Using the gravity observation data of Mulanshan short gravity baseline field in 2018 and 2022, we established a high-precision short gravity baseline field of Mulanshan based on the relative gravity joint measurement method under the control of absolute gravity. We also analyzed and discussed the accurate calibration of the monomial coefficient of the relative gravimeter during the construction of the gravity short baseline field, the distribution of gravity values in the gravity baseline field of Mulanshan and the contribution of various environmental factors in the gravity variation results, these results show that:

(1)Maximum gravity segment difference of Mulanshan calibration baseline is 102.176mGal from G01 to G03 stations, and the average accuracy of gravity value of each measuring station reaches 4.8μGal. The geological structure of the Mulanshan baseline is stable, and the gravity change of measuring stations is not obvious. From 2018 to 2022, the gravity variation range of measuring stations was 5.9~12.8μGal, with an average of 9.5μGal, and the average uncertainty was ±5.7μGal. The gravity field mainly showed a positive change. The variation range of gravity in each measurement section is -4.8~6.9μGal, with an average of(1.8±8.6)μGal. The change of the surrounding environment has a certain impact on the gravity field, and the contribution of the new buildings near the G01 and G02 to the gravity change is 3.6μGal and -0.51μGal, respectively. These gravity changes of measuring stations in the IOS and Mulanshan baseline caused by vertical surface movement are(2.17±0.44)μGal and(1.67±0.45)μGal. The gravity effect caused by the change of surface water storage is(1.07±0.84)μGal, which cannot be ignored. Compared with observation results, the gravity change of each measuring station and section after correction is reduced, and the average gravity change values are reduced by 38.2% and 50.8%, respectively. The corrected gravity change results are more accurate. Due to the cumulative effect of errors in the correction process, the uncertainty of gravity change results after correction increases accordingly, and the uncertainty of gravity change results of measuring station and measuring section increases by 2.5% and 2.8%compared with observation results, respectively. Combined with the gravity change results of the measuring station and the measuring section, we can effectively extract abnormal information in gravity dynamic change results.

(2)There are differences in monomial coefficients of different gravity sections of the relative gravimeter. The results of CG-6 and CG-5 relative gravimeters are relatively consistent, and there is no systematic deviation between the two gravimeters. The difference in the monomial coefficient between the Wuhan-Yichang section(sub-section)and the Wuhan-Lücongpo section(total section)is 4.809‰, which has a great influence on the gravity observation results. The monomial coefficient needs to be accurately measured. The difference of the monomial coefficient in the sub-section is negatively correlated with the proportion of the gravity segment difference in the sub-section to the total section; the monomial coefficient of the total section is a weighted average result of each sub-section, and the proportion of gravity segment difference in sub-section to total section is the corresponding weight factor. Accurate calibration of the monomial coefficient of the relative gravimeter is a technical guarantee to obtaining high-precision gravity observation results. The gravity segment difference of sub-segments cannot cover the gravity range of the measurement area due to smaller segment difference, which will lead to the extrapolation of the monomial coefficient, so it cannot effectively calibrate the monomial coefficient of the relative gravimeter applicable to the whole measurement area. The total section can cover the gravity range of the measurement area, and the monomial coefficient is the ratio between the segment difference measured by the relative gravimeter and the known segment difference, and its calibration accuracy is inversely proportional to the gravity segment difference, so when using the total section as a reference for calibration of the monomial coefficient of the relative gravimeter, accuracy of the calibration can be guaranteed and precision of the calibration can be improved, so calibration result of the monomial coefficient using the total section is more accurate. The existing widely used relative gravimeters(such as LCR, CG-5, BURRIS, CG-6, and so on)have time-varying characteristics of the monomial coefficient, weakening the errors caused by changes of the monomial coefficient is essential to improve the accuracy of observations, and corresponding calibration is required before each period of gravity observation. The monomial coefficient of the relative gravimeters needs to be calibrated using a large segment difference, and the segment difference(or the accumulated segment difference)should be greater than 300mGal.

