Stability maintenance of gravity comparison sites (2017–2024): Environmental factors and data processing strategies 

Stability maintenance of gravity comparison sites (2017–2024): Environmental factors and data processing strategies | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Stability maintenance of gravity comparison sites (2017–2024): Environmental factors and data processing strategies Lishuang Mou, Dong Wang, Jinyang Feng, Qiyu Wang, Jiamin Yao, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8305711/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract To ensure the sustained stability of absolute gravity benchmark points from 2017 to 2024, this work comprehensively examined observational records from superconducting gravimeters (SG) and absolute gravimeters, while quantitatively assessing environmental effects on gravitational acceleration. The annual fluctuation of the SG (iGrav-012k) scale factor reached up to 2.68 nm/s 2 /V, with a weighted average of (–928.702 ± 0.003) nm/s 2 /V (relative accuracy of 0.3‰), offering precise calibration parameters for long-term SG monitoring. By eliminating step discontinuities in SG data using FG5-X249 absolute gravimeter measurements, the residual fitting error decreased to 6.3 µGal. Additionally, SG drift was estimated as 1.0 µGal/year through international comparison datasets and FG5 measurements, considerably improving time series consistency. Further investigation indicated that SG residuals exhibited clear seasonal oscillations, mainly attributed to local hydrological processes and ground deformation near the benchmark sites. By integrating groundwater level, rainfall, and deformation monitoring data, and applying a neural network model to separate hydrological load components, the peak-to-peak residual amplitude was reduced from 15 µGal to 7 µGal. Quantitative analysis revealed that hydrological effects contributed roughly 10 µGal to the seasonal variation, whereas surface deformation exerted only a minor impact (< 2 µGal). The findings confirm that careful data correction and isolation of environmental effects are effective in sustaining the long-term stability of gravity benchmarks. The developed workflow provides a reproducible framework for high-precision gravity site maintenance and supports future dynamic monitoring of regional environmental load responses. Superconducting gravimeter seasonal gravity variation absolute gravity benchmark points Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Precise measurement of gravitational acceleration is a fundamental requirement in Earth science, resource exploration, and space research (Su et al., 2020 ). The intercomparison of absolute gravimeters and the maintenance of gravity comparison points are key to ensuring traceability and reliability in gravity metrology. In 2017, the 10th International Absolute Gravity Comparison, organized by the Chinese Institute of Metrology, strengthened the global gravity standard and ensured the stability of reference sites over time (Wang et al., 2019 ; Wu et al., 2021 ). However, during continuous superconducting gravimeter observations, maintaining data integrity and separating environmental interference became major challenges affecting long-term reliability. This study emphasizes the stability maintenance of the gravitational reference origin established in 2017. Systematic evaluation of superconducting gravimeter records from 2017 to 2024 revealed that “step variations” caused by helium leakage and instrumental drift disrupted data continuity, posing greater challenges in deriving gravity residuals. To address these issues, a refined processing procedure was established, including corrections for step offsets and drift analysis, producing a high-precision residual sequences. Additionally, a neural network model was employed to distinguish gravitational fluctuations linked to groundwater dynamics. When integrated with satellite-derived surface deformation data, it was evident that groundwater variation played the dominant role in seasonal gravity changes. This outcome provides theoretical support for eliminating environmental noise and improving the stability of comparison points, thereby refining the methodology for long-term gravity benchmark maintenance. Superconducting gravimeter scale factor The superconducting gravimeter, as a highly sensitive relative gravimeter, outputs voltage signals that must be converted into gravitational acceleration through a scale factor. Four principal methods are commonly used to determine this scale factor (Rosat et al., 2009 ): (1) Long-term tidal observation Continuous tidal monitoring for 2–3 years, using standard tidal amplitudes to calibrate the superconducting gravimeter. (2) Calibration platforms Employing precision calibration platforms to define the conversion coefficient between voltage and gravity. (3) Mass-shift calibration Performing calibration using a large movable mass (e.g., a “mass sled” or controlled displacement system). (4) Co-located measurement with an absolute gravimeter Carrying out simultaneous observations with an absolute gravimeter (generally FG5) at the same site. Among these, method (4) is most widely adopted worldwide. Hinderer (1991) conducted 24-h continuous simultaneous measurements using a superconducting gravimeter and FG5 