A data-adaptive network design for the regional gravity field modelling using spherical radial basis functions

A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained widespread attention,while the modelling precision is primarily influenced by the base function network.In this study,we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise(HDBSCAN)algorithm,and the performance of the algorithm is verified by the observed gravity data in the Auvergne area.Furthermore,the turning point method is used to optimize the bandwidth of the basis function spectrum,which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously.Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model.Compared to the existing methods,the number of SRBFs used for modelling has been reduced by 15.8%,and the time cost to determine the centre positions of SRBFs has been saved by 12.5%.Hence,the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.

Joint inversion of gravity and magnetic data for a two-layer model

Based on the synchronous joint gravity and magnetic inversion of single interface by Pilkington and the need of revealing Cenozoic and crystalline basement thickness in the new round of oil-gas exploration, we propose a joint gravity and magnetic inversion methodfor two-layer models by concentrating on the relationship between the change of thicknessI and position of the middle layer and anomaly and discuss the effects of the key parameters. Model tests and application to field data show the validity of this method.

对中直接投资立地选择因素分析——Gravity Model分析

利用中国与对中直接投资12个主要国家(地区)的1990年至2006年的面板数据,通过重力模型实证分析对中直接投资的决定因素。结果表明,经济规模对直接投资的吸引起到正面的有益的影响,而距离的增加对直接投资的吸引则有负面影响,虚拟变量的说服力也很高。通过分析,得出两国间贸易额的影响比其他变量的影响更为显著的结果。

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

Robust inversion analysis of local gravity anomalies caused by geological dislocation model of faults

Theoretical analysis and practical observations show that fault dislocations can change the gravity field around the fault. Gravity changes which were caused by the repeated dislocations over a long period of time were superimposed on the Bougeur gravity anomalies. These anomalies became the evidence of historical movement of fault as well as provide a way for the study of paleo earthquakes. This paper investigates inversion methods for the geological dislocation modeling of faults using the local Bouguer's gravity anomalies. To remove the effects of the irrelevant part of gravity anomalies to fault movements, we propose the robust nonlinear inversion method and set up the corresponding algorithm. Modeling examples indicate that the Marquardt's and Baye's least squares solutions depart from the true solution due to the attraction of gross errors in the data. The more seriously the data is contaminated, the more seriously the solutions are biased. In contrast, the proposed robust Marquardt's and Baye's inversion solutions can still maintain consistency with the solution without gross errors, even though 50 percent of the data is contaminated. This indicates that the proposed robust methods are effective. Using the proposed methods, we invert the geological dislocation models of the faults around the Erhai Lake in West Yunnan. The results show that the Northern Cangdong fault and the Erhai fault are normal dip slip faults with about 4 to 5 km dislocations; and that the Southern Cangdong fault has a less dip slip compared with the former two. A satisfactory fitting between the theoretical values of the inversion solution and the actual local gravity field is achievable.

A High-Resolution Earth’s Gravity Field Model SGG-UGM-2 from GOCE,GRACE,Satellite Altimetry,and EGM2008

This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.

Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.

Crustal structure of the western Indian shield: Model based on regional gravity and magnetic data

Regional surface gravity data and global satellite magnetic data have been utilized to generate a preliminary model of the crustal structure along a southwest-northeast profile （Gadra-Fatehpur） through western Rajasthan.The study area represents the western part of the Indian continental landmass which has undergone several major episodes of repeated subduction/collision,plume traces and rifting from Archaean to recent times.The temporal and spatial relationship between the various geotectonic provinces is quite complex,thereby limiting the emergence of a suitable crustal structure model for this region.Exposures of the Malani Igneous Suite （MIS）,a product of bimodal volcanism （～780 Ma）,and considered to be the third largest felsic magmatic province of the world,is evident along the profile and also to the southwest of the study area.The easternmost part of the profile is close to the DAFB （Delhi Aravalli Fold Belt）,a Proterozoic orogenic belt.This study probes the geometry of the different crustal units in terms of density and susceptibility variations in order to decipher the imprints of the major tectonic processes the region has undergone.In order to decipher the crustal geometry of the Gadra-Fatehpur profile,two NW-SE gravity and magnetic profile vertical sections （A-A＇ in the south and B-B＇ in the north） are modelled on the basis of the constraints provided from previous seismic models.The crustal model of the Gadra-Fatehpur profile is composed of alluvium,Tertiary sediments,MIS,Marwar Supergroup,low-density layers （LDLs） and the middle-lower crustal layers,with a distinct change in configuration from the southwest to northeast.The Moho dips from SW to NE,the MIS in the SW gives way to the thick pile of the Marwar Supergroup to the NE.The evolution of MIS has been suggested to have occurred as a consequence of delamination of the upper mantle.LDLs are incorporated in Gadra-Fatehpur model.In the SW,LDL （2550 kg/m3） lies below the MIS in the NE,another LDL （2604 kg/m3） is depicted below the mid-crustal layer.