The gravity inversion results of three-dimensional density interface are often not unique, which brings some difficulties to further scientific research. The classical particle swarm optimization algorithm has a higher global extremum search ability, faster inversion speed in computing high-dimensional nonlinear inversion problems, and the final solution is independent of the initial model compared with traditional inversion density interface algorithms such as L-M, Tikhonov regularization, Gauss-Newton method, etc. However, in classical particle swarm optimization, the initial model setting and parameter selection are not perfect. Therefore, this paper further enhances the algorithm based on the classical particle swarm optimization algorithm, referring to the previous optimization ideas. The test results of various models show that the optimized particle swarm optimization algorithm has a stable ability to search for the optimal global solution, and the depth error is smaller. In addition, if we adopt parallel computing, the inversion speed can be effectively improved.

We obtained the Indosinian density interface depth model of the Changning area by inversion using multiple measured high-density gravity profile data based on the improved algorithm. The overall scope of the survey area is small and diamond-shaped, including the complete Changning-Shuanghe anticline and some surrounding synclines. The inversion results show that the Indosinian density interface generally presents the characteristics of uplift in the middle and depressions around it, and the depth range is 0.3~3.3km, which is basically consistent with the inversion results of the drilling data and previous gravity data, and the details are more prominent. It can better express its structural characteristics. The depression degree of the interface on the right side is significantly larger than that on the left side. The uplift part corresponds to the Changning-Shuanghe complex large anticline, and the depth varies from 0.3km to 1.9km. The core of the anticline is exposed to the surface by uplifting and erosion of the tectonic movement. The inversion result provides essential information for studying the seismotectonic environment and is also a vital reference for studying the multi-layer density interface model.

Density interface fluctuation is the product and sign of a specific area under the action of multi-stage tectonic movement, which plays an essential role in studying basin basement, regional structure, and deep structural fluctuation. It provides critical information for the analysis of the origin of earthquakes. Therefore, we analyzed the structural characteristics of this area and its relationship with earthquakes combined with the undulating morphology of the Indosinian surface. Earthquakes in the Changning area are concentrated on the north and south sides of the large anticline. The seismic distribution pattern and focal parameters on both sides are obviously different. The main reason for this phenomenon is that there are significant differences in the causes of earthquakes. The Indosinian surface in the north wing of the anticline is steeper than that in the south wing. The location of the strip distributed shallow earthquakes in the north wing is highly related to the fluctuation of the Indosinian surface, and they mainly occur at the places where the Indosinian surface fluctuates violently. The local density changes drastically, and the earthquakes’ occurrence is greatly affected by hidden faults. The clumped distributed shallow earthquakes in the south wing occur at locations where there is an apparent depression on the Indosinian surface, which may be caused by shale gas exploitation, and the earthquakes are more affected by local stress changes. Deep earthquakes may be closely related to the revival of basement faults. There may still be seismic risk in the northeast wing of the large anticline in the future.

In general, the optimized particle swarm algorithm has achieved good results in both model testing and practical applications. In order to further improve the accuracy of the inversion results, we will focus on improving the applicability of the algorithm in various situations and the ways of adding multiple constraint information. More detailed geophysical research should be carried out in this area, which will help to better understand its crustal structure, earthquake mechanism, geological structure, and the development of earthquake prevention and disaster reduction.