absolute gravimeter, achieving a calibration precision of 0.72%. Y. Tamura (Chen et al., 2013) attained 0.2% precision from four days of co-located observations with FG5-109. In China, Chen Xiaodong (Su et al., 2020 ) obtained 0.2% precision through five days of continuous observation using FG5-112 and a superconducting gravimeter. In this research, the superconducting gravimeter was calibrated following the same approach. Data from FG5 and the superconducting gravimeter were fitted using least-squares regression (Francis and Van Dam, 2002 ; Francis et al., 1998 ), as expressed by the following equation: 1 In this expression, y i represents the absolute gravimeter readings (nm/s 2 ), and x i corresponds to the superconducting gravimeter readings (V). The slope b denotes the calibration factor (nm/s 2 /V), and a is the intercept (nm/s 2 ). Measurements are typically conducted during spring tides, and neither gravimeter requires correction for barometric pressure or polar motion. The calibration outcomes of the superconducting gravimeter at the China Institute of Metrology between 2017 and 2024 are summarized in Table 1 and illustrated in Figure. 1. Table 1 Scale factor table Start time Total Observation Duration/h Data Number Scale factor and Accuracy / nm/s 2 /V 2017/11/01 80 8000 -927.554 ±0.497 2018/05/15 73 7300 -928.526 ±0.687 2019/01/04 60 6000 -929.001 ±1.072 2020/08/03 64 6400 -928.702 ±0.887 2021/06/09 25 2500 -928.442 ±1.559 2022/12/07 72 7200 -929.170 ±1.301 2023/12/26 72 7200 -927.970 ±0.727 2024/11/01 60 6000 -930.650 ±0.571 Calibration is typically conducted during spring tides, with about 100 data sets collected per hour (Jia et al., 2015 ; Wang et al., 2018 ). The calibration duration ranges from a minimum of 25 h to a maximum of 80 h. When the total number of drops exceeds 5000, both the calibration value and its precision become stable (Su et al., 2020 ). Except for the 2021 calibration, which involved a smaller data volume, all other calibration sessions recorded more than 5000 drops. The calibration factor varies between − 927 nm/s 2 /V and − 931 nm/s 2 /V, with a maximum annual fluctuation of 2.68 nm/s 2 /V and a minimum of 0.26 nm/s 2 /V. Overall, the calibration factor remains stable, indicating that no external interference occurred during the induction of the superconducting sphere within the magnetic fields of the upper and lower coils. Figure 2 illustrates the distribution of the calibration factor and its standard deviation. In 2024, construction activities within the campus affected gravity observations, resulting in a notable deviation. The weighted average of calibration factors from 2017 to 2024 is (–928.702 ± 0.265) nm/s 2 /V, corresponding to a relative precision of 0.3‰. Subsequent SG data processing employed this weighted average calibration factor. The Steps and drift of the SG 2.1 Correction of the steps During the replacement of the superconducting gravimeter’s cold head in 2020 and 2023, the extended maintenance time led to helium depletion, resulting in step discontinuities in the SG observation data. To obtain continuous gravity observations, these steps required correction. After calibration, the FG5 and SG instruments were co-located for measurement, applying corrections for solid Earth tides and polar motion. The results are shown in Figure. 2, where the black solid line denotes SG observations linked to the 2017 international comparison point (KCRV value), and the red points represent FG5 results with a 2 µGal uncertainty. Both datasets were corrected for solid Earth tides and polar motion. To maintain continuous gravity records at the comparison site, the step offsets in SG data were modeled as follows: $$\:{g}_{1}-{g}_{A}=k\bullet\:{t}_{1}+{b}_{1}$$ 2 $$\:{g}_{2}-{g}_{A}=k\bullet\:{t}_{2}+{b}_{2}$$ 3 $$\:{g}_{3}-{g}_{A}=k\bullet\:{t}_{3}+{b}_{3}$$ 4 Here, g 1 , g 2 , and g 3 are the three SG data segments, g a denotes the corresponding FG5 observations, b 1 –b 3 are the intercepts, and k is the SG drift. The difference (b 2 – b 1 ) represents the first step magnitude, and (b 3 – b 2 ) represents the second. Applying least-squares regression yielded b 1 = 5.4 µGal, k = 0.69 µGal/year, b 2 = 36.6 µGal, and b 3 = 51.8 µGal. Hence, the 2020 step amplitude was 31.2 µGal and the 2023 step was 15.2 µGal, with a residual variance of 6.3 µGal. Due to varying personnel adjustments and imperfect beam waist corrections during long-term FG5 measurements, the derived drift may contain bias. Therefore, a refined drift model will be introduced later. By integrating the step and drift corrections into SG continuous data, the resulting absolute gravity time series (Figure. 3) was obtained. In 2023, the FG5 participated in the international comparison, yielding a beam waist correction of 4.9 µGal and a self-gravity correction of − 1.05 µGal. The comparison report listed an equivalence (Doe) of 1.94 µGal for the FG5, thus the applied correction was 1.91 µGal (Newell et al., 2024 ). After removing the steps and drift from SG data, the corrected results aligned closely with absolute gravimeter measurements, confirming the validity of this quantitative correction method. 