An internally damped inertial platform for marine gravimetry and a test case in the South China Sea

To dampen periodic off-levelling motions within an inertial platform while undergoing horizontal accelerations of the same period and to achieve a levelling accuracy of a few tens of arcseconds with that system,an internally damped inertial platform for a marine scalar gravity system was the developed.Methods for attenuating horizontal acceleration and reducing off-levelling error by a satisfactory gyro-levelling loop,which are fundamental to the internally damped inertial platform,were designed and implemented.In addition,phase delays are introduced by the levelling loop.The resulting off-levelling gravity errors were analyzed and modeled.A series of tests on a motion simulator were performed in laboratory for a variety of simulated sea conditions.We found that the motion of the platform is a function of the amplitude and period of the simulated ship motions and ranges between 10 and 40 arcseconds.In addition,the phase lag between platform motion and ship motion is not constant but ranges 180°-270°,depending on the period and amplitude of the motion.Then,the platform,on which a gravimeter was mounted,was installed on the R/V Shiyan 2 to conduct a gravity survey in the South China Sea.Despite rough sea conditions,it was shown that in short periods of 2-30 s,the off-levelling angle was less than 30 arcseconds,and the phase lagged the horizontal acceleration by 230°-260°.From a repeated survey line and intersecting survey points,the estimated errors of gravity measurements were between 1.3 and 1.7 mGal.The marine measurements results were compared with those of satellite altimetry data and show a mean value of 0.5 mGal in a standard deviation of 1.5 mGal.

Chinese Gravimetry Augment and Mass Change Exploring Mission Status and Future

The satellite gravimetry technology effectively recovers the global Earth’s gravity field.Since 2000s,HL-SST satellite CHAMP,LL-SST satellite GRACE,Gravity Gradient Measurement(GGM)satellite GOCE have been launched successfully,producing some Earth’s gravity models solely from satellites data.However,the space and time resolution of the Earth’s gravity fields do not adequately satisfy scientific objectives.The main reason is that the gravimetry satellites are not enough and observation data insufficient.The paper outlines the current and future status of Chinese gravity satellite missions.The Chinese gravimetry satellite system,named Chinese Gravimetry augment and Mass change exploring mission(ChiGaM),successfully launched in Dec.2021 after four years of production and over a year of calibration and valiation.The accelerometer,K-band ranging system and the three stellar sensors,among others,were precisely calibrated and trimmed.The satellite mass center was determined and coordinated with the proof center of accelerometer with an accuracy 100μm.The inter-satellite ranging system and BDS/GPS receiver operate together seamlessly.The range and range rate noise is less than 3μm/Hz^(1/2) and 1μm/s/Hz^(1/2),respectively,in band of 0.025~0.1 Hz.The electrostatic suspension accelerometer is working well.Its high-sensitive axis noise level is 3×10^(-10) m/s^(2)/Hz^(1/2)near the frequency 0.1 Hz,and 1×10^(-9) m/s^(2)/Hz^(1/2) for the less-sensitive axis.Meanwhile the BDS/GPS receiver is used to achieve data for precise orbit determination,yielding an orbit result with accuracy better than 2 cm.When compared with KBR observations,the RMS of the bias is less than 1 mm.Besides above mission,next gravimetric satellite is being developed now.TQ-2 mission is designed as a totally experimental satellite for gravitational wave detection at low Earth orbit,which can detect the Earth’s gravity field simultaneously.The Bender-type mission is considered the most promising configuration for TQ-2 and consists of two polar satellites and two inclined satellites.Due to the extra observations at the east-west direction derived from the inclined satellite pair,significant improvements has been made in detecting temporal signals with higher accuracy and spatial-temporal resolution.To achieve the scientific goal,the ACC MBW can shift from 0.001~0.1 Hz to 0.004~0.1 Hz for ACC,and the LRI MBW can shift from 0.01~1 Hz to 0.1~1 Hz.For future research,a gravimetric potential survey using cold-atomic-clock based on the general relativity theory,cold atom gradiometer should be pursued.Gravimetric technologies should be mined and researched,and the gravimetry satellite constellation should be developed,so as to improve the time resolution and space resolution for meeting the requirements of geophysics,geodesy,earthquake,water resources environment,oceanography,etc.

