On August 6, 2023, an earthquake with M_S5.5 occurred in Pingyuan County, Dezhou City, Shandong Province, which is the largest earthquake in the Shandong region in the past 40 years. Before the earthquake, Shandong Earthquake Agency conducted biannual mobile gravity measurements near the epicenter, observed the spatiotemporal gravity field changes for the four years leading up to the earthquake, and made a certain degree of medium-term prediction, predicting that the epicenter location(36.00°N, 116.10°E)would be about 130km from the actual epicenter. This suggests that it is potentially feasible to carry out medium-term prediction of moderate earthquakes based on the temporal and spatial variations of the gravity field in the tectonically weak North China. Therefore, the study of the gravity changes before the 2023 Pingyuan M_S5.5 earthquake can help to deepen the understanding of the relationship between the time-space variations of the gravity field and the moderate earthquakes, enrich the database of “magnitude and gravity anomalies” in North China, and improve the science and accuracy of identifying and determining the medium- and long-term anomalies of earthquakes.

The mobile gravity data utilized in this paper were processed and calculated using the classical adjustment method in LGADJ software. This process involved corrections for earth tide, instrument height, monomial coefficient, air pressure, and zero drift, resulting in absolute gravity values for each measurement point. Eight absolute gravity points, including Jiaxiang, Tai'an, and Zibo, served as the starting reference points. The average accuracy of the observed data point values during each period ranged from 8.5 to 16.0μGal, indicating relatively high precision. Subsequently, the calculation results of the two data sets were subtracted to obtain the relative gravity change. This change was then interpolated on a continuous grid using the Surface module of GMT mapping software and subjected to 50-km low-pass filtering. Finally, the dynamic evolution image of the gravity field was generated.

Based on these results, this study analyzes the characteristics of regional gravity field changes since September 2019. These findings are integrated with information on deformation fields, seismic source mechanisms, and dynamic environments to explore the relationship between gravity changes before the earthquake and the seismic mechanism. The results indicate the following:

(1)Since May 2022, precursory anomalies have been detected in the gravity field changes around the epicenter. Between May 2022 and April 2023, there was a significant increase in positive gravity changes exceeding +50μGal and a spatial extent exceeding 160km in the south of the epicenter, with positive-negative differences exceeding 70μGal on both sides of the epicenter. However, the gravity changes near the epicentre remained stable and in a “locked” state. The magnitude, range, and duration of gravity changes before the earthquakes align with previously summarized indicators.

(2)Between September 2021 and September 2022, distinct four-quadrant distribution characteristics emerged in the regional gravity field changes. And the spatial distribution of regional gravity field changes corresponds to horizontal deformation fields, seismic source mechanisms, and coseismic displacement fields. Precisely, the compression zones of the seismic source mechanism and the inflow and subsidence areas of the coseismic displacement field correspond to regions of surface compression and gravity decrease before the earthquake. Similarly, the expansion zones of the seismic source mechanism and the outflow and uplift areas of the coseismic displacement field correspond to of surface expansion and gravity increase before the earthquake.

(3)The leading cause of the gravity changes anomaly before the Pingyuan M_S5.5 earthquake was the migration of deep-seated fluid materials, with the gravity effects generated by upper crustal deformation being a secondary factor. It is believed that the subduction of the Pacific Plate caused high-speed eastward migration of the relatively weak lower crust flow, dragging the upper crust eastward. The more rigid upper crust accumulated stress and strain during this process, developing numerous micro-fractures, while tectonic heterogeneity led to an east-west compression and north-south extension pattern. The fluid migration from compressed to expanded areas caused positive and negative differential changes in the gravitational field around the epicenter, culminating in the earthquake.

