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.

Based on the absolute gravity observation data of 10 gravity datum stations of the Crustal Movement Observation Network of China(CMONOC)in Yunnan and adjacent areas during 2010-2020, the gravity datum and its dynamic variation of each gravity datum station are obtained. The gravity variation trend of 9 stations at three different time scales and time periods shows that the gravity variation increased first and then decreased, and the turning point occurred around 2014, while Kunming Station is just the opposite. The Ludian M_S6.5, Yingjiang M_S6.1 and Jinggu M_S6.6 events occurred successively in 2014 when the gravity change increased to the turning point. Thereafter, the gravity change trend decreased until the occurrence of the Yangbi M_S6.4 earthquake in 2021. The results show that the variation of the gravity field in Yunnan and adjacent area is large and fast, and the transition period of increasing to decreasing is short and the variation trend is consistent. The gravity field change mechanism may be dominated by that the Qinghai-Tibetan plateau moves to the northeast caused by the push of Indian Plate, then is blocked by the Sichuan Basin, and the crustal material under the Qinghai-Tibetan plateau moves forward to Yunnan and its adjacent regions. The repeated observations of the absolute gravity survey network covering the whole country provide abundant and reliable data for obtaining the time-variable gravity field which is related to the crustal movement. Many scholars have done a lot of research on the results of the absolute gravity dynamic changes in the Chinese mainland, but the region is mainly focused on the Qinghai-Tibetan plateau, while the results of the absolute gravity dynamic change in other regions are still rarely revealed.

(1)The absolute gravity observation data of 10 gravity datum stations in Yunnan and Panzhihua from 2010 to 2020 show that except Kunming observation station, the gravity change trend increased first and then decreased, and the turning point occurred around 2014. Kunming station is the only station in the cave among the 10 observation stations, and its gravity change may be affected by the water content of the mountain. Five gravity observation campaigns at each observation station were carried out in different months of different years. Due to the lack of hydrological data at each observation station, the seasonal gravity change was not considered. Therefore, eliminating its influence is one of the important jobs in our future study.

(2)Earthquakes of M_S6.1, M_S6.5 and Ms6.6 occurred on May 31, August 3 and October 7, 2014 in Yingjiang, Ludian and Jinggu, Yunnan Province, respectively. The epicentral distances of all the gravity datum stations to the three events are more than 100km, so the coseismic gravity changes caused by events can be ignored.

(3)The Ludian M_S6.5, Yingjiang M_S6.1 and Jinggu M_S6.6 earthquakes occurred successively during the turning point period, and the gravity changes show a decreasing trend until the occurrence of the Yangbi M_S6.4 event in 2021. The mechanism of gravity field change of Yunnan and the adjacent areas may be as follows: The Qinghai-Tibetan plateau is pushed to the northeast by the Indian plate, then blocked by the Sichuan Basin, and the crustal material under the Qinghai-Tibetan plateau moves forward to Yunnan and its adjacent regions.

(4)Yunnan and the adjacent areas are characterized by complex tectonic environment and rapid seismic energy accumulation and release, which puts forward new demands for absolute gravity measurement mode, adding absolute gravity measurement stations and shortening observation period, so as to enhance the ability of more absolute gravity measurement to serve for monitoring the seismic activity and regional geological tectonic activity in Chinese mainland.

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.

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.