Research Progress in Surface and Marine Gravimetry

Gravity field is the most basic physical field generated by the material properties of the Earth system.It reflects the spatial distribution,movement and change of materials determined by the interaction and dynamic process inside the Earth.Over the years,a variety of technical means have been used to detect the Earth’s gravity field and supported numerous studies on the global change,resource detection,geological structure movement,water resources change and other related fields of research.Here is part of the progress in surface and marine gravimetry obtained by Chinese geodesy scientists from 2019 to 2023 from the following aspects,including:①Continuous gravity network in Chinese mainland;②Application of superconducting gravity measurement;③Network adjustment for continental-scale gravity survey campaign and data quality control;④Regional time-variable gravity field and its application;⑤Research progress on novel technologies for gravity inversion;⑥Research progress on marine gravity field determination;⑦Application research on marine gravity field.

Certification of a Multicomponent Reference Material from Natural Gas Mixture by Gravimetry and Dual GC-FID/TCD System

Natural gas (NG) is one of the most important sources of energy for industrial and domestic consumption in the present era because it is cheap and free from sulfur impurities. Therefore, accurate and precise measurement of its composition is of fundamental importance for trade reasons. To improve the quality of NG gas measurements, certified reference materials (CRMs) should be used for calibration of measuring equipment in order to ensure the traceability of the measurement results to the SI units. For the traceability purpose, a multicomponent natural gas mixture was prepared gravimetrically as a reference material according to ISO 6142 from pure helium, hydrogen, n-pentane, i-pentane, n-butane, i-butane, propane, ethane, hexane, methane and nitrogen. The preparation was done in two dilution steps in 5 L aluminum cylinders. The calculated mole fractions and associated uncertainties of natural gas components were verified by a dual GC-FID/TCD system in accordance with ISO 6143 calibrated by a series of primary gas mixtures (CRMs) produced by an NMI. The results obtained by gravimetry and by GC measurements have been checked for compatibility as required by ISO 6142 and were found in very good agreement. Details of the preparation and calculation of the mole fractions and uncertainties of all gas components are explained in this article.

Effect and Prospect of Basic Geological Survey Based on Airborne Gravimetry in China

The airborne gravimetry was an important leap and innovation in the world＇s history of geophysical exploration. China＇s first test of the airborne gravity geological survey in the onshoreoffshore transitional area of the western and southern part of the Bohai Sea was successful and effective in geology. Based on the airborne gravity data, and combining previous ground gravity, seismic and drilling data etc., we carried out the geological interpretation by forward and inverse methods. The result shows that the airborne Bouguer gravity anomaly was clear, the fracture interpretation was reliable, and the inversion depth of the main geological interfaces was relatively accurate. This airborne gravity geological survey not only filled the exploring gaps in the onshore- offshore transitional area, and realized the geological and tectonic junction between the sea and the land, but also discovered four local gravity anomalies, 11 fractures and three sags or subsags, and so on. The good geological effect of airborne gravimetry not restricted by terrain condition shows that it can be served as a new geophysical method in the exploration of complex terrain physiognomy area such as mountain, jungle, desert, marsh, onshore-offshore transitional area and so on, and has an extensive application prospect in China in the future.

Terrestrial water storage variation in Hebei plain area of China,based on ground surface gravimetry

Variation of terrestrial water storage in the Hebei plain area from March 2010 to June 2014 was studied using ground gravimetry combined with vertical displacement data from the Global Navigation Satellite System.Results show that observed gravity variation in this area increased continuously,basically reflecting a trend toward land subsidence.With the effect of this subsidence removed,a dominantnegative change in gravity variation was evident,reflecting an average rate of decrease in terrestrial water in this area of 0.10±0.053 m/y,and this is equivalent to a volume of 81.5±43.2×108 m^(3)and is consistent with the spatial distribution of groundwater change from measured hydrologic data.These results can be an essential reference and supplement for the study of terrestrial water variation in the Hebei plain area,and indicate that ground surface gravimetry can be used as an important mean for studying changes in terrestrial water.

