GRACE time-variable gravity and its application to geoscience:Quantitative analysis of relevant literature

The Gravity Recovery and Climate Experiment(GRACE)is the most important gravity satellite to date in human history.Since its launch in 2002,GRACE time-varying gravity has had an unprecedented impact on earth science and has generated revolutionary changes.Because of natural phenomena such as climate warming,glacial melting,sea level rise,and earthquakes,earth science research has become an increasingly popular discipline in recent years.This article summarizes the importance of GRACE time-varying gravity,its application to geoscience,and its development.We analyzed the historical development and current status of GRACE time-varying gravity as well as research hotspots by searching the literature in the core collection databases of the China National Knowledge Infrastructure and the Web of Science over the past 20 years.The CiteSpace and VOSviewer software packages were applied with reference to the principle of literature metrology.Our investigation and analysis of characteristic indexes,such as the numbers of publications,co-occurrence of keywords,and co-citation of documents,uncovered the wide application and promotion of gravity satellites,especially GRACE time-varying gravity,in earth science.The results showed that the number of publications addressing GRACE data and time-varying gravity theory is increasing annually and that the USA,China,and Germany are the main producers.The Chinese Academy of Sciences,the National Aeronautics and Space Administration of the United States,and the Helmholtz Association of German Research Centres rank among the top three institutions in the world in terms of producing the most publications on this topic.We found that GRACE time-varying gravity plays unique roles in measuring changes in terrestrial water storage changes,ice and snow melting and sea level changes,and(co)seismic gravity changes,as well as in promoting other disciplines.

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.

Spatial distribution characteristics and mechanism of nonhydrological time-variable gravity in China's Mainland

The purpose of this study is to explore nonhydrological mass transfer in China's Mainland.For this purpose,gravity recovery and climate experiment(GRACE)data were obtained to study the spatial distribution of time variant gravity signals in China's Mainland.Then,from auxiliary hydrological data processed according to the current hydrological model,a new more comprehensive hydrological model of China's Mainland was constructed.Finally,the time variant signals of this new hydrological model were removed from the time variant gravity field computed from GRACE data,thus obtaining a description of the nonhydrological mass transfer of China's Mainland.The physical sources and mechanisms of the resulting mass transfer are then discussed.The improved,more realistic,hydrological model used here was created by selecting the hydrological components with the best correlations in existing hydrological models,by use of correlation calculation,analysis,and comparison.This improved model includes water in soils and deeper strata,in the vegetation canopy,in lakes,snow,and glaciers,and in other water components(mainly reservoir storage,swamps,and rivers).The spatial distribution of the transfer signals due to nonhydrological mass in China's Mainland was obtained by subtracting the combined hydrological model from the GRACE time-variable gravity field.The results show that the nonhydrological signals in China's Mainland collected in GRACE data were mainly positive signals,and were distributed in the Bohai Rim and the northern and eastern parts of the Tibetan Plateau.The above nonhydrological mass transfer signals have been studied further and are discussed.The results show that the nonhydrological mass migration signals in the Bohai Rim region originate primarily from sea level change and marine sediment accumulation.The mass accumulation from Indian plate collision in the Tibetan Plateau appears to be the main reason for the increase in the residual gravity field in that region.

Seismologic applications of GRACE time-variable gravity measurements

The Gravity Recovery and Climate Experiment（GRACE） has been measuring temporal and spatial variations of mass redistribution within the Earth system since2002. As large earthquakes cause significant mass changes on and under the Earth＇s surface,GRACE provides a new means from space to observe mass redistribution due to earthquake deformations. GRACE serves as a good complement to other earthquake measurements because of its extensive spatial coverage and being free from terrestrial restriction. During its over 10 years mission,GRACE has successfully detected seismic gravitational changes of several giant earthquakes,which include the 2004 Sumatra–Andaman earthquake,2010 Maule（Chile） earthquake,and 2011 Tohoku-Oki（Japan） earthquake. In this review,we describe by examples how to process GRACE timevariable gravity data to retrieve seismic signals,and summarize the results of recent studies that apply GRACE observations to detect co- and post-seismic signals and constrain fault slip models and viscous lithospheric structures. We also discuss major problems and give an outlook in this field of GRACE application.