Spatial-temporal Evolution and Determinants of the Belt and Road Initiative: A Maximum Entropy Gravity Model Approach

The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

3D Modelling from New and Existing Gravity Data of an Intrusive Body in the Northern Part of Kribi-Campo Sub-Basin in Cameroon

A new gravity survey was carried out in the northern part of the onshore Kribi- Campo sub-basin in Cameroon. The data were incorporated to the existing ones and then analyzed and modeled in order to elucidate the subsurface structure of the area. The area is characterized in its north-western part by considerably high positive anomalies indicative of the presence of a dense intrusive body. We find, 1) from the analysis of the gravity residual anomaly map, the high positive anomalies observed are the signature of a shallow dense structure;2) from the multi-scale analysis of the maxima of the horizontal gradient, the structure is confined between depths of 0.5 km and 5 km;3) from the quantitative interpretation of residual anomalies by spectral analysis, the depth to the upper surface of the intrusive body is not uniform, the average depth of the bottom is h1 = 3.6 km and the depths to particular sections of the roof of the intrusion are h2 = 1.6 km and h3 = 0.5 km;4) and the 3D modeling gives results that are suggestive of the presence of contacts between rocks of different densities at different depths and a dense intrusive igneous body in the upper crust of the Kribi zone. From the 3D model the dense intrusive igneous block is surrounded by sedimentary formations to the south-west and metamorphic formations to the north-east. Both formations have a density of about 2.74 g/cm3. The near surface portions of this igneous block lie at a depth range of 0.5 km to 1.5 km while its lower surface has a depth range of 3.6 km to 5.2 km. The shape of the edges and the bottom of the intrusive body are suggestive of the fact that it forms part of a broader structure underlying the Kribi-Campo sub-basin with a great influence on the sedimentary cover.

Empirical Analysis of Xinjiang's Bilateral Trade: Gravity Model Approach

Based on the basic trade gravity model and Xinjiang's practical situation, new explanatory variables (GDP, GDPpc and SCO) are introduced to build an extended trade gravity model fitting for Xinjiang's bilateral trade. From the empirical analysis of this model, it is proposed that those three variables affect the Xinjiang's bilateral trade posi- tively. Whereas, geographic distance is found to be a significant factor influencing Xinjiang’s bilateral trade negatively. Then, by the extended trade gravity model, this article analyzes the present trade situation between Xinjiang and its main trade partners quantitatively in 2004. The results indicate that Xinjiang cooperates with its most trade partners successfully in terms of present economic scale and developing level. Xinjiang has established successfully trade part- nership with Central Asia, Central Europe and Eastern Europe, Western Europe, East Asia and South Asia. However, the foreign trade development with West Asia is much slower. Finally, some suggestions on developing Xinjiang's for- eign trade are put forward.

A Solvable Model in Two—Dimensional Gravity Coupled to a Nonlinear Matter Field

The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.

A 3D Geological Model Constrained by Gravity and Magnetic Inversion and its Exploration Implications for the World-class Zhuxi Tungsten Deposit, South China

The Zhuxi tungsten deposit in Jiangxi Province,South China,contains a total W reserve of about 2.86 Mt at an average grade of 0.54 wt%WO3,representing the largest W deposit in the world.Numerous studies on the metallogeny of the deposit have included its timing,the ore-controlling structures and sedimentary host rocks and their implications for mineral exploration.However,the deep nappe structural style of Taqian-Fuchun metallogenic belt that hosts the W deposit,and the spatial shape and scale of deeply concealed intrusions and their sedimentary host rocks are still poorly defined,which seriously restricts the discovery of new deposits at depth and in surrounding areas of the W deposit.Modern 3 D geological modeling is an important tool for the exploration of concealed orebodies,especially in brownfield environments.There are obvious density contrast and weak magnetic contrast in the ore-controlling strata and granite at the periphery of the deposit,which lays a physical foundation for solving the 3 D spatial problems of the ore-controlling geological body in the deep part of the study area through gravity and magnetic modeling.Gravity data(1:50000)and aeromagnetic data(1:50000)from the latest geophysical surveys of 2016-2018 have been used,firstly,to carry out a potential field separation to obtain residual anomalies for gravity and magnetic interactive inversion.Then,on the basis of the analysis of the relationship between physical properties and lithology,under the constraints of surface geology and borehole data,human-computer interactive gravity and magnetic inversion for 18 cross-sections were completed.Finally,the 3 D geological model of the Zhuxi tungsten deposit and its periphery have been established through these 18 sections,and the spatial shape of the intrusions and strata with a depth of 5 km underground were obtained,initially realizing―transparency‖for ore-controlling bodies.According the analysis of the geophysical,geochemical,and geological characteristics of the Zhuxi tungsten deposit,we discern three principles for prospecting and prediction in the research area,and propose five new exploration targets in its periphery.