The rupture process of earthquake generally involves multiple fault activities. The seismogenic fault is generally not a single fault plane, but a combination of multiple fault planes. Based on the principle that clustered small earthquakes often occur near the fault plane, and assuming that the hypocenters obey three-dimensional normal distribution around the center of the sub-fault planes, the three-dimensional spatial structure of the Yangbi earthquake fault in Yunnan Province is estimated based on the fuzzy clustering algorithm. The results in this paper are estimated from the perspective of data analysis. The results will be more accurate if the comprehensive analysis can be carried out in combination with geological, geophysical exploration and other means. The fuzzy clustering analysis is mainly carried out for regions with dense seismic source data. Because the program compiled by this method runs fast on an ordinary computer and can be calculated many times in a short time, the best result can be obtained. In this study, the shape of fault zone can be quickly calculated and analyzed, the shape and spatial distribution of branch fault zone is roughly consistent with the seismic distribution, which verifies that this method has certain predictive effect and application value.
Firstly, GK(Gustafson, Kessel)fuzzy clustering method is used to obtain the partition matrix for all sub classes of hypocenter, then the outliers are removed by using the partition matrix and appropriate threshold, and the subclasses containing fault planes are extracted. Finally, the parameters of each fault plane(including position, strike and dip)with 95%confidence level are determined. It is inferred from the results that the hypocenters are distributed along the fault zone almost parallel to the Weixi-Qiaohou Fault and gradually divided into three fault branches to southeast direction. The east branch dips to southwest, which is the main fault, corresponding to two sub fault planes, with strike of 134.22°, 132.65°and dip angle of 87.14°, 81.96°, respectively; the west branch nearly parallels to the east branch with strike and dip of 129.45°and 74.77°, respectively. Except for the three main faults, a blind fault near the Weixi Qiaohou fault zone is identified in this study, with a strike of 235.66°and dip of 66.30°. In this study, we determined the fault structure of the Yunnan Yangbi earthquake sequence by fuzzy clustering algorithm, which is independent of other methods by using seismic wave data, geodetic data and geological data. It is of significance for tectonic and geodynamic studies.
This data analysis algorithm can be applied to the shape analysis and prediction of fault zone by a large number of such source data. In consideration of earthquake prediction and earthquake disaster assessment, the knowledge of fault network structure in the vicinity of large earthquakes will also help to test different assumptions about stress transfer effects.

Using seismic observation data of Shandong seismic network, we relocated 2 927 earthquakes(M_L≥0.2) recorded from Feb. 2017 to Apr. 2019 with double-difference algorithm in Changdao area. The fault plane parameters are calculated with 1 631 relocated earthquakes in the northern and southern earthquake swarms based on the simulated annealing and Gauss-Newtonian nonlinear inversion algorithms. There are two different earthquake swarms in both sides of 38°N. In order to distinguish the different earthquake swarms, we divide them into the northern earthquake swarm locating in the north of 38°N and starting from Feb. 2017, and the southern earthquake swarm locating in the south of 38°N and starting from Aug. 2017.
The stress field of Changdao area is inverted with 7 266 P wave polarities of 2 518 earthquakes in the swarms using the composite focal mechanism method. This method takes full advantage of all P wave polarities, thus avoiding the errors brought about by inverting focal mechanism with P wave polarities. The study region is divided into grids of 0.25°×0.25° before the stress field inversion for the northern and southern earthquake swarms. The rake on the fault plane of the northern and southern earthquake swarms is calculated using the stress field and fault plane parameters.
1 432 and 219 earthquakes are used to calculate the fault plane parameters for the northern and southern earthquake swarms, respectively. The result shows that the fault plane parameters are different between the northern and southern swarm. The strike, dip and rake of fault plane are 287.18°, 84.09° and -18.3° in the northern earthquake swarm, which is nearly the same with the previous results of shallow-depth acoustic reflection profiling. The fault plane parameters for the southern earthquake swarm are 269.67°, 67.46° and -3.6°. This result is similar to that of marine geophysical survey and the seismo-geological studies. The type of both fault planes is sinistral strike-slip according to the rake on the fault plane.
The stress field is inverted with a 50km radius smoothing in this paper. In general, the stress field calculated by this paper is basically identical with the previous results obtained by focal mechanism inversion and hydraulic fracturing in-situ stress measurement in Changdao area and is consistent with the stress field of the North China area. The stress field is controlled by pushing and subduction of the Pacific Plate from east to west. But there is a slight difference in the stress field between the northern and southern earthquake swarms. The compressive axis of stress field is rotated between the northern and the southern earthquake swarms. The stress field is in strike-slip regime in the northern earthquake swarm. The direction of P-axis is NEE-SWW, with a nearly horizontal plunge, and the direction of T-axis is NNW-SSE with a low plunge. In the southern earthquake swarm, the stress field is in a regime of normal faulting with a small amount of strike-slip component. The P axis is in NE-SW direction with plunges varying from 30° to 50°, and the T axis is the same as the northern swarm.
Based on the fault plane fitting, the seismogenic fault for the northern earthquake swarm is maybe the buried NW extension of the Dazhu Island-Weihaibei Fault, and the southern earthquake swarm occurred on a secondary EW-trending fault. According to the rakes of seismogenic faults, both of them are of strike-slip movement, and the stress field is in strike-slip regime in the northern earthquake swarm and normal with a small amount of strike-slip in the southern swarm. Both northern and southern earthquake swarms are controlled by the sinistral strike-slip Penglai-Weihaibei Fault, but the southern swarm is also under the influence of SN extension. We believe that the reason for the different fault plane parameters and stress fields is the different structure of the northern and southern earthquake swarms.