Analytical study on abnormal change in time-variable gravity at Yichang seismostation before the M5.1 Badong earthquake

An M5.1 earthquake occurred in Badong County, only 66 km from the Three Gorges Dam, on De- cember 16, 2013. The continuous gravity observation data obtained at Yichang seismostation nearest to the epi- center （96 km） were analyzed, and it was found that the continuous gravity observation data obtained in this rainy season did not exhibit a characteristic of seasonal change in gravity identical to that in the past years, and thereafter the M5.1 Badong earthquake occurred. Numerical simulation revealed that the water storage and discharge of the Three Gorges reservoir generated seasonal change in gravity, and the changes in atmospheric pressure and gravity load were not the main sources of the seasonal change of continuous gravity observation data whether in respect of magnitude or phase and did not have obvious breaking change on annual variation before the earthquake. Through analysis of the seasonal change data observed on the same site including cavern temperature, rainfall data and global terrestrial water model （CPC） simulated water load, it was thought that, in the observation room with cavern temperature change of only -0.1 l^C/a at Yichang seismostation, the sea- sonal change of continuous gravity observation result mainly originated from the seasonal change in rainfall. In the case that the changes in rainfall and its water load did not have evident breaking change on annual varia- tion law before the earthquake, if the MS. 1 Badong earthquake was the cause of the breaking change on annual variation law in Yichang this time, then it was believed through analysis of crust expansion ratio that similar a- nomaly should occur at a crust expansion and compression intersection, no more than 100 km away from the epicenter.

Effectiveness of empirical orthogonal function used in decorrelation of GRACE time-variable gravity field

Empirical orthogonal function （EOF） was used to process the spherical harmonic coefficient （SHC） of 115 Gravity Recovery and Climate Experiment （GRACE） RL05 monthly gravity field models from March 2003 to February 2013 released by CSR （Center for Space Research）. We analyzed the effectiveness of EOF in decorrelation of gravity field. Results show that only a small Gaussian smoothing radius was needed by EOF to significantly weaken the north -south stripes compared with the empirical moving-window filtering algorithm. The comparative experiments with a Global Land Data Assimilation System （GLDAS） hydrological model also show that EOF did not much affect the real geophysical signals, and that the removed signals were nearly uncorrelated with the real geophysical signals. As the Gravity Recovery and Climate Experiment （GRACE） missions continue, EOF can be used to significantly remove the correlated errors from monthly gravity fields and reserve rich effective signals.

Characteristics and control factors of feldspar dissolution in gravity flow sandstone of Chang 7 Member,Triassic Yanchang Formation,Ordos Basin,NW China

To clarify the formation and distribution of feldspar dissolution pores and predict the distribution of high-quality reservoir in gravity flow sandstone of the 7^(th) member of Triassic Yanchang Formation(Chang 7 Member)in the Ordos Basin,thin sections,scanning electron microscopy,energy spectrum analysis,X-ray diffraction whole rock analysis,and dissolution experiments are employed in this study to investigate the characteristics and control factors of feldspar dissolution pores.The results show that:(1)Three types of diagenetic processes are observed in the feldspar of Chang 7 sandstone in the study area:secondary overgrowth of feldspar,replacement by clay and calcite,and dissolution of detrital feldspar.(2)The feldspar dissolution of Chang 7 tight sandstone is caused by organic acid,and is further affected by the type of feldspar,the degree of early feldspar alteration,and the buffering effect of mica debris on organic acid.(3)Feldspars have varying degrees of dissolution.Potassium feldspar is more susceptible to dissolution than plagioclase.Among potassium feldspar,orthoclase is more soluble than microcline,and unaltered feldspar is more soluble than early kaolinized or sericitized feldspar.(4)The dissolution experiment demonstrated that the presence of mica can hinder the dissolution of feldspar.Mica of the same mass has a significantly stronger capacity to consume organic acids than feldspar.(5)Dissolution pores in feldspar of Chang 7 Member are more abundant in areas with low mica content,and they improve the reservoir physical properties,while in areas with high mica content,the number of feldspar dissolution pores decreases significantly.