Trends in gravity changes from 2009 to 2013 derived from ground-based gravimetry and GRACE data in North China

North China is a key region for studying geophysical progress. In this study, ground-based and Gravity Recovery and Climate Experiment（GRACE） gravity data from 2009 to 2013 are used to calculate the gravity change rate（GCR） using the polynomial fitting method. In general, the study area was divided into the Shanxi rift, Jing-Jin-Ji（Beijing-Tianjin-Hebei Province）, and Bohai Bay Basin（BBB） regions. Results of the distribution of the GCR determined from ground-based gravimetry show that the GCR appears to be ＂negativepositive-negative＂ from west to east, which indicates that different geophysical mechanisms are involved in the tectonic activities of these regions. However, GRACE solutions are conducted over a larger spatial scale and are able to show a difference between southern and northern areas and a mass redistribution of land water storage.

Research and Evaluation on Key Technological Indicators for Airborne and Shipborne Gravimetry

Gravimetry technical guides are the scientific basis for air-sea gravimetry. However, the existing technical guides in China are behind the application requirements. This study analyzed the most important indicators of air-sea gravimetry, including the density of survey lines, gravimetry accuracy and space resolution, stability and reliability of the air-sea gravimeter, and proposed a gravimetry accuracy assessment system consisting of gravity RMS of error, systematic error and mean error, and an assessment system for the gravimeter stability consisting of the relative accuracy of the scale value, monthly zero-drift, RMS of the monthly nonlinear zero-drift variation and the threshold of the monthly nonlinear zero-drift variation. The mathematic models for the measurement point determination in shipborne gravimetry, E tv s correction for airborne gravimetry, platform tilt correction and evaluation air-sea gravimetry were also analyzed and modified. This work will provide technology support for the composition of the military-civil air-sea gravimetry technical guides.

Downward continuation of airborne gravimetry data based on Poisson integral iteration method

The research and application of airborne gravimetry technology has become one of the hottest topics in gravity field in recent years. Downward continuation is one of the key steps in airborne gravimetry data processing, and the quality of continuation results directly influence the further application of surveying data. The Poisson integral iteration method is proposed in this paper, and the modified Poisson integral discretization formulae are also introduced in the downward continuation of airborne gravimerty data. For the test area in this paper, compared with traditional Poisson integral discretization formula, the continuation result of modified formulae is improved by 10.8 mGal, and the precision of Poisson integral iteration method is in the same amplitude as modified formulae. So the Poisson integral iteration method can reduce the discretization error of Poisson integral formula effectively. Therefore, the research achievements in this paper can be applied directly in the data processing of our country＇s airborne scalar and vector gravimetry.

A Fast Local Level Set Method for Inverse Gravimetry

We propose a fast local level set method for the inverse problem of gravimetry.The theoretical foundation for our approach is based on the following uniqueness result:if an open set D is star-shaped or x3-convex with respect to its center of gravity,then its exterior potential uniquely determines the open set D.To achieve this purpose constructively,the first challenge is how to parametrize this open set D as its boundary may have a variety of possible shapes.To describe those different shapes we propose to use a level-set function to parametrize the unknown boundary of this open set.The second challenge is how to deal with the issue of partial data as gravimetric measurements are only made on a part of a given reference domainΩ.To overcome this difficulty,we propose a linear numerical continuation approach based on the single layer representation to find potentials on the boundary of some artificial domain containing the unknown set D.The third challenge is how to speed up the level set inversion process.Based on some features of the underlying inverse gravimetry problem such as the potential density being constant inside the unknown domain,we propose a novel numerical approach which is able to take advantage of these features so that the computational speed is accelerated by an order of magnitude.We carry out numerical experiments for both two-and three-dimensional cases to demonstrate the effectiveness of the new algorithm.

SmallSat swarm gravimetry:Revealing the interior structure of asteroids and comets

A growing interest in small body exploration has motivated research into the rapid char-acterization of near-Earth objects to meet economic or scientific objectives.Specifically,knowledge of the internal density structure can aid with target selection and enables an understanding of prehistoric planetary formation to be developed.To this end,multi-layer extensions to the polyhedral gravity model are suggested,and an inversion technique is implemented to present their effectiveness.On-orbit gravity gradiometry is simulated and employed in stochastic and deterministic algorithms,with results that imply robustness in both cases.

