <italic>M</italic>s7.8 Tangshan mainshock

Abstract

The focal region of a strong approaching earthquake can become very unstable, small and moderate-sized earthquakes could respond to tiny stress changes. In this study, we focused on the M s7.8 Tangshan mainshock (date of occurrence: July 28, 1976), which ruptured along the Tangshan fault in the Hebei Province, China, and investigate the correlation between the variations in rate of Earth’s rotation and the occurrence of earthquakes around the focal region before the occurrence of the M s7.8 Tangshan mainshock. More specifically, we associated the M L≥2.0 earthquakes occurring from January 1970 to June 1976 around the rupture zone of the M s7.8 Tangshan mainshock with the phases of the Earth’s rotation. We thus determined the signals that triggered the small earthquakes before the M s7.8 Tangshan mainshock. The procedure is briefly described below. From the time series of the seasonal changes in the Earth’s rotation rate, we assigned a phase angle of the Earth’s rotation to the occurrence time of each earthquake. We defined the phase angle as 0° at each maximum of rate of Earth’s rotation, −180°and 180° at the first minimum respectively on the left and right of the maximum. The phase angle (between −180 ° and 180 ° ) was assigned by 180 ° multiplying the time interval from the occurrence time of each earthquake to the maximum divided by the time interval from −180 ° to 0 ° (or from 0 ° to 180 ° ). The rate of Earth’s rotation increases for the phase angle from −180° to 0 ° , and decreases for that from 0° to 180 ° . After determining the phase angles for all the earthquakes, we statistically test whether they concentrate near some particular angle or not by using the Schuster’s test. The results of the test were evaluated by the P -values. Given N earthquakes, the P -value can be calculated by Equations (2) and (3) in the text. The P -value ranges between 0 and 1, and represents the significance level at which we reject the null hypothesis: that earthquakes are random events with no dependence on the phase angle of the Earth’s rotation. The smaller the P -value, the higher is the correlation between the Earth’s rotation and earthquake occurrence. Generally, a P -value below 5% can sufficiently judge a significant correlation: In this case, earthquakes are non-random events. Moving a two-year time window at 3-month intervals, we calculated the temporal evolution of the P -value for earthquakes with various magnitudes ( M L≥2.0, M L≥2.3 and M L≥2.5). For M L≥2.5 earthquakes occurring before the M s7.8 Tangshan mainshock, The P -values were below 1%. Eighty percent of the earthquakes with the lowest P -values occurred during the acceleration phase of the Earth’s rotation. Furthermore, by moving a spatial window of 2° ´ 2° by 0.2°-intervals in both the latitudinal and longitudinal directions, we resolved the spatial distribution of the P -value within a considerably large region (33°–44°N, 113°–122°E). Low- P -values (below 2%) were observed in the northeastern end region of the rupture zone of the M s7.8 Tangshan mainshock. The rupture start point of the M s7.8 Tangshan mainshock, located in the southwestern end region of the rupture zone, was relatively close to the low- P -value region. Low- P -values (below 2%) were also observed in the west of the Xingtai region of Hebei. Further analysis revealed that these low- P -values were related to an earthquake cluster occurring in October 1974. No conspicuous low- P -value (below 1%) regions in other parts of north China, except in the northeastern end region of the rupture zone of the M s7.8 Tangshan mainshock. Additionally, at the time of the M s7.8 Tangshan mainshock, the Earth’s rotation had just completed an approximately maximal seasonal acceleration. We conclude that the acceleration of the Earth’s rotation promoted the M s7.8 Tangshan mainshock.