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.

An investigation on the wind profiles and gravity wave dynamics in MLT region based on the meteor radars from the Meridian Project

The meteor radar can detect the zenith angle,azimuth,radial velocity,and altitude of meteor trails so that one can invert the wind profiles in the mesosphere and low thermosphere(MLT)region,based on the Interferometric and Doppler techniques.In this paper,the horizontal wind field,gravity wave(GW)disturbance variance,and GW fluxes are analyzed through the meteor radar observation from 2012−2022,at Mohe(53.5°N,122.4°E)and Zuoling(30.5°N,114.6°E)stations of the(Chinese)Meridian Project.The Lomb−Scargle periodogram method has been utilized to analyze the periodic variations for time series with observational data gaps.The results show that the zonal winds at both stations are eastward dominated,while the meridional winds are southward dominated.The variance of GW disturbances in the zonal and meridional directions increases gradually with height,and there is a strong pattern of annual variation.The zonal momentum flux of GW changes little with height,showing weak annual variation.The meridional GW flux varies gradually from northward to southward with height,and the annual periodicity is stronger.For both stations,the maximum values of zonal and meridional wind occur close to the peak heights of GW flux,with opposite directions.This observational evidence is consistent with the filtering theory.The horizontal wind velocity,GW flux,and disturbance variance of the GW at Mohe are overall smaller than those at Zuoling,indicating weaker activities in the MLT at Mohe.The power spectral density(PSD)calculated by the Lomb−Scargle periodogram shows that there are 12-month period and 6-month period in horizontal wind field,GW disturbance variance and GW flux at both stations,and especially there is also a 4-month cycle in the disturbance variance.The PSD of the 12-month and 6-month cycles exhibits maximum values below 88 km and above 94 km.

Gravity and magnetic anomalies field characteristics in the South China Sea and its application for interpretation of igneous rocks

Igneous rocks in the South China Sea have broad prospects for oil and gas exploration.Integrated geophysical methods are important approaches to study the distribution of igneous rocks and to determine and identify igneous rock bodies.Aimed at the characteristics of gravity and magnetic fields in the South China Sea,several potential field processing methods are preferentially selected.Reduction to the pole by variable inclinations in the area of low magnetic latitudes is used to perform reduction processing on magnetic anomalies.The preferential continuation method is used to separate gravity and magnetic anomalies and extract the gravity and magnetic anomaly information of igneous rocks in the shallow part of the South China Sea.The 3D spatial equivalent distribution of igneous rocks in South China Sea is illustrated by the 3 D correlation imaging of magnetic anomalies.Since the local anomaly boundaries are highlighted gravity and magnetic gradients,the distribution characters of different igneous rocks are roughly outlined by gravity and magnetic correlation analysis weighted by gradient.The results show the distribution of igneous rocks is controlled and influenced by deep crustal structure and faulting.

Discovering Crustal Deformation Bands by Processing Regional Gravity Field

Objectives： This article presents a new computational procedure to discover scratches buried in the earth＇s crust. We also validate this new interdisciplinary analysis method with regional gravity data located in a well-known Dabie orogenic zone for test. Methods： Based on the scratch analysis method evolved with mathematical morphology of surfaces, we present a procedure that extracts information of the crustal scratches from regional gravity data. Because the crustal scratches are positively and highly correlated to crustal deformation bands, it can be used for delineation of the crustal deformation belts. The scratches can be quantitatively characterized by calculation of the ridge coefficient function, whose high value traces delineate the deformation bands hidden in the regional gravity field. In addition, because the degree of crustal deformation is an important indicator of tectonic unit divisions, so the crust can be further divided according to the degree of crustal deformation into some tectonic units by using the ridge coefficient data, providing an objective base map for earth scientists to build tectonic models with quantitative evidence. Results： After the ridge coefficients are calculated, we can further enhance the boundary of high ridge-coefficient blocks, resulting in the so-called ridge-edge coefficient function. The high-value ridge-edge coefficients are well correlated with the edge faults of tectonic units underlay, providing accurate positioning of the base map for compilation of regional tectonic maps. In order to validate this new interdisciplinary analysis method, we select the Dabie orogenic zone as a pilot area for test, where rock outcrops are well exposed on the surface and detailed geological and geophysical surveys have been carried out. Tests show that the deformation bands and the tectonic units, which are conformed by tectonic scientists based on surface observations, are clearly displayed on the ridge and ridge-edge coefficient images obtained in this article. Moreover, these computer-generated images provide more accurate locations and geometric details. Conclusions： This work demonstrates that application of modern mathematical tools can promote the quantitative degree in research of modern geosciences, helping to open a door to develop a new branch of mathematical tectonics.

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth＇s gravitational field measured from the gravity field and steady-state ocean circulation explorer（GOCE）,up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry（SGG） are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth＇s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth＇s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.

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.