Corrosion behavior of magnesium in aqueous sulfate-containing electrolytes

Studies have been conducted on the corrosive behavior of magnesium in aqueous sulfate electrolytes(0.5 mol/L MgSO_(4);0.5 mol/L Na2SO_(4);0.5 mol/L MgSO_(4)+0.5 mol/L Na2SO_(4)).The composition structure and morphology of the surface of the samples were studied using scanning electron microscopy in combination with X-ray spectral microanalysis.The results of the experiments showed the formation of a surface film inhomogeneous in its structure and composition with the main components Mg(OH)_(2)and Mg O.An increase in the exposure time of the electrode in solution led to the formation of microcracks on the main film caused by internal stress because of hydration of magnesium oxide produced during corrosion.The salt composition of the electrolyte determines the morphology and thickness of corrosion films due to differences in the solubility of the products formed during the hydrolysis of magnesium oxide and the kinetics of this process.Applying the methods of scanning electron microscopy X-ray electron analysis gravimetry and voltammetry it has been established that at various stages of magnesium corrosion in different electrolytes the growth rates of corrosion films are determined by the kinetics of magnesium oxide formation its hydration and dissolution followed by crystallization in the form of a brucite phase of loose sediments on the surface.

Theories and applications of earthquake-induced gravity variation:Advances and perspectives

Earthquake-induced gravity variation refers to changes in the earth’s gravity field associated with seismic activities.In recent years,development in the theories has greatly promoted seismic deformation research,laying a solid theoretical foundation for the interpretation and application of seismological gravity monitoring.Traditional terrestrial gravity measurements continue to play a significant role in studies of interseismic,co-seismic,and post-seismic gravity field variations.For instance,superconducting gravimeter networks can detect co-seismic gravity change at the sub-micro Gal level.At the same time,the successful launch of satellite gravity missions(e.g.,the Gravity Recovery and Climate Experiment or GRACE)has also facilitated applied studies of the gravity variation associated with large earthquakes,and several remarkable breakthroughs have been achieved.The progress in gravity observation technologies(e.g.,GRACE and superconducting gravimetry)and advances in the theories have jointly promoted seismic deformation studies and raised many new research topics.For example,superconducting gravimetry has played an important role in analyses of episodic tremor,slow-slip events,and interseismic strain patterns;the monitoring of transient gravity signals and related theories have provided a new perspective on earthquake early warning systems;the mass transport detected by the GRACE satellites several months before an earthquake has brought new insights into earthquake prediction methods;the use of artificial intelligence to automatically identify tiny gravity change signals is a new approach to accurate and rapid determination of earthquake magnitude and location.Overall,many significant breakthroughs have been made in recent years,in terms of the theory,application,and observation measures.This article summarizes the progress,with the aim of providing a reference for seismologists and geodetic researchers studying the phenomenon of gravity variation,advances in related theories and applications,and future research directions in this discipline.

Recent gravity changes in China Mainland

Based on results of the mobile gravity measurements of the Crustal Movement Observation Network of China and Digital Earthquake Observation Network of China, this paper shows the pattern of temporal gravity changes in China mainland on a time scale of 2 - 3 years since 1998, and gives an analysis of the patterns. The result shows that the temporal gravity changes basically reflect the current mass movement and occurrence of strong earthquakes.

Recent developments in seismological geodesy

With the advanced development of the modern geodetic techniques, the geodetic obser- vations have been proved to be more powerful to uncover the geophysical phenomena, especially the seismic one, than that in the past time. The recent developments and achievements in the seismological geodesy are summarised here. Several popular geodetic techniques, such as high-rate GNSS, InSAR and Satellite Gravimetry, are introduced first to present their recent contributions in studying the seismic deformations. The developments of the joint inversion of the seismic source parameters from multiple observations are then highlighted. Some outlooks in seismological geodesy are presented in the end.

Temporal gravity changes before the 2008 Yutian Ms7.3 earthquake

Based on the data of the repeated gravity observation network in Chinese mainland since 1998, we analyzed the temporal changes of regional gravity field before the 2008 Yutian Ms7.3 earthquake. The result shows some mid-to-long term （two to ten years） changes during the earthquake＇ s preparation. Notable fea- tures are a gravity increase lasting several years and a relatively large-scaled gradient zone of gravity change, the former indicating a continuous energy accumulation and the latter a possible location of seismic rupture. These gravity changes showed a trend of increase-accelerated increase-decelerated increase, similar to that of the Tangshan Ms7.8 earthquake in 1976. The maximum accumulated gravity change related to the earthquake reached 200 × 10 -8 ms -2.