Results of surface geological survey and deep geophysical exploration indicate that there are significant lateral differences in the crustal structure and deformation of the northern and middle sections of the Red River fault zone. In order to detect the current material migration and deformation characteristics in the crust along the Red River fault zone, we analyzed and removed the gravity changes caused by vertical surface movement, surface water circulation, denudation, and glacial isostatic adjustment effects based on mobile gravity observation data of 3 profiles in the northern and middle section of the Red River fault zone from 2013 to 2019, and obtained the trend of gravity change caused by the migration of materials in the deep crust. Based on recent gravity changes and crustal structure models, the deformation characteristics of Moho surface along the northern, middle, and middle-southern sections of the Red River fault zone are inverted. The results of the study are as follows:
(1)Average gravity change caused by vertical crustal movement is(-0.11±0.21)μGal/a, (0.22±0.21)μGal/a and(0.16±0.21)μGal/a in the northern, middle and middle-southern sections of the Red River fault zone, respectively. The surface crust of the Red River fault zone and its adjacent areas uplifts globally with a rate of((0.92±1.17)mm/a), which is identical to the background trend of uplift of Qinghai-Tibet plateau. Gravity change caused by the surface water reserves cannot be ignored, and the magnitude of the change is -10~10μGal. Gravity change trends on both sides of the Red River fault zone are accordant, but differences in the middle section are higher than that in the northern section.
(2)Recent gravity change of the Red River fault zone has segmental characteristics: The northern section of the Red River fault zone shows a negative gravity change trend with a rate of(-0.39±1.30)μGal/a. Bounded by the Red River fault zone, gravity change in northeastern side of the northern section of the Red River fault zone is negative, while the southwestern side shows positive change, with a gravity change rate increasing with(3.1±0.55)μGal/a·100km relative to the northeastern side, reflecting the constant mass accumulation in the process of deep material flow after crossing the Red River fault zone and then blocked by the Lancan River rigid block under the background of eastward material flow in the Qinghai-Tibet Plateau. Gravity change in the middle section of the Red River fault zone is(0.16±1.57)μGal/a, indicating a low-speed positive change trend. Gravity change in the middle Red River fault zone is lower than that in both sides, which reflects deep boundary control of the Red River fault zone. Recent gravity change rate gradually decreases with(-1.01±0.58)μGal/a·100km from the southwest to the northeast, which indicates more mass accumulation in the northeastern side. Middle-southern section of the Red River fault zone is the junction area between the IndoChina/Sichuan-Yunnan rhomboid and South China block, its positive gravity change trend(with(0.29±1.25)μGal/a on average)reflects the characteristics of mutual lateral compression and material accumulation between blocks. Magnitude of gravity change in northeastern Red River fault zone is greater than that in southwest. Gravity change decreases from southwest to northeast with an average rate of(-0.21±0.48)μGal/ a·100km.
(3)Combining the results of gravity changes caused by deep crustal material migration and Moho density interface model, we can get the recent Moho deformation information. Results indicates that depth of the Moho is generally increasing from southeast(about 36km)to northwest(about 50km), with the Red River fault zone as the boundary. Moho depth in the eastern side is generally deeper than that of the western side, and crustal structure on both sides of the Red River fault zone has significant lateral difference. Moho beneath the Red River fault zone uplifts continuously with an average rate of 0.54cm/a in recent period. Average deformation rate of the northern, middle, and middle-southern section of the Red River fault zone is -0.06cm/a, 1.36cm/a and 0.32cm/a, reflecting the effect of regional unbalanced tectonic movement to a certain extent. Moho beneath the northern section changes gradually from sinking to uplift from northeast to southwest. Moho of the middle section shows uplift in the northeast and sinking in the southwest. The middle-southern section's deformation rate is lower than that in the northern and middle-southern section, and the difference is small between the two sides. Deformation rate in the Red River fault zone is significantly lower than that in its both sides, which shows a strong boundary control effect on deep crustal deformation. The results can not only provide new constraint for fault activity study of the southeastern margin of Tibetan plateau, but also provide evidence to the study of strong earthquake preparation background in the northern and middle section of the Red River fault zone.

The Yangbi M_S6.4 earthquake in Yunnan Province and Maduo M_S7.4 earthquake in Qinghai Province occurred in western China on May 21 and May 22, 2021, respectively, which caused huge loss of life and property. Gravity changes in the epicentral area and its surroundings before the two earthquakes can provide important reference for studying the seismogenic environment and background. The ground gravity observation is relatively sparse in western China and satellite gravity can supplement this deficiency. GRACE(Gravity Recovery and Climate Experiment)(from March 2002 to June 2017)and GRACE-FO(GRACE Follow-on)(from May 2018 to March 2021)can produce the wide-area space, quasi-real-time, long-term and near-continuous observation data, which will provide large-scale background information for the ground gravity research.

