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.

On April 25, 2015, a strong earthquake with magnitude 7.8(M_W)and focal depth of 8.2km(according to USGS)occurred in Nepal(28.15°N, 84.71°E), which caused heavy casualties and property losses to Nepal, China, and some neighboring countries. The focal mechanism solution shows that the earthquake is a low-angle thrust earthquake, resulting from the collision and following long-term compression between the Indian Plate and Eurasian Plate. In this paper, we analyze the magnetic disturbance characteristics before the Nepal M_W7.8 earthquake using polarization method based on the geomagnetic second data of 48 stations in mainland China.
Polarization method uses the ratio of the vertical component(Z)to the horizontal component(H)of the geomagnetic field, i.e. Z/H. This method can suppress external interference and thus extract seismo-magnetic anomaly information. Previous geophysical studies have shown that the perturbation in geomagnetic field during the earthquake preparation has a far greater impact on Z than H. The high polarization anomaly may contain some magnetic field information related to earthquake preparation. The calculation of geomagnetic second data includes three main parts: spectrum analysis, polarization calculation and abnormal signal extraction. The dominant frequency band(0.01~0.2Hz)is selected for subsequent calculation and analysis.
(1)By analyzing the relationship between the polarization and the perturbation in the geomagnetic field through spectrum analysis, we find that the polarization value at each stage is obviously negatively correlated with the geomagnetic K index, indicating that the high polarization anomaly is almost not related to the geomagnetic activity and therefore can be used to analyze the pre-seismic anomaly. In order to ensure the reliability of the calculation results, it is recommended that the data length should exceed 1 year, based on the annual variation characteristics of polarization value.
(2)The polarization value of the Lhasa station(epicentral distance of 628km)and the Shiquanhe station(epicentral distance of 652km)had risen for 3 days before the Nepal earthquake, and the anomaly amplitude of the Lhasa station, which is closer to the epicenter, is significantly higher than that of the Shiquanhe station. We analyze the polarization value of stations within 1 500km from the epicenter of the Nepal earthquake, which reveals a synchronous increase of polarization value starting about 98 days before the earthquake. Considering the regional synchronization of the perturbation in the geomagnetic field, a daily correlation analysis method is proposed to analyze the polarization of stations within 1 500km from the epicenter. We find that there is a significant increase in polarization correlation during earthquake preparation, and the earthquake occurred at the synchronization transition phase. It is suggested that the synchronization may be attributed to the additional effect of the source field associated with earthquake on the regional geomagnetic field. Certainly, this method requires higher data quality, and some certain interference factors need to be eliminated to reduce the influence of individual data on the overall results.
(3)The pre-seismic magnetic disturbance changes of each station are different in anomaly amplitude, which is associated with the spatial position, tectonic setting, and signal source of the abnormality. Subsequently, spatial analysis based on the relative variation of polarization value is necessary. The results show that continuous polarization anomalies exceeding 3 days before the earthquake occurred in more than 20% of stations, the spatial scope and abnormal amplitude experience a change trend from increasing to reducing, however, the spatial distribution of anomalies which has obvious regional characteristics always revolves around the epicenter. The time-space changing process of polarization anomalies really reflects the dynamic changes of the regional geomagnetic field, which is the result of external influence with strong dynamic characteristics. Plate movement is the main driving force of the perturbation in the regional geomagnetic field, while a large amount of melting fluid substances provide good channel for preparation and propagation of geomagnetic field. Thus, the generation and distribution of polarization anomalies are closely related to the geodynamic evolution of geological structures. Stress accumulation caused by geological activities is the main reason for the perturbation in the geomagnetic field.
(4)The study suggests that multiple synchronous polarization abnormality and turning in daily correlation have important indications for strong earthquakes, which will provide a new approach for monitoring and prediction. However, the quantitative relationship between anomaly amplitude and epicentral distance is not obvious, which is affected by tectonic environment of station, seismogenic background, complexity of changes of spatial geomagnetic field and fewer seismic examples. Therefore, in order to obtain more evidence and improve reliability, more seismic examples and theoretical analysis is necessary.