2.2 Drift of the SG Estimated from the previous fitting included errors introduced by beam waist inaccuracy and inconsistent optical alignment. For precise long-term monitoring, a more accurate drift estimation was needed. To enhance accuracy, after correcting for steps, a new model was constructed to recalculate SG drift. Because SG drift is extremely small, extending the fitting period improves its reliability (Van Camp and Francis, 2007 ). To minimize uncertainties, beam waist parameters of the absolute gravimeter were recalibrated and the operator was fixed. As shown in Figure. 4, the 2017 KCRV value and ten absolute gravimeter datasets (corrected for self-gravity and beam waist, and adjusted using the 2023 comparison equivalence) were fitted against co-located SG observations using the following relation: $$\:{g}_{1}-{g}_{A}=k\bullet\:{t}_{1}+{b}_{1}$$ 5 In the formula, g 1 is the SG observation, g a is the absolute gravimeter reading, and their initial difference is set to 0 µGal. The SG drift rate was determined as 1.0 µGal/year, 0.31 µGal/year higher than that obtained by the 2.1 method. After applying the step and drift corrections, continuous gravity values at the comparison site were generated, as shown in the figure below. The absolute gravimeter data were corrected for beam waist, self-gravity, and systematic deviations reported in the 2023 international comparison. Minor mismatches at certain points mainly resulted from inaccurate FG5 lighting and beam waist adjustments. After reapplying the beam waist correction, both datasets showed strong agreement. Analysis of seasonal variations in gravity acceleration at comparison points 3.1 Gravity and groundwater level analysis Groundwater fluctuations can significantly affect surface gravitational acceleration (Boy and Hinderer, 2006 ; Crossley et al., 2005 ; Neumeyer et al., 2006 ; Sato et al., 2006 ). To accurately quantify gravity changes, it is essential to remove groundwater-induced variations near comparison sites (Pálinkáš et al., 2013 ). A survey of wells around the Changping campus of the National Institute of Metrology of China was therefore conducted. The China Institute of Geo-Environment Monitoring operates a water-level monitoring station west of Sanhe Village in Nanshao Town, recording monthly water-level data. The figure below presents observations from January 1, 2018, to December 31, 2024. In this figure, the red curve shows the processed gravity data described earlier, while the black curve represents groundwater-level variations. A visible correlation and phase delay can be observed between the two datasets. Considering the nonlinear relationship between gravity and groundwater, this study employed correlation analysis combined with a neural network model to separate groundwater-induced gravity changes. 3.1.1 Program design Based on the gravity residual data and groundwater-level elevation data obtained earlier, the analysis program was developed as illustrated in the figure below. After initial preprocessing, the data were interpolated to synchronize the gravity acceleration and groundwater-level time series. Cross-correlation analysis was then applied to determine the optimal lag step between the two datasets. Using this lag, both series were time-adjusted accordingly. Following the cross-correlation step, neural network modeling and correction were performed. The dataset was divided into training and testing subsets, with 70% of the data used for model training and 30% reserved for testing. This procedure ultimately yielded the corrected gravity acceleration results. 3.1.2 Results After processing through the cross-correlation and neural network algorithms, the gravity acceleration before and after groundwater correction is shown in the figure below. The black curve represents the uncorrected gravity acceleration, while the red curve indicates the data after groundwater-level correction. It is evident from the figure that the peak-to-peak amplitude of gravity acceleration decreased from 15 µGal before correction to 7 µGal after correction. The correction significantly improved data quality, effectively minimizing the seasonal precipitation impact on gravity acceleration. 3.2 Changes in gravitational acceleration caused by ground deformation To obtain information on ground subsidence near the reference point, support was sought from the Chinese Academy of Surveying and Mapping. The academy provided satellite-derived deformation results for the region surrounding the reference point from September 2023 to October 2024, as shown in the accompanying figure. Point 14 in the figure corresponds to the reference point location. The overall deformation rate ranged from − 7 to − 5 mm/year, corresponding to a gravity variation of about 1.5–2 µGal/year (Berrino et al., 1984 ; Ukawa et al., 2008 ). This variation is much smaller than that caused by groundwater fluctuations, indicating that changes in gravitational acceleration at the reference point are primarily governed by groundwater-level variations. Conclusion The superconducting gravimeter installed at the comparison site has exhibited stable operation. Over seven years, the maximum annual change in the scale factor reached 2.68 nm/s 2 /V. After weighting, the average scale factor was determined as (–928.702 ± 0.265) nm/s 2 /V, corresponding to an accuracy of 0.3‰. By fitting the data with the absolute gravimeter FG5, the step variations of the superconducting gravimeter were quantitatively