Impact Estimation and Filtering of Disturbances in FG5 Absolute Gravimeter Observations

Instrumental and environmental disturbances do affect FG5 absolute gravimeter observations and the estimated gravity values, sometimes to the degree that entire measurement campaigns are discarded. We propose a method which moves towards the re-assessment of previously discarded observations. Once an estimate of the frequency and amplitude of a disturbance in a FG5 data set exists, the proposed method can estimate its impact on the estimated gravity value. This is performed through a Gaussian Bell Summation approach of the functional relationship between disturbance frequency and standard deviation of gravity. The filtering of the identified disturbance is realized through a modification of the functional model of the equation of motion in the least squares adjustment of FG5 observations. The results reveal that the Gaussian Bell Summation approximates the frequency—gravity impact relationship sufficiently well with negligible uncertainties, while the accuracy of the detected disturbance frequency defines a limiting factor for the gravity impact estimation. A realistic disturbance of 15 Hz with an amplitude of 1.5 nm had an impact of ≈48 [μGal] on the gravity estimate. The proposed filter approach reduced the impact to ≈12 [μGal], with the remaining effect being almost entirely associated to the uncertainty in disturbance frequency detection.

The absolute gravity measurement by FG5 gravimeter at Great Wall Station,Antarctica

Gravity measurement is of great importance to the height datum in Antarctica. The absolute gravity measurement was carried out at Great Wall Station, Antarctica, using FG5 absolute gravity instrument. The gravity data was processed with corrections of earth tide, ocean tide, polar motion and the atmospher, and the RMS is within -3×10^-8 ms^-2. The vertical and horizontal gravity gradients were measured using 2 LaCoaste ＆ Romberg （LCR） gravimeters. The absolute gravity measurement provides the fundamental data for the validation and calibration of the satellite gravity projects such as CHAMP, GRACE and GOCE, and for the high accuracy geold model.

Zero drift and solid Earth tide extracted from relative gravimetric data with principal component analysis

Zero drift and solid Earth tide corrections to static relative gravirnetric data cannot be ignored. In this paper, a new principal component analysis （PCA） algorithm is presented to extract the zero drift and the solid Earth tide, as signals, from static relative gravimetric data assuming that the components contained in the relative gravimetric data are uncorrelated. Static relative gravity observations from Aug. 15 to Aug. 23, 2014 are used as statistical variables to separate the signal and noise with PCA to obtain desired signals. The results of the linear drift extracted by PCA are consistent with those calculated by the least squares linear fitting, and the differences only reach to 10-2μGal/day order of magnitude. Furthermore, PCA is used to estimate the solid Earth tide from the relative gravimetric data corrected by the zero drift. The statistical results are consistent with the results derived from the solid Earth tide correction provided by the internal software of the CG-5 gravimeter （SCINTREX Limited Ontario Canada）. The statistical results of the differences between the two methods are both less than 8 ,Gal, and the RMSs for 9 days are all less than 5 μGal.

Quantifying Maternal Blood Loss from the Hysterotomy at Cesarean Delivery

Background: With newer protocols, such as delayed cord clamping, becoming routine practice, determining the potential maternal consequences is important. In particular, establishing normative values for blood loss from the hysterotomy would be helpful in addressing techniques to minimize total blood loss for cesarean deliveries. Objective: Blood loss from the hysterotomy during cesarean delivery has not been reported using quantitative methods. We aimed to quantify the rate of blood loss during cesarean delivery from the hysterotomy between creation and closure. Methods: This single center, prospective, case series was collected in 2018. Women with singleton pregnancies undergoing cesarean delivery at ≥37 0/7 weeks at Brigham and Women’s Hospital were included. Delayed cord clamping was performed which allowed for quantification of blood loss through gravimetric methods and descriptive statistics were performed. Results: Twenty patients were included. The mean hysterotomy closure delay for cord blood collection was 47 seconds (SD 10.2) and the mean maternal blood volume collected was 110.8 mL (SD 53.4 mL). Blood loss per minute was calculated with a median of 150 mL/minute (IQR 88.8 mL, 95% CI 109.2 - 190.4 mL). The mean post-operative hematocrit drop was 4.4%, and there were no blood transfusions. There was a single hysterotomy extension and a quantified blood loss of 413 mL per minute. Conclusion: We found a mean blood loss of 150 mL/min without hysterotomy extension. With a hysterotomy extension, the blood lost per minute was more profound. This normative data can be helpful for surgical planning with regards to delayed cord clamping or cord blood collection for banking.