Four-component borehole strainmeter (FCBS) is one kind of high-precision borehole strain observation instruments invented in China. As a kind of near-surface deformation observation instrument, FCBS is also easily disturbed by the external environment factors. As a common factor, pumping has significant influence on FCBS observation. Existing studies mostly identify the pumping interference from the perspective of observation curve morphology, relatively few studies focus on its interference mechanism. In order to truly capture earthquake precursor information, it is necessary to study the interference mechanism. In recent years, RZB-3 type FCBS at Tai'an seismic station has been seriously affected by pumping, so it is necessary and also feasible to study the interference mechanism of pumping. Since the influence of pumping interference on borehole strainmeter is common, this work would be very practical and be used for reference by other borehole strain observation stations.
We find that the original observation curves and observed surface strain, shear strain from RZB-3 type FCBS at Tai'an seismic station have the characteristics of synchronous change with the borehole water level, in which the linear correlation coefficient between the two observed shear strain curves and borehole water level reached 0.70 and 0.82 respectively. We further find that the principal strain direction of borehole and borehole water level after normalization meet the nonlinear function as y=1.217arctan(x)^0.224-0.284. The above phenomenon indicates that the observation of RZB-3 type FCBS at Tai'an seismic station is significantly affected by the borehole water level, and the influence is more obvious and the gradient is larger at the stage of low water level. Pumping interference often appears in low water level stage and changes the rock pore pressure state. Statistics show that pumping interference affects the borehole strain state.
To investigate the interference mechanism of pumping to RZB-3 type FCBS at Tai'an seismic station, we take a known pumping as an example, in which we study the principal strain state of the borehole in three periods of normal pumping, interruption of pumping and resuming pumping respectively. During each period, we solve 3 parameters of the principal plane strain state, i.e. the maximum principal strain rate, the minimum principal strain rate and the maximum principal strain direction from four observation equations of FCBS by nonlinear iterative least squares algorithm. On the other hand, concentrated load model (CLM) is used to simulate the mechanical mechanism of pumping. Firstly, the depth of FCBS relative to pumping source and the concentrated load at pumping source are inversed, then, the strain state surrounding the pumping well, including the state at RZB-3 borehole, is simulated by forward modeling. By comparing these results, we find that:
(1)The concentrated load at pumping source inversed by CLM during periods of normal pumping and resuming pumping are both located at or near the bottom of the pumping well, which is consistent with the actual situation, indicating that mechanism and degree of the influence of pumping on borehole strain are well simulated by CLM.
(2)The observed strain state is consistent with the simulation result of pumping interference by forward modeling, indicating that the principal strain state of borehole calculated based on observation of FCBS reflects the true strain state of borehole under different pumping states.(3)The inversed concentrated load at pumping source during pumping periods is significant greater than the load of the pumped water, indicating that the pumping process has more significant influence on the pore pressure of rocks than the load of the pumped water.
Even though CLM is an approximate simulation since it's based on some elastic assumptions, the interference mechanism of pumping on RZB-3 type FCBS at Tai'an seismic station is well explained, which is maybe very helpful for studying the influence of pumping interference on other deformation instruments, locating the unknown pumping source and studying the characteristics of pore pressure of rocks.

Following the 11 March 2011 Japan M_W9.0 earthquake, frequent moderate and small events occurred on the Yishu fault zone and its either side. Using continuous GPS data and a sliding block model, this work studies the relationship between the energy release of these shocks and the block relative motion of either side of the Yishu fault zone. The results show that(1)the equivalent magnitude M from released energy and the two blocks' relative motion are well correlated when earthquakes are selected in a retrieval circle(whose center is the midpoint of the Yishu fault zone)with a radius of 250~500km and using a sliding time window of 3~10 months. The best correlation coefficient between M and the two blocks' relative motion is 0.74 and the T test shows a significant linear correlation between them.(2)Spatial distribution of the correlation coefficients shows that the relative motion of the blocks on both sides affects the energy release in the area from the north part of Yishu fault zone to the Jiaodong Peninsula area and southwest Shandong-Henan border area obviously.(3)Since June 2014, the relative motion of the two blocks on both sides of the Yishu fault zone presents a wave of change, which may be an expression of the accumulation of seismic strain energy in the Yishu fault zone and its two sides. The linear relationship between the equivalent magnitude M from released energy and two blocks' relative motion V can be fitted by linear equation M=0.51*V+3.9, showing that strain energy accumulation could be released by the moderate and small earthquakes in a timely manner, which may favorable to delay the seismic risk in the study area. It also shows, on the other hand, that earthquake energy was not released so completely in the study area since the end of 2015 to 2016, which is likely associated with the Changdao earthquake swarm in 2017.