corrected, yielding a fitting residual of 6.3 µGal. Using the 2017 comparison reference value and FG5 measurements from the 2023 international comparison, the SG drift was determined to be 1.0 µGal/year. After applying step and drift corrections, the SG observations closely matched those from the FG5. The residuals of the corrected SG data showed noticeable seasonal variations. By analyzing groundwater-level and ground-deformation data around the comparison site and employing neural network separation of groundwater effects, the peak-to-peak gravity residual decreased from 15 µGal before correction to 7 µGal. From 2023 to 2024, the observed ground deformation remained minimal, producing gravity changes within about 2 µGal. Thus, the seasonal variation of gravitational acceleration at the comparison site is mainly attributed to hydrological factors. Declarations Code and data availability Not applicable Interactive computing environment Not applicable Sample availability Not applicable Video supplement Not applicable Supplement link Not applicable Author contribution Author Lishuang Mou: was responsible for the conception and design of the research study, led the planning of the experimental protocol, and played a key role in formulating the core arguments of the article. Authors Dong Wang and Jinyang Feng: were jointly responsible for performing the experiments, data collection, and validation. Author Qiyu Wang:and Jiamin Yao were responsible for the statistical analysis and interpretation of the data and contributed to the creation of the visualizations for the results. Author Huijuan Ma: was responsible for writing the initial draft of the manuscript and incorporated revisions and feedback from all co-authors. Author Xiaodong Chen: was responsible for literature review, manuscript revision, and language polishing. Author Miaomiao Zhang: provided crucial research tools or experimental materials and offered expert interpretation of the research findings. Author Chunjian Li as the project leader, was responsible for overseeing the entire research process, acquired the funding, and provided final approval of the manuscript. Competing interests The authors declare that they have no conflict of interest. Disclaimer Not applicable Acknowledgements Thank you to the Chinese Academy of Surveying and Mapping and the China Institute of Geo Environment Monitoring for providing data support Financial support This work is supported by the Science and Technology on Metrology and Calibration Laboratory (Grant No. JLJK2024001B003), Central-to-Local Science and Technology Development Special Project in Hubei Province (Grant No. 2025CFC006), and the Fundamental Research Funds for National Institute of Metrology, China (Grant No. AKYZZ2403, AKYZZ2501) Review statement the review statement will be included by Copernicus. References Berrino G, Corrado G, Luongo G, Toro B (1984) Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift. Bull Volcanol 47:187–200. https://doi.org/10.1007/BF01961548 Boy JP, Hinderer J (2006) Study of the seasonal gravity signal in superconducting gravimeter data. 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J Geodesy 95:63. https://doi.org/10.1007/s00190-021-01517-5 Tamura Y, Sato T, Fukuda Y et al (2004) Scale factor calibration of a superconducting gravimeter at Esashi Station, Japan, using absolute gravity measurements[J]. J Geodesy 78(7–8):481–488. 10.1007/s00190-004-0415-0 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8305711","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":580428690,"identity":"1d702d9c-21f7-46c8-8423-6e74f527a944","order_by":0,"name":"Lishuang Mou","email":"","orcid":"","institution":"National Institute of Metrology","correspondingAuthor":false,"prefix":"","firstName":"Lishuang","middleName":"","lastName":"Mou","suffix":""},{"id":580428691,"identity":"c325e787-16eb-4118-b692-b808fba2f3db","order_by":1,"name":"Dong Wang","email":"","orcid":"","institution":"National Institute of 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09:49:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8305711/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8305711/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101234001,"identity":"8c1dc911-632a-46d2-9374-d44410a479a5","added_by":"auto","created_at":"2026-01-27 14:16:25","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":71130,"visible":true,"origin":"","legend":"\u003cp\u003eScale factors.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/eeb3a2645446555c9ec87e8e.png"},{"id":101234004,"identity":"23bf82cd-a969-4d35-8085-5085e293a54f","added_by":"auto","created_at":"2026-01-27 14:16:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78702,"visible":true,"origin":"","legend":"\u003cp\u003eGravity at the comparison sites.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/c1c25e3270a108650c78474f.png"},{"id":101297427,"identity":"c989270f-6238-4ba2-9d19-d823c5d065f7","added_by":"auto","created_at":"2026-01-28 09:27:07","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":83169,"visible":true,"origin":"","legend":"\u003cp\u003eGravity at the comparison sites after correction.