Preparation of electrolytic copper powders with high current efficiency enhanced by super gravity field and its mechanism

Super gravity field was employed to enhance electrolytic reaction for the preparation of copper powders.The morphology, microstructure and size of copper powders were characterized by scanning electron microscopy,X-ray diffractometry and laser particle analysis.The results indicated that current efficiencies of electrolytic copper powders under super gravity field increased by more than 20% compared with that under normal gravity condition.Cell voltage under super gravity field was also much lower.The size of copper powders decreased with the increase of gravity coefficient(G).The increase of current efficiency can be contributed to the disturbance of electrode/electrolyte interface and enhanced mass transfer of Cu2+ in super gravity field.Meanwhile,the huge gravity acceleration would promote the detachment of copper powders from electrode surface during electrolytic process,which can prevent the growth of copper powders.

Analysis of the impact on the gravity field determination from the data with the ununiform noise distribution using block-diagonal least squares method

The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field determination. On the basis of block-diagonal least squares method, three data processing strategies are employed to determine the gravity field models using three kinds of simulated global grid data with different noise spatial distri- bution in this paper. The numerical results show that when we employed the weight matrix corresponding to the noise of the observation data, the model computed by the least squares using the full normal matrix has much higher precision than the one estimated only using the block part of the normal matrix. The model computed by the block-diagonal least squares method without the weight matrix has slightly lower precision than the model computed using the rigorous least squares with the weight matrix. The result offers valuable reference to the using of block-diagonal least squares method in ultra-high gravity model determination.

Analysis of limitations on recovery of gravity field based on satellite gravity gradient data

Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model,accuracy of the long-wavelength part of gravity field model recovered by them are poor,which leads to only a few applications in time-variable gravity investigation.The reason is that some factors limit the accuracy of the gravity field recovered using gradient data,including accuracy of the gravity gradient observations,measurement bandwidth(MBW)of gradiometer,satellite inclination,etc.This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations.Firstly,for arbitrary satellite orbit inclination,we give the frequency distributions of all the components of gravity gradients(i.e.Txx;Tyy;Tzz;Txy;Txz and Tyz,).The results show that the maximum frequency of each component of the gravity gradients is the same,i.e.l=Ts(l is degree of the gravity field model,Ts is the orbital periods),and it is not influenced by the inclination of the satellite orbits.Secondly,the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps.Big polar gaps are experimented by a numerical test with inclination of 45°.Finally,considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer(SGG)compared to gradiometer used in Gravity field and steadystate Ocean Circulation Explorer(GOCE),the possibility of detecting time-variable gravity using gravity gradient observations is discussed.The results show that the SGG creates errors in MBW with magnitude of 0.014 m E,which is smaller than the magnitude of the time-variable gravity gradient signals(i.e.,0.02 m E)derived from Gravity Recovery and Climate Experiment(GRACE)gravity field models.This indicates the potential of SGG in time-variable gravity detection.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Bearing capacity of surface circular footings on granular material under low gravity fields

Low gravity fields have been simulated through magnetic acceleration to conduct experimental study on bearing capacity of circular footings on a type of crushable planetary regolith simulant,which has comparable density and particle size distribution of lunar soil.The loadesettlement responses of surface spread footings are obtained by investigating the relative density,footing size and gravity effects.Applying the hyperbolic asymptote method,normalised foundation stiffness and ultimate bearing capacity are obtained by curve fitting and predicted by power functions using multivariate nonlinear regression.The results show that the nonlinear gravity effect is not negligible,related to stress condition,soil dilatancy and mobilised friction angle.A cone penetration test(CPT)-based method for prediction of bearing capacity is proposed with correlations between ultimate bearing capacity of footings and shallow penetration stiffness of CPTs,avoiding the uncertainties of soil property estimations.Analyses of allowable bearing capacity and footing influence zone in consideration of footing size and gravity effects could therefore improve the design of shallow foundations on the Moon and Mars,and provide new understandings and potential implications to the bearing capacity of shallow foundations on crushable granular material in both terrestrial and extraterrestrial geotechnical engineering.

Characteristics of gravity fields in the Jinggu M6. 6 earthquake

Based on the study of high-precision gravity data obtained from recent studies and the regional gravi- ty network for Yunnan province, a variation in the regional gravity field was identified before the occurrence of the Yunnan Jinggu M6.6 earthquake.

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.

Comparison of Present SST Gravity Field Models

Taking the main land of Europe as the region to be studied, the potential of the new satellite gravity technique: satellite-to-satellite tracking (SST) and improving the accuracy of regional gravity field model with the SST models are investigated. The drawbacks of these models are discussed. With GPM98C as the reference, the gravity anomaly residuals of several other models, the latest SST global gravity field models (EIGEN series and GGM series), were computed and compared. The results of the comparison show that in the selected region, some systematic errors with periodical properties exist in the EIGEN and GGM’s S series models in the high degree and order. Some information that was not shown in the classic gravity models is detected in the low and middle degree and order of EIGEN and GGM’s S series models. At last, the effective maximum degrees and orders of SST models are suggested.