Based on the rupture models of the 2015 Nepal earthquake sequence and half space homogeneous elastic model, the displacement field near the epicenters is estimated. The horizontal components converge to the epicenters from north and south with maximum value of 871~962mm. The farther the epicenter distance is, the smaller of the horizontal displacement occurred. The displacement on the south side of the epicenters decreases more rapidly than that on the north side as the distance from the epicenter increased. Significant settlement occurred on the north side of the epicenters with maximum of 376~474mm, while large uplift occurred on the epicenters and its south side with maximum value of 626~677mm. Then, the displacement of the peaks of the Himalaya near the epicenters is estimated. The largest displacement occurred at the peak of Shishapangma with 393mm horizontal component and 36mm settlement. Mt. Everest, the world's highest peak, moves 36mm in nearly southward direction with 9mm settlement. The displacements of other peaks of the Himalaya are different with the epicentral distance and azimuth of the 2015 Nepal earthquake sequence.

A collapse happened in Pingyi County, Shandong Province, on December 25, 2015. The displacement field, stress field and Coulomb failure stress change on the Mengshan frontal fault generated by the collapse are calculated by using point collapse model in isotropic medium. The result shows that: (1) The maximum horizontal displacement is located at the center of the collapse with value of~18mm. The horizontal displacements are greater than 1mm within~5km of the collapse with its direction pointing to the collapse center. The maximum subsidence is located at the center of the collapse with the value of 4mm. The subsidence is greater than 1mm within ~3km of the collapse. The displacement field decays so rapidly that can be ignored at far away from the collapse for the shallow source, which caused local displacement field. (2) Influenced by the free surface, the contraction area stress within ~5km of the collapse with the order of 1000Pa and expansion area stress in farther away areas at depth of 2km are estimated. the expansion area stress of 1000Pa is estimated at the~5km from the collapse center. Then the expansion area stress decays to 100Pa at the distance of ~10km from the collapse. The maximum compressive and extensional principal stresses are estimated as 10000Pa at the depth of 2km. The compressive stress axes present radical direction pointing to the collapse within ~5km of the center. In farther away from the collapse, The extensional principal stress axes present radical direction pointing to the center of the collapse. With farther distance to the collapse, the compressive and extensional stress decay rapidly to the order of 100Pa. (3) The Coulomb failure stress on the northwestern part of the Mengshan frontal fault, which is known as active segment of the Mengshan frontal fault, is decreased by the collapse with maximum value of 2500Pa. Whereas, the Coulomb failure stress on the southeastern part of the Mengshan frontal fault, which is known as left-lateral normal slip fault segment in Quaternary period, is increased by the collapse with maximum of 2400Pa, to which attention would be paid in seismic hazard analysis.