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.

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.

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.

Isostatic gravity anomaly is considered a sign of the isostatic state of the crust, and studies show that the isostatic state of crust is closely connected with the structural features and seismicity in many areas. In order to investigate the isostatic state of crust and to understand its relation to structural features and seismicity in North China Craton, a new isostatic residual gravity map of North China Craton has been computed using recently released earth gravitational model and digital terrain models. Free-air gravity anomalies of North China Craton have been prepared using the gravity data set of Earth Gravitational Model 2008(EGM2008). EGM2008 data set is believed to be reliable and studies show that EGM2008 free-air gravity anomalies have a general accuracy of 10.5mGal(1mGal=10^-3cm/s²)in China. The topographic-isostatic corrections were computed based on an Airy-Heiskanen model of local compensation using a strict algorithm based on digital elevation model(DEM), the average crust thickness of the study area was derived from CRUST2.0, and the topographic and bathymetric data sets were derived from digital elevation model ASTER GDEM 2009(1arc second resolution)and ETOPO1(1arc minute resolution)respectively. Topographic-isostatic corrections were then added to the free-air gravity anomalies to determine the isostatic gravity anomalies of North China Craton with a gridding resolution of 5arc minutes. According to the results of calculations, distribution of isostatic gravity anomalies and its relations to structural features and seismicity of North China Craton were discussed. The results indicate that the spatial distribution of isostatic gravity anomalies is remarkably uneven in North China Craton, and isostatic gravity anomalies are very different between different fault blocks. Isostatic gravity anomalies of North China Craton are mainly controlled by neo-tectonic movements, and are significantly influenced both by lateral variations in crust density and deep structures. The close relation between isostatic gravity anomalies and neo-tectonic movements may imply that there are crustal features that are not compensated regionally and isostatic disequilibrium in North China Craton. The results also indicate that there are some connections between the distributions of isostatic gravity anomalies and seismicity in North China Craton, earthquakes tend to occur around areas with remarkable high or low isostatic gravity anomalies and at transition zones between positive and negative gravity anomalies, and we suggest that special attention should be paid to areas with similar isostatic gravity anomaly characteristics when performing seismic hazard analysis.

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.