Influence of topography on the fine structures of stratospheric gravity waves:An analysis using COSMIC-2 temperature data

We derive the potential energy of gravity waves(GWs)in the upper troposphere and stratosphere at 45°S-45°N from December 2019 to November 2022 by using temperature profiles retrieved from the Constellation Observing System for Meteorology,Ionosphere,and Climate-2(COSMIC-2)satellite.Owing to the dense sampling of COSMIC-2,in addition to the strong peaks of gravity wave potential energy(GWPE)above the Andes and Tibetan Plateau,we found weak peaks above the Rocky,Atlas,Caucasus,and Tianshan Mountains.The land-sea contrast is responsible for the longitudinal variations of the GWPE in the lower and upper stratosphere.At 40°N/S,the peaks were mainly above the topographic regions during the winter.At 20°N/S,the peaks were a slight distance away from the topographic regions and might be the combined effect of nontopographic GWs and mountain waves.Near the Equator,the peaks were mainly above the regions with the lowest sea level altitude and may have resulted from convection.Our results indicate that even above the local regions with lower sea level altitudes compared with the Andes and Tibetan Plateau,the GWPE also exhibits fine structures in geographic distributions.We found that dissipation layers above the tropopause jet provide the body force to generate secondary waves in the upper stratosphere,especially during the winter months of each hemisphere and at latitudes of greater than 20°N/S.

Probing signals of atmospheric gravity waves excited by the July 29,2021 M_(W)8.2 Alaska earthquake

It is commonly believed that the atmosphere is decoupled from the solid Earth.Thus,it is difficult for the seismic wave energy inside the Earth to propagate into the atmosphere,and atmospheric pressure wave signals excited by earthquakes are unlikely to exist in atmospheric observations.An increasing number of studies have shown that earthquakes,volcanoes,and tsunamis can perturb the Earth's atmosphere due to various coupling effects.However,the observations mainly focus on acoustic waves with periods of less than 10 min and inertial gravity waves with periods of greater than 1 h.There are almost no clear observations of gravity waves that coincide with observations of low-frequency signals of the Earth's free oscillation frequency band within 1 h.This paper investigates atmospheric gravity wave signals within1 h of surface-atmosphere observations using the periodogram method based on seismometer and microbarometer observations from the global seismic network before and after the July 29,2021 M_(w)8.2 Alaska earthquake in the United States.The numerical results show that the atmospheric gravity wave signals with frequencies similar to those of the Earth's free oscillations _(0)S_(2) and _(0)T_(2) can be detected in the microbaro meter observations.The results con firm the existence of atmospheric gravity waves,indicating that the atmosphere and the solid Earth are not decoupled within this frequency band and that seismic wave energy excited by earthquakes can propagate from the interior of the Earth to the atmosphere and enhance the atmospheric gravity wave signals within 1 h.

Quintessence anisotropic stellar models in quadratic and Born-Infeld modified teleparallel Rastall gravity

This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.

Gravity Fault Subsidence and Beach Ridges Progradation in Quinta-Cassino (RS) Coastal Plain, Brazil

Ground penetrating radar (GPR) surveys have being applied to investigate very near-surface stratification of sedimentary units in coastal plains and to define their depositional conditions. This paper presents, however, low-frequency GPR survey to investigate fault-related depositional systems at greater depths. The Quinta-Cassino area in the Rio Grande do Sul Coastal Plain (RGSCP, Brazil) shows a wide strandplain that is made off by very long, continuous, and linear geomorphic features (beach ridges). This strandplain extends for ~70 km southward. The beach ridges show low-angle truncations against the Quinta escarpment, and also truncations in the strandplain. The traditional approach points that RGSCP was developed by juxtaposition of four lagoons/barrier systems as consequence of sea level changes;previous model assumes that no deformational episode occurred in RGSCP. The geophysical and geological surveys carried out in this area showed the existence of listric fault controlling the beach ridges in the escarpments and hanging-wall blocks. The radargrams could distinguish Pleistocene basement unit anticlockwise rotation, thickening of beach ridges radarfacies close to listric normal faults, and horst structures. These deformational features indicate that the extensional zone of a large-scale gravity-driven structure controlled the mechanical subsidence, the Holocene sedimentation and its stratigraphic and geomorphic features in the Quinta-Cassino area to build up an asymmetric delta. The results point to a new approach in dealing with RGSCP Holocene evolution.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

The Structure of Gravity Funnels and Stability Considerations of Matter in SI Units

This article describes an extension of the theory of vortices to electromagnetic types with a start point from known fluid systems. From this, properties of gravity-generating objects (particles and black holes) can be derived, which can also describe their possible interior. This also leads to questions about stability, which are then addressed and ultimately lead to considerations of black holes and their possible internal structure. The results fit into the observable areas and can also be directly verified because they were analytically calculated in SI units.