SIMULATION OF TEMPERATURE FIELD IN ULTRA-HIGH FREQUENCY INDUCTION HEATING AND VERIFICATION

An experimental and numerical study on the temperature field induced in the ultra-high frequency induction heating is carried out.With an aim of predicting the thermal history of the workpiece,the influence factors of temperature field,such as the induction frequency,the dimension of coil and the gap between coil and workpiece,are investigated considering temperature-dependent material properties by using FLUX 2Dsoftware.The temperature field characteristic in ultra-high induction heating is obtained and discussed.The numerical values are compared with the experimental results.A good agreement between them is observed with 7.9% errors.

Dynamic pattern characteristics of fault deformation and gravity field in the development process of Yongdeng M_S=5.8 earthquake

In this paper, the fault deformation abnormality, dynamic evolution features of gravity and vertical deformation field in the seismogenic process of the Yongdeng, Gansu Province earthquake on July 22, 1995 are studied primarily. There appeared α β γ tri stage anomaly at three sites near the epicenter, and there appeared anomalies of step and sudden jump at more than 10 sites in outer region since 1993. The high value area before shock, coseismic effect and process of recovery aftershock were monitored by portable gravity data. Data reflects the changing process of fault movement from the quasi linear to the nonlinear in the near source region during seismogenic development of the Yongdeng earthquake and evolution of gravity field from heterogeneity of seismogenic term to quasi homogeneity of postseismic term. There exists close relationship between strong earthquake and dynamic evolution of regional stress strain field. Considering all above, the experience and lessons in this medium short term prediction test are summarized.

Monthly gravity field solution from GRACE range measurements using modified short arc approach

In this paper we present a series of monthly gravity field solutions from Gravity Recovery and Climate Experiment（GRACE） range measurements using modified short arc approach,in which the ambiguity of range measurements is eliminated via differentiating two adjacent range measurements.The data used for developing our monthly gravity field model are same as Tongji-GRACEOl model except that the range measurements are used to replace the range rate measurements,and our model is truncated to degree and order 60,spanning Jan.2004 to Dec.2010 also same as Tongji-GRACE01 model.Based on the comparison results of the C_（2,0）,C_（2,1）,S_（2,1）,and C_（15,15）,S_（15,15）,time series and the global mass change signals as well as the mass change time series in Amazon area of our model with those of Tongji-GRACE01 model,we can conclude that our monthly gravity field model is comparable with Tongji-GRACE01 monthly model.

Study on Evolution of Gravity Fieldand Earthquake Prediction in theNorth-south Seismic Belt and theEastern Qinghai-Xizang Block

The relation between the dynamic evolution feature of gravity field and strong seismicity is studied. The result shows that the regional gravity field variation enjoys inhomogeneity of spatial and temporal distribution and gravity change in different regions. It may be resulted from active faults and seismogenic process, and may be due to microdynamic activity of regional strain energy, which might be accumulated or released in different stages, and there exists transformation process of stress.

Dynamic changes of gravity fields before and after the 2008 Wenchuan earthquake(Ms8.0)

The pattern evolution and dynamic mechanism of the dynamic changes of regional gravity fields occurring before and after the Wenchuan Ms8.0 earthquake are analyzed, based on five epochs of 1998 -2007 mobile gravity data from the middle-south section of the north-south seismic belt, and two epochs of field research data collected after the 2008 Wenchuan earthquake in combination with GPS data, leveling observations, and geotectonic environment data. The regional dynamic gravity changes demonstrate the effects of the eastward flow of solid matter in the Qinghai-Tibetan plateau and the preparation of the 2008 Wenchuan earthquake （2- 10 yr）. The two most meaningful gravity indicators of the Wcnchuan earthquake preparation are the positive （increasing） gravity changes occurring over many years in the southwest epicenter and the largescale gradient zone of gravity variation, with the cumulative difference between the two sides of the gradient zone of gravity exceeding 200 μGal. The positive gravity changes may facilitate a constant energy accumulation and the gradient belt may support seismic shear breakage. Overall, the gravity changes associated with the earthquake preparation indicate a pattern of accelerating increase-decelerating increase-earthquake occurrence. The Songpan-Ganzi block generally displays a negative gravity change, providing evidence for a local upwarp- ing of the deep crust-mantle and an interior expansion of the deep crust attributable to high temperatures. The viewpoint is consistent with the dilatant mechanism for earthquake preparation.

Gravity field recovery from GOCE orbits using the energy conservation approach

The sum of the dissipative energy and energy constant of the GOCE satellite is found by a priori gravity field model at first, and the GOCE dissipative energy is obtained by computing the adjacent epoch difference via the differential method. Then, a gravity field model GOCE-ECPO1, which up to the degree and order 80, is recovered by the energy conservation approach from the 103-day precise orbital data of the GOCE satellite collected from November 1, 2009 to January 12, 2010. Finally, the model is compared with existing models EGM96, ITG-CHAMP05S, EIGEN-GRACE2010S, EIGEN-6C and GO CONS GCF 2 DIR_R3. The results show that at the same order and degree, the accuracy of model GOCE-EBPO1 is higher than those of models EGM96 and ITG-CHAMP05S, but lower than those of models EIGEN-GRACE2010S, EIGEN-6C and GO_CONS_GCF 2 DIR_R3, which is mainly caused by the pole gap.