In this paper, the epicenters of the two earthquakes and their surrounding area were taken as the study area(18°~45°N, 83°~115°E). We used GRACE, GRACE-FO and GLDAS(Global Land Data Assimilation System)data to calculate long-term gravity spatial-temporal distribution in the study area with 300km fan filter. We presented the gravity rate, cumulative gravity changes, differential gravity changes in the study area for about 20 years, and the gravity time series of Maduo earthquake and Yangbi earthquake. We simulated the theoretical co-seismic gravity variation of Maduo earthquake and evaluated the possibility of detecting the co-seismic gravity signal for GRACE-FO. The research results showed that:

(1)Long-term gravity changes in the study area were mainly characterized by positive-negative-positive-negative spatial layout in four quadrants. Gravity increased in Qinghai-Tibet block and South China block, and gravity decreased in Indian block and North China block. However, the North-South seismic belt and Bayankala block were located at the low-value areas in four quadrants and their gravity changes were relatively small. This was the large-scale gravity seismogenic background in western China.

(2)The epicenters of Maduo earthquake and Yangbi earthquake were both located in the center of the four quadrants and also at the corner of the high gradient zone of satellite gravity change. And their gravity changes were very small in the last 20 years, which was consistent with the basic characteristics of the ground gravity location prediction. After a year of continuous increase in the last two years before the Maduo earthquake, the gravity in Maduo area experienced a four-month period of decrease, then it increased again. This was similar to the process of gravity change before the Tangshan earthquake.

(3)M_S≥7.0 Earthquakes in the study area since 2002, such as Wenchuan M_S8.0 earthquake, Yushu M_S7.1 earthquake, Lushan M_S7.0 earthquake, Jiuzhaigou M_S7.0 earthquake, Maduo M_S7.4 earthquake and Nepal M_S8.1 earthquake, basically occurred in the central area of the four quadrants or at the corner of the tectonic-related high gradient zone, which was consistent with the earthquake case results of earthquake prediction based on the ground gravity observations. This study provided more earthquake cases for ground gravity prediction.

(4)Based on dislocation theory simulation, the magnitude of co-seismic gravity change of Maduo earthquake in Qinghai Province reached -40~151μGal. It is difficult for GRACE-FO to detect the co-seismic gravity change of Maduo earthquake with the current accuracy. And it could be possible only when the time-variable gravity accuracy of gravity satellite was improved by 1-2 orders of magnitude. This research provided earthquake case supports for the demand demonstration of gravity satellites in China in the future.

In this study, the temporal and spatial evolution of gravity in the western region of China and its surrounding areas from March 2002 to March 2021, which coverd the epicenters of Yangbi and Maduo earthquakes, was obtained by using the satellite gravity and global hydrological data after considering the influence of periodic signals. The theoretical coseismic effects of the Maduo earthquake on the local gravity field were analyzed and the accuracy of gravity satellite to detect this seismic signal was evaluated. This study provided the important background information of large-scale gravity field for the study of Maduo earthquake in Qinghai Province and Yangbi earthquake in Yunnan Province, and also provided valuable material for the seismic demand analysis of gravity satellite in China.

Using the fault model issued by the USGS, and based on the dislocation theory and local crust-upper-mantle model layered by average wave velocity, the co-seismic and post-seismic deformation and gravity change caused by the 2021 Maduo M_S7.4 earthquake in an elastic-viscoelastic layered half space are simulated. The simulation results indicate that: the co-seismic deformation and gravity change show that the earthquake fault is characterized by left-lateral strike-slip with normal faulting. The changes are concentrated mainly in 50km around the projection area of the fault on the surface and rapidly attenuate to both sides of the fault, with the largest deformation over 1 000mm on horizontal displacement, 750mm on the vertical displacement, and 150μGal on gravity change. The horizontal displacement in the far field(beyond 150km from the fault)is generally less than 10mm, and attenuates outward slowly. The vertical displacement and gravity change patterns show a certain negative correlation with a butterfly-shaped positive and negative symmetrical four-quadrant distribution. Their attenuation rate is obviously larger than the horizontal displacement, and the value is generally less than 2mm and 1 micro-gal. The post-seismic effects emerge gradually and increase continuously with time, similar to the coseismic effects and showing an increasing trend of inheritance obviously. The post-seismic viscoelastic relaxation effects can influence a much larger area than the co-seismic effect, and the effects during the 400 years after the earthquake in the near-field area will be less than twice of the co-seismic effects, but in the far-field it is more than 3 times. The viscoelastic relaxation effects on the horizontal displacement, vertical displacement and gravity change can reach to 100mm, 130mm and 30 micro-gal, respectively. The co-seismic extremum is mainly concentrated on both sides of the fault, while the post-earthquake viscoelastic relaxation effects are 50km from the fault, the two effects do not coincide with each other. The post-seismic horizontal displacement keeps increasing or decreasing with time, while the vertical displacement and gravity changes are relatively complex, which show an inherited increase relative to the co-seismic effects in the near-field within 5 years after the earthquake, then followed by reverse-trend adjustment, while in the far-field, they are just the opposite, with reverse-trend adjustment first, and then the inherited increase. The horizontal displacement will almost be stable after 100 years, while the viscoelastic effects on the vertical displacement and gravity changes will continue to 300 years after the earthquake. Compared with the GNSS observation results, we can find that the observed and simulated results are basically consistent in vector direction and magnitude, and the consistency is better in the far-field, which may be related to the low resolution of the fault model. The simulation results in this paper can provide a theoretical basis for explaining the seismogenic process of this earthquake using GNSS and gravity data.