A VGGNet-based correction for satellite altimetry-derived gravity anomalies to improve the accuracy of bathymetry to depths of 6500 m

Understanding the topographic patterns of the seafloor is a very important part of understanding our planet.Although the science involved in bathymetric surveying has advanced much over the decades,less than 20%of the seafloor has been precisely modeled to date,and there is an urgent need to improve the accuracy and reduce the uncertainty of underwater survey data.In this study,we introduce a pretrained visual geometry group network(VGGNet)method based on deep learning.To apply this method,we input gravity anomaly data derived from ship measurements and satellite altimetry into the model and correct the latter,which has a larger spatial coverage,based on the former,which is considered the true value and is more accurate.After obtaining the corrected high-precision gravity model,it is inverted to the corresponding bathymetric model by applying the gravity-depth correlation.We choose four data pairs collected from different environments,i.e.,the Southern Ocean,Pacific Ocean,Atlantic Ocean and Caribbean Sea,to evaluate the topographic correction results of the model.The experiments show that the coefficient of determination(R~2)reaches 0.834 among the results of the four experimental groups,signifying a high correlation.The standard deviation and normalized root mean square error are also evaluated,and the accuracy of their performance improved by up to 24.2%compared with similar research done in recent years.The evaluation of the R^(2) values at different water depths shows that our model can achieve performance results above 0.90 at certain water depths and can also significantly improve results from mid-water depths when compared to previous research.Finally,the bathymetry corrected by our model is able to show an accuracy improvement level of more than 21%within 1%of the total water depths,which is sufficient to prove that the VGGNet-based method has the ability to perform a gravity-bathymetry correction and achieve outstanding results.

A method for extracting the preseismic gravity anomalies over the Tibetan Plateau based on the maximum shear strain using GRACE data

The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass,which consequently cause changes in gravity.The Gravity Recovery And Climate Experiment(GRACE)satellite data can be used to detect gravity changes associated with large earthquakes.However,previous GRACE satellite-based seismic gravity-change studies have focused more on coseismic gravity changes than on preseismic gravity changes.Moreover,the noise of the north–south stripe in GRACE data is difficult to eliminate,thereby resulting in the loss of some gravity information related to tectonic activities.To explore the preseismic gravity anomalies in a more refined way,we first propose a method of characterizing gravity variation based on the maximum shear strain of gravity,inspired by the concept of crustal strain.The offset index method is then adopted to describe the gravity anomalies,and the spatial and temporal characteristics of gravity anomalies before earthquakes are analyzed at the scales of the fault zone and plate,respectively.In this work,experiments are carried out on the Tibetan Plateau and its surrounding areas,and the following findings are obtained:First,from the observation scale of the fault zone,we detect the occurrence of large-area gravity anomalies near the epicenter,oftentimes about half a year before an earthquake,and these anomalies were distributed along the fault zone.Second,from the observation scale of the plate,we find that when an earthquake occurred on the Tibetan Plateau,a large number of gravity anomalies also occurred at the boundary of the Tibetan Plateau and the Indian Plate.Moreover,the aforementioned experiments confirm that the proposed method can successfully capture the preseismic gravity anomalies of large earthquakes with a magnitude of less than 8,which suggests a new idea for the application of gravity satellite data to earthquake research.

Predicting bathymetry based on vertical gravity gradient anomaly and analyses for various influential factors

The prediction of bathymetry has advanced significantly with the development of satellite altimetry.However,the majority of its data originate from marine gravity anomaly.In this study,based on the expression of vertical gravity gradient(VGG)of a rectangular prism,the governing equations for determining sea depths to invert bathymetry.The governing equation is solved by linearization through an iterative process,and numerical simulations verify its algorithm and its stability.We also study the processing methods of different interference errors.The regularization method improves the stability of the inversion process for errors.A piecewise bilinear interpolation function roughly replaces the low-frequency error,and numerical simulations show that the accuracy can be improved by 41.2%after this treatment.For variable ocean crust density,simulation simulations verify that the root-mean-square(RMS)error of prediction is approximately 5 m for the sea depth of 6 km if density is chosen as the average one.Finally,two test regions in the South China Sea are predicted and compared with ship soundings data,RMS errors of predictions are 71.1 m and 91.4 m,respectively.