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/9af292951c136333dba0e391.png"},{"id":101234011,"identity":"984f0921-12fc-4bb4-85e5-8f710276263e","added_by":"auto","created_at":"2026-01-27 14:16:26","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":57835,"visible":true,"origin":"","legend":"\u003cp\u003eGravity at the comparison sites without drift correction.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/cff0fa682bf4fd04242bb941.png"},{"id":101234007,"identity":"86079d65-aa79-47e0-8619-53f12239c9dc","added_by":"auto","created_at":"2026-01-27 14:16:26","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":118152,"visible":true,"origin":"","legend":"\u003cp\u003eGravity at the comparison sites after correction.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/38df056d7624b4190b05f7dc.png"},{"id":101234009,"identity":"ef2047ff-2ec0-44f8-ac0d-cc6c25a7e9d3","added_by":"auto","created_at":"2026-01-27 14:16:26","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":114341,"visible":true,"origin":"","legend":"\u003cp\u003eGraty and the groundwater level.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/aa60a06aa856d3b82ddaddf0.png"},{"id":101234013,"identity":"d1531ef8-cba8-4a4a-b8e6-b223a4f75a2f","added_by":"auto","created_at":"2026-01-27 14:16:26","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":148429,"visible":true,"origin":"","legend":"\u003cp\u003eThe analysis program.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/cedfe4333e252e82f778f598.png"},{"id":101234003,"identity":"0b7007a9-b9fc-4235-a9dd-0537f5eb7c86","added_by":"auto","created_at":"2026-01-27 14:16:25","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":61361,"visible":true,"origin":"","legend":"\u003cp\u003eGravity changes before and after groundwater correction.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/f7f3de80a9101e4db6890e64.png"},{"id":101234010,"identity":"361f5c3d-e1fe-4420-8db1-dc974d211e1f","added_by":"auto","created_at":"2026-01-27 14:16:26","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":1279431,"visible":true,"origin":"","legend":"\u003cp\u003eGround Deformation near the comparison sites.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/b7ceb4a7ba2e16f3cbb0f68b.png"},{"id":106707720,"identity":"b08885ae-bb2e-4145-a2d5-5f49faa1d860","added_by":"auto","created_at":"2026-04-12 09:55:52","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3110207,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8305711/v1/a206b81d-0363-4507-8796-0232771f83b5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Stability maintenance of gravity comparison sites (2017–2024): Environmental factors and data processing strategies ","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePrecise measurement of gravitational acceleration is a fundamental requirement in Earth science, resource exploration, and space research (Su et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The intercomparison of absolute gravimeters and the maintenance of gravity comparison points are key to ensuring traceability and reliability in gravity metrology. In 2017, the 10th International Absolute Gravity Comparison, organized by the Chinese Institute of Metrology, strengthened the global gravity standard and ensured the stability of reference sites over time (Wang et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wu et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, during continuous superconducting gravimeter observations, maintaining data integrity and separating environmental interference became major challenges affecting long-term reliability.\u003c/p\u003e \u003cp\u003eThis study emphasizes the stability maintenance of the gravitational reference origin established in 2017. Systematic evaluation of superconducting gravimeter records from 2017 to 2024 revealed that \u0026ldquo;step variations\u0026rdquo; caused by helium leakage and instrumental drift disrupted data continuity, posing greater challenges in deriving gravity residuals. To address these issues, a refined processing procedure was established, including corrections for step offsets and drift analysis, producing a high-precision residual sequences.\u003c/p\u003e \u003cp\u003eAdditionally, a neural network model was employed to distinguish gravitational fluctuations linked to groundwater dynamics. When integrated with satellite-derived surface deformation data, it was evident that groundwater variation played the dominant role in seasonal gravity changes. This outcome provides theoretical support for eliminating environmental noise and improving the stability of comparison points, thereby refining the methodology for long-term gravity benchmark maintenance.\u003c/p\u003e"},{"header":"Superconducting gravimeter scale factor","content":"\u003cp\u003eThe superconducting gravimeter, as a highly sensitive relative gravimeter, outputs voltage signals that must be converted into gravitational acceleration through a scale factor. Four principal methods are commonly used to determine this scale factor (Rosat et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2009\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e(1) Long-term tidal observation\u003c/p\u003e \u003cp\u003eContinuous tidal monitoring for 2\u0026ndash;3 years, using standard tidal amplitudes to calibrate the superconducting gravimeter.\u003c/p\u003e \u003cp\u003e(2) Calibration platforms\u003c/p\u003e \u003cp\u003eEmploying precision calibration platforms to define the conversion coefficient between voltage and gravity.