Three earthquakes occurred in Yangbi County, Dali, Yunnan Province with the maximum magnitude M6.4, on May 21, 2021, and caused huge economic losses and human casualties. In this paper, the existing high-precision gravity data, mobile gravity survey data and EGM2008 model data were fused into high-precision grid data with 2.5km point distance to clarify the seismogenic structure and seismogenic environment of Yangbi earthquake. With the Yangbi earthquake as the center location, two long gravity profiles and 10 short gravity profiles are extracted, and the three-dimensional crustal imaging characteristics in the study area are obtained by the normalized full gradient imaging method, and the deep and shallow contact relationship and deep seismogenic environment along the northern section of Honghe fault zone, Weixi-Weishan Fault, Yongsheng-Binchuan Fault, Eryuan-Heqing Fault in the Yangbi earthquake area are analyzed. In this paper, the vertical and transverse characteristics of the upper crustal structure of the northern section of Red River Fault in Yangbi and its surrounding areas along the gravity profiles were obtained, the deep structural differences of the southern Yunnan block, Sichuan-Yunnan block and large faults were revealed, and the seismogenic structure and environment of the three Yangbi earthquakes were analyzed and discussed. The results of the study are as follows:

(1)The sudden change zone of dip angle and dip direction of the normalized gravity gradient is in good agreement with the medium and large geological faults, such as Nujiang Fault, Lancangjiang Fault, Red River Fault, Anninghe Fault, and Zemuhe Fault, etc.

(2)When the continuity of normalized gravity gradient of the middle and lower crust is good, and the middle and upper crust is in the high-low transition zone, earthquakes greater than M6.0 will occur frequently, especially in the intersection area of Weixi-Weishan Fault, Yongsheng-Binchuan Fault and the northern section of Red River Fault.

(3)Near the epicenter of Yangbi earthquake, there is a strong deformation belt of high and low normalized gravity gradients in the upper crust converging at a depth of about 15km, and the epicenter projection intersected with the Weixi-Weishan Fault and the secondary fault at a depth of about 10km, the continuity of normalized gravity gradient values is very well below the depth of 20km in the crust, it is inferred that the seismogenic structure of the three earthquakes in Yangbi are the Weixi-Weishan Fault and its secondary fault.

(4)Earthquakes of M6.0 or higher normally occur where the geological strata connect and are relatively young. Strong earthquakes occurred at the junction of the Triassic and Permian in the east of Dali. At the same time, analyzing the distribution characteristics of the normalized gravity gradient value(G_h)can provide a reference for the division and correction of stratigraphic boundaries.

(5)In the deformation process of geological structure, when the high-low gradient deformation zones of G_h value are formed in the middle and upper crust, whilst G_h values have good continuity in the middle and lower crust, earthquakes of M6.0 or higher normally occur. These features can be used as an important marker to judge the preparation and occurrence of strong earthquakes.

Based on the geological and geophysical characteristics and the distribution characteristics of M≥6.0 earthquakes, the relationship between the change of G_h values and the occurrence of moderate and strong earthquakes, the stratigraphic boundary, the strike and dip angle of structural faults in the study area were analyzed, and the seismogenic structure and environment of the three Yangbi earthquakes on May 21 in 2021 were discussed. This study can provide a scientific basis and important reference value for determining the seismogenic mechanism and location of moderate-strong earthquakes.