Comparative Study on Deformation Prediction Models of Wuqiangxi Concrete Gravity Dam Based on Monitoring Data

The deformation prediction models of Wuqiangxi concrete gravity dam are developed,including two statistical models and a deep learning model.In the statistical models,the reliable monitoring data are firstly determined with Lahitte criterion;then,the stepwise regression and partial least squares regression models for deformation prediction of concrete gravity dam are constructed in terms of the reliable monitoring data,and the factors of water pressure,temperature and time effect are considered in the models;finally,according to the monitoring data from 2006 to 2020 of five typical measuring points including J23(on dam section 24^(#)),J33(on dam section 4^(#)),J35(on dam section 8^(#)),J37(on dam section 12^(#)),and J39(on dam section 15^(#))located on the crest of Wuqiangxi concrete gravity dam,the settlement curves of the measuring points are obtained with the stepwise regression and partial least squares regression models.A deep learning model is developed based on long short-term memory(LSTM)recurrent neural network.In the LSTM model,two LSTMlayers are used,the rectified linear unit function is adopted as the activation function,the input sequence length is 20,and the random search is adopted.The monitoring data for the five typical measuring points from 2006 to 2017 are selected as the training set,and the monitoring data from 2018 to 2020 are taken as the test set.From the results of case study,we can find that(1)the good fitting results can be obtained with the two statistical models;(2)the partial least squares regression algorithm can solve the model with high correlation factors and reasonably explain the factors;(3)the prediction accuracy of the LSTM model increases with increasing the amount of training data.In the deformation prediction of concrete gravity dam,the LSTM model is suggested when there are sufficient training data,while the partial least squares regression method is suggested when the training data are insufficient.

Reducing Influence of Gravity Model Error in Precise Orbit Determination of Low Earth Orbit Satellites

Based on the orbit integration and orbit fitting method, the influence of the characters of the gravity model, with different precisions, on the movement of low Earth orbit satellites was studied. The way and the effect of absorbing the influence of gravity model error on CHAMP and GRACE satellite orbits, using linear and periodical empirical acceleration models and the so-called "pseudo-stochastic pulses" model, were also analyzed.

Analysis of the Processes of Gravity in the Framework of Curvature of Space and the Substantiation of the New Model

The paper belongs to the sphere of quantum physics, physics of waves and physical fields, in particular—to the gravitation. Their study provides a better understanding of the problems of natural sciences at all levels, from elementary particles, to Universe as a whole. Therefore, the solution of these problems is an urgent and important task, which to the works of many generations of scientists of the world was dedicated. However, they have not been fully resolved. In well-known works, including general relativity, determination of the wave and energy parameters of the gravitational field of the Universe and their numerical values are absent. Solutions found are limited to tensor equations of a general form, which allows their interpretation of over a wide range. Other disadvantages of famous models are: 1) the voluminous world of the Universe reduced to the planes on which space objects and other objects move, sagging planes due to their own mass;2) signs of “top” and “bottom” of the system, which are not in the real Universe, just as they are not on Earth and not in the Solar system;3) the formation of “voids” between the object and the curved space and others. Main goals of the work to identify these contradictions and find ways to resolve them are performed. The main difference and the scientific novelty of the work performed are the justification of the gravity model based on a rigorous determination of the wave and energy parameters of the gravitational field of the Universe and their numerical values. The initial parameters of this worked—is the frequency oscillation νG of the waves of the gravitational field (Nastasenko’s constant) found in 2011. Research Results: Knowing νG can find all wave parameters of the gravitational field and their numerical values. The proposed new spatial-wave model of the action of gravity is based on the wave parameters of the gravitational fields of material objects. In the framework of their unity with electromagnetic fields, it reduces their structures to similar ones and eliminates the drawbacks of the previous model—of replaced gravity on curvature of space.

Analyses on gravity variation before and after the Lijiang earthquake based on a finite rectangular dislocation model

The methods were discussed to calculate the gravity variation due to crustal deformation based on a model of dis-location on a finite rectangular plane. Taking the Lijiang MS=7.0 earthquake as an example the calculating princi-ple of fault parameters were determined, and the results were given. Of particular interests were the characteristics of the gravity variations in different dislocation types. With comparison between the calculated results and the practical measurements, it was found that the model could to some extent account for the observations. But it failed to give explanations to the more far spatial gravity variation.

A new high-precision gravity solid tidal model for Precision Gravity Measurement Facility

It is significant for establishing gravity datum to construct precise gravity solid tidal model,A simple method with relatively low performance is to interpolate tidal parameters from the global gravity solid tide models.A competitive approach is to determine local gravity solid tidal model by harmonic analysis using long-time serial gravity observations.In this paper a new high-precision gravity solid tidal model for Precision Gravity Measurement Facility is estimated from two co-site gravimeters in the cave laboratory using modern international standard data processing techniques,whose accuracy is evaluated further by comparing with previous publications.The results show that:(1)the determined gravity solid tidal models from two co-site gravimeters are in good agreement with each other,of which the maximum differences for amplitude factors and phase delays don’t exceed 0.01700%and 2.50990°,respectively.(2)the performance of the obtained gravity solid tidal model is 0.00411 for amplitude factors and 0.24120°for phase delays,which is a little better than that of previous publications using superconducting gravity data from Wuhan station.(3)our results and methods are corrective and effective.(4)our model is tiny different from that provided by Wuhan station,which implies that it is necessary to construct a gravity solid tidal model for Precision Gravity Measurement Facility,rather than just adopting existing models at Wuhan station.Our results are helpful in realizing the goal of Precision Gravity Measurement Facility.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.