Gravity and the Nature of Physical Interactions

This work is a kind of thought experiment aimed at answering the question: what might a theory look like in which time and space (spacetime) are not fundamental? The article formulates theoretical frameworks that introduce the number of spacetime dimensions, the principle of equivalence of mass, and the value of the gravitational constant not as empirically given data, but as results of theoretical deduction. This analysis opens up potential connections between gravitational and electrostatic interactions, proposing a new approach to traditional physical assumptions. The theory is presented in a preliminary form, intended to inspire possible further research. The final part of the paper proposes experiments to verify these ideas.

Analysis of gravity wave activity during stratospheric sudden warmings in the northern hemisphere

Due to the significant changes they bring to high latitude stratospheric temperature and wind,stratospheric sudden warmings(SSWs)can have an impact on the propagation and energy distribution of gravity waves(GWs).The variation characteristics of GWs during SSWs have always been an important issue.Using temperature data from January to March in 2014−2016,provided by the Constellation Observing System for Meteorology,Ionosphere and Climate(COSMIC)mission,we have analyzed global GW activity at 15−40 km in the Northern Hemisphere during SSW events.During the SSWs that we studied,the stratospheric temperature rose in one or two longitudinal regions in the Northern Hemisphere;the areas affected extended to the east of 90°W.During these SSWs,the potential energy density(E_(p)of GWs expanded and covered a larger range of longitude and altitude,exhibiting an eastward and downward extension.The E_(p)usually increased,while partially filtered by the eastward zonal winds.When zonal winds weakened or turned westward,E_(p)began to strengthen.After SSWs,the E_(p)usually decreased.These observations can serve as a reference for analyzing the interaction mechanism between SSWs and GWs in future work.

Data processing method for aerial testing of rotating accelerometer gravity gradiometer

A novel method for noise removal from the rotating accelerometer gravity gradiometer(MAGG)is presented.It introduces a head-to-tail data expansion technique based on the zero-phase filtering principle.A scheme for determining band-pass filter parameters based on signal-to-noise ratio gain,smoothness index,and cross-correlation coefficient is designed using the Chebyshev optimal consistent approximation theory.Additionally,a wavelet denoising evaluation function is constructed,with the dmey wavelet basis function identified as most effective for processing gravity gradient data.The results of hard-in-the-loop simulation and prototype experiments show that the proposed processing method has shown a 14%improvement in the measurement variance of gravity gradient signals,and the measurement accuracy has reached within 4E,compared to other commonly used methods,which verifies that the proposed method effectively removes noise from the gradient signals,improved gravity gradiometry accuracy,and has certain technical insights for high-precision airborne gravity gradiometry.

Flow Rate Measurement of Gravity Infusion Set and Functional Evaluation of Drop Counter: A Pilot Study

Developing a novel drop counter by introducing the Internet of Things concept has been vigorously conducted in recent years. Understanding the newly introduced drop counter’s flow rate control accuracy and flow rate count feature is essential for improving safety in infusion management. This study aimed to verify if the new drop counters could secure accurate flow rate and drip count by conducting actual flow rate measurements using gravimetry and functional evaluation. A drop counter was attached to each drip chamber of the infusion set, and an IV drip was conducted at the 100 ml/h flow rate. The weight of discharged physiological saline was measured to plot trumpet curves. Next, three different types of drop counters were evaluated to determine if they maintained drip count accuracy according to the changes in their position angles. The flow rate errors in all conditions indicated trumpet-like curves, exhibiting an overall error range within ±10% in all observation windows. Although every drop counter successfully detected and measured dripping, it was challenging in some counters to detect dripping when the drip chamber was tilted. In comparing adult and pediatric IV sets, the adult IV set was found to be less likely to detect dripping in the angled position. No significant differences in results were confirmed between high and low flow rates, suggesting that the drop count function would not be affected by the flow rate in the ranges of typical infusion practices. Doppler sensors have a wide range of measurements and high sensitivity;the dripping was detected successfully even when the drip chamber was tilted, probably due to the advantages of these sensors. In contrast, miscounts occurred in those equipped with infrared sensors, which could not detect light intensity changes in tilted positions. Understanding the tendencies in flow rate errors in infusion can be valuable information for infusion management.