The main rupture of Ludian M_S6.5 earthquake is directed to the northwest, which occurred in the east of Xianshuihe-Xiaojiang fault zone. The epicenter is in the transitional zone of the Sichuan-Yunnan block and the South China block, where there are many slip and nappe structures. Some controversy still remains on the earthquake tectonic environment. So, Bouguer gravity anomalies calculated by EGM2008 were broken down into 1-5 ranks using the way of Discrete Wavelet Transform(DWT), then we get the lateral heterogeneity in different depths of the crust. The distribution characteristics of Bouguer gravity anomaly are analyzed using measured gravity profile data. We also get its normalized full gradient(NFG)picture, and study the differences between different depths in crust. The results show that: (1)the characteristic of Buoguer gravity anomaly in southwest to northeast is high-low-high between the Lianfeng Fault(LFF)and Zhaotong-Ludian Fault(ZLF). The mainshock and aftershocks are distributed in the middle of the low-value zone, which means that the east moving materials of Qinghai-Tibet plateau broke through the southern section of Lianfeng Fault(LFF), moving along the Baogunao-Xiaohe zone(low-value belt)to the southeast, stopped by the Zhaotong-Ludian Fault(ZLF), and then earthquake occurred.(2)The third-order discrete wavelet transform(DWT)details show that: there is a good consistency between the negative gravity anomaly in upper crust and the distribution of major faults, which reflects that the rupture caused by the movements of the faults in crust has reduced gravity anomaly. There is a NW-trending negative anomaly belt near the epicenter, which may has some relationship to the southward development of the Daliangshan Fault(DLSF). So we speculate that the southward movement of Daliangshan Fault is the main direct force source of Ludian earthquake.(3)In the picture of the fourth-order DWT details, there is an obvious positive gravity anomaly under the epicenter of Ludian earthquake, which confirms the presence of a high-density body in the middle crust. While the fifth-order DWT details show that: A positive anomaly belt is below the epicenter too, which may be caused by mantle material intruding to the lower crust. Tensile force in crust caused by mantle uplift and extrusion-torsion force caused by Indian plate push are the main force source in the tensile and strike slip movement of the Ludian earthquake.(4)The normalized total gradient of Bouguer gravity anomalies of Huili-Ludian-Zhaotong profile shows that: there is obvious ‘deformation’ in the Xiaojiang fault zone which dips to the east and controls the local crust movement. There is a local ‘constant body’ at the bottom of the epicenter. The stable constant body in density has limiting effects to the earthquake rupture, which is the reason that the earthquake rupture' scale in strike and in depth are limited.(5)The ability of earthquake preparation in Zhaotong-Ludian Fault is lower than the Xianshuihe-Xiaojiang fault zone, and the maximum earthquake capacity in this area should be around magnitude 7.

In this paper, based on three gravity profiles in Yunnan Ludian M_S6.5 earthquake and adjacent area, we obtained Bouguer gravity anomaly, residual density correlation image and crustal stratification structure along the profiles. The study shows a saddle-shaped distribution of Bouguer gravity anomalies along the Huili-Ludian-Zhaotong, Panzhihua-Menggu-Dajing and Shekuai-Tangdan-Huize profile, with the values ranging -278～-197×10～5ms^-2, -273～-200×10～5ms^-2, -280～-254×10～5ms^-2, respectively; the local low values locate in the Xiaojiang fault zone, the amplitude difference decreases gradually from the north to the south; the density in the Xiaojiang fault zone is lower than that of the sides, the low density zone extends to the middle and lower crust, and the material density in the east is lower than that in the west; positive and negative density anomalies overlap, indicating a poor stability of the lower crust. The Ludian earthquake occurred in this region. Layered crustal structure shows the undulation of Moho surface, with uplift beneath the Xiaojiang fault zone as the center and change of the maximum depth of Moho from 50km up to 41km from north to south. This reflects the position of Xiaojiang Fault in the regional geological structure as block boundary of Sichuan-Yunnan block and South China block.