\u003c/p\u003e \u003cp\u003e(3) Mass-shift calibration\u003c/p\u003e \u003cp\u003ePerforming calibration using a large movable mass (e.g., a \u0026ldquo;mass sled\u0026rdquo; or controlled displacement system).\u003c/p\u003e \u003cp\u003e(4) Co-located measurement with an absolute gravimeter\u003c/p\u003e \u003cp\u003eCarrying out simultaneous observations with an absolute gravimeter (generally FG5) at the same site.\u003c/p\u003e \u003cp\u003eAmong these, method (4) is most widely adopted worldwide. Hinderer (1991) conducted 24-h continuous simultaneous measurements using a superconducting gravimeter and FG5 absolute gravimeter, achieving a calibration precision of 0.72%. Y. Tamura (Chen et al., 2013) attained 0.2% precision from four days of co-located observations with FG5-109. In China, Chen Xiaodong (Su et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) obtained 0.2% precision through five days of continuous observation using FG5-112 and a superconducting gravimeter. In this research, the superconducting gravimeter was calibrated following the same approach. Data from FG5 and the superconducting gravimeter were fitted using least-squares regression (Francis and Van Dam, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Francis et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1998\u003c/span\u003e), as expressed by the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this expression, y\u003csub\u003ei\u003c/sub\u003e represents the absolute gravimeter readings (nm/s\u003csup\u003e2\u003c/sup\u003e), and x\u003csub\u003ei\u003c/sub\u003e corresponds to the superconducting gravimeter readings (V). The slope b denotes the calibration factor (nm/s\u003csup\u003e2\u003c/sup\u003e/V), and a is the intercept (nm/s\u003csup\u003e2\u003c/sup\u003e). Measurements are typically conducted during spring tides, and neither gravimeter requires correction for barometric pressure or polar motion.\u003c/p\u003e \u003cp\u003eThe calibration outcomes of the superconducting gravimeter at the China Institute of Metrology between 2017 and 2024 are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and illustrated in Figure. 1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eScale factor table\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStart time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal Observation Duration/h\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eData Number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eScale factor and Accuracy / nm/s\u003csup\u003e2\u003c/sup\u003e/V\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2017/11/01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-927.554\u0026nbsp;\u0026plusmn;0.497\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2018/05/15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-928.526\u0026nbsp;\u0026plusmn;0.687\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2019/01/04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-929.001\u0026nbsp;\u0026plusmn;1.072\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020/08/03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-928.702\u0026nbsp;\u0026plusmn;0.887\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2021/06/09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-928.442\u0026nbsp;\u0026plusmn;1.559\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2022/12/07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-929.170\u0026nbsp;\u0026plusmn;1.301\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2023/12/26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-927.970\u0026nbsp;\u0026plusmn;0.727\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2024/11/01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e-930.650\u0026nbsp;\u0026plusmn;0.571\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCalibration is typically conducted during spring tides, with about 100 data sets collected per hour (Jia et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The calibration duration ranges from a minimum of 25 h to a maximum of 80 h. When the total number of drops exceeds 5000, both the calibration value and its precision become stable (Su et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Except for the 2021 calibration, which involved a smaller data volume, all other calibration sessions recorded more than 5000 drops. The calibration factor varies between \u0026minus;\u0026thinsp;927 nm/s\u003csup\u003e2\u003c/sup\u003e/V and \u0026minus;\u0026thinsp;931 nm/s\u003csup\u003e2\u003c/sup\u003e/V, with a maximum annual fluctuation of 2.68 nm/s\u003csup\u003e2\u003c/sup\u003e/V and a minimum of 0.26 nm/s\u003csup\u003e2\u003c/sup\u003e/V. Overall, the calibration factor remains stable, indicating that no external interference occurred during the induction of the superconducting sphere within the magnetic fields of the upper and lower coils. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the distribution of the calibration factor and its standard deviation. In 2024, construction activities within the campus affected gravity observations, resulting in a notable deviation. The weighted average of calibration factors from 2017 to 2024 is (\u0026ndash;928.702\u0026thinsp;\u0026plusmn;\u0026thinsp;0.265) nm/s\u003csup\u003e2\u003c/sup\u003e/V, corresponding to a relative precision of 0.3\u0026permil;. Subsequent SG data processing employed this weighted average calibration factor.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"The Steps and drift of the SG","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Correction of the steps\u003c/h2\u003e \u003cp\u003eDuring the replacement of the superconducting gravimeter\u0026rsquo;s cold head in 2020 and 2023, the extended maintenance time led to helium depletion, resulting in step discontinuities in the SG observation data. To obtain continuous gravity observations, these steps required correction. After calibration, the FG5 and SG instruments were co-located for measurement, applying corrections for solid Earth tides and polar motion. The results are shown in Figure. 2, where the black solid line denotes SG observations linked to the 2017 international comparison point (KCRV value), and the red points represent FG5 results with a 2 \u0026micro;Gal uncertainty. Both datasets were corrected for solid Earth tides and polar motion.\u003c/p\u003e \u003cp\u003eTo maintain continuous gravity records at the comparison site, the step offsets in SG data were modeled as follows:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{g}_{1}-{g}_{A}=k\\bullet\\:{t}_{1}+{b}_{1}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{g}_{2}-{g}_{A}=k\\bullet\\:{t}_{2}+{b}_{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{g}_{3}-{g}_{A}=k\\bullet\\:{t}_{3}+{b}_{3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, g\u003csub\u003e1\u003c/sub\u003e, g\u003csub\u003e2\u003c/sub\u003e, and g\u003csub\u003e3\u003c/sub\u003e are the three SG data segments, g\u003csub\u003ea\u003c/sub\u003e denotes the corresponding FG5 observations, b\u003csub\u003e1\u003c/sub\u003e\u0026ndash;b\u003csub\u003e3\u003c/sub\u003e are the intercepts, and k is the SG drift. The difference (b\u003csub\u003e2\u003c/sub\u003e \u0026ndash; b\u003csub\u003e1\u003c/sub\u003e) represents the first step magnitude, and (b\u003csub\u003e3\u003c/sub\u003e \u0026ndash; b\u003csub\u003e2\u003c/sub\u003e) represents the second.\u003c/p\u003e \u003cp\u003eApplying least-squares regression yielded b\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;5.4 \u0026micro;Gal, k\u0026thinsp;=\u0026thinsp;0.69 \u0026micro;Gal/year, b\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;36.6 \u0026micro;Gal, and b\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;51.8 \u0026micro;Gal. Hence, the 2020 step amplitude was 31.2 \u0026micro;Gal and the 2023 step was 15.2 \u0026micro;Gal, with a residual variance of 6.3 \u0026micro;Gal. Due to varying personnel adjustments and imperfect beam waist corrections during long-term FG5 measurements, the derived drift may contain bias. Therefore, a refined drift model will be introduced later. By integrating the step and drift corrections into SG continuous data, the resulting absolute gravity time series (Figure. 3) was obtained.\u003c/p\u003e \u003cp\u003eIn 2023, the FG5 participated in the international comparison, yielding a beam waist correction of 4.9 \u0026micro;Gal and a self-gravity correction of \u0026minus;\u0026thinsp;1.05 \u0026micro;Gal. The comparison report listed an equivalence (Doe) of 1.94 \u0026micro;Gal for the FG5, thus the applied correction was 1.91 \u0026micro;Gal (Newell et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). After removing the steps and drift from SG data, the corrected results aligned closely with absolute gravimeter measurements, confirming the validity of this quantitative correction method.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Drift of the SG\u003c/h2\u003e \u003cp\u003eEstimated from the previous fitting included errors introduced by beam waist inaccuracy and inconsistent optical alignment. For precise long-term monitoring, a more accurate drift estimation was needed. To enhance accuracy, after correcting for steps, a new model was constructed to recalculate SG drift. Because SG drift is extremely small, extending the fitting period improves its reliability (Van Camp and Francis, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). To minimize uncertainties, beam waist parameters of the absolute gravimeter were recalibrated and the operator was fixed. As shown in Figure. 4, the 2017 KCRV value and ten absolute gravimeter datasets (corrected for self-gravity and beam waist, and adjusted using the 2023 comparison equivalence) were fitted against co-located SG observations using the following relation:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{g}_{1}-{g}_{A}=k\\bullet\\:{t}_{1}+{b}_{1}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the formula, g\u003csub\u003e1\u003c/sub\u003e is the SG observation, g\u003csub\u003ea\u003c/sub\u003e is the absolute gravimeter reading, and their initial difference is set to 0 \u0026micro;Gal.\u003c/p\u003e \u003cp\u003eThe SG drift rate was determined as 1.0 \u0026micro;Gal/year, 0.31 \u0026micro;Gal/year higher than that obtained by the 2.1 method. After applying the step and drift corrections, continuous gravity values at the comparison site were generated, as shown in the figure below. The absolute gravimeter data were corrected for beam waist, self-gravity, and systematic deviations reported in the 2023 international comparison. Minor mismatches at certain points mainly resulted from inaccurate FG5 lighting and beam waist adjustments. After reapplying the beam waist correction, both datasets showed strong agreement.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Analysis of seasonal variations in gravity acceleration at comparison points","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Gravity and groundwater level analysis\u003c/h2\u003e \u003cp\u003eGroundwater fluctuations can significantly affect surface gravitational acceleration (Boy and Hinderer, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Crossley et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Neumeyer et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Sato et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). To accurately quantify gravity changes, it is essential to remove groundwater-induced variations near comparison sites (P\u0026aacute;link\u0026aacute;š et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). A survey of wells around the Changping campus of the National Institute of Metrology of China was therefore conducted. The China Institute of Geo-Environment Monitoring operates a water-level monitoring station west of Sanhe Village in Nanshao Town, recording monthly water-level data. The figure below presents observations from January 1, 2018, to December 31, 2024. In this figure, the red curve shows the processed gravity data described earlier, while the black curve represents groundwater-level variations. A visible correlation and phase delay can be observed between the two datasets. Considering the nonlinear relationship between gravity and groundwater, this study employed correlation analysis combined with a neural network model to separate groundwater-induced gravity changes.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 Program design\u003c/h2\u003e \u003cp\u003eBased on the gravity residual data and groundwater-level elevation data obtained earlier, the analysis program was developed as illustrated in the figure below. After initial preprocessing, the data were interpolated to synchronize the gravity acceleration and groundwater-level time series. Cross-correlation analysis was then applied to determine the optimal lag step between the two datasets. Using this lag, both series were time-adjusted accordingly. Following the cross-correlation step, neural network modeling and correction were performed. The dataset was divided into training and testing subsets, with 70% of the data used for model training and 30% reserved for testing. This procedure ultimately yielded the corrected gravity acceleration results.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 Results\u003c/h2\u003e \u003cp\u003eAfter processing through the cross-correlation and neural network algorithms, the gravity acceleration before and after groundwater correction is shown in the figure below. The black curve represents the uncorrected gravity acceleration, while the red curve indicates the data after groundwater-level correction. It is evident from the figure that the peak-to-peak amplitude of gravity acceleration decreased from 15 \u0026micro;Gal before correction to 7 \u0026micro;Gal after correction. The correction significantly improved data quality, effectively minimizing the seasonal precipitation impact on gravity acceleration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Changes in gravitational acceleration caused by ground deformation\u003c/h2\u003e \u003cp\u003eTo obtain information on ground subsidence near the reference point, support was sought from the Chinese Academy of Surveying and Mapping. The academy provided satellite-derived deformation results for the region surrounding the reference point from September 2023 to October 2024, as shown in the accompanying figure. Point 14 in the figure corresponds to the reference point location. The overall deformation rate ranged from \u0026minus;\u0026thinsp;7 to \u0026minus;\u0026thinsp;5 mm/year, corresponding to a gravity variation of about 1.5\u0026ndash;2 \u0026micro;Gal/year (Berrino et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Ukawa et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). This variation is much smaller than that caused by groundwater fluctuations, indicating that changes in gravitational acceleration at the reference point are primarily governed by groundwater-level variations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe superconducting gravimeter installed at the comparison site has exhibited stable operation. Over seven years, the maximum annual change in the scale factor reached 2.68 nm/s\u003csup\u003e2\u003c/sup\u003e/V. After weighting, the average scale factor was determined as (\u0026ndash;928.702\u0026thinsp;\u0026plusmn;\u0026thinsp;0.265) nm/s\u003csup\u003e2\u003c/sup\u003e/V, corresponding to an accuracy of 0.3\u0026permil;. By fitting the data with the absolute gravimeter FG5, the step variations of the superconducting gravimeter were quantitatively corrected, yielding a fitting residual of 6.3 \u0026micro;Gal. Using the 2017 comparison reference value and FG5 measurements from the 2023 international comparison, the SG drift was determined to be 1.0 \u0026micro;Gal/year. After applying step and drift corrections, the SG observations closely matched those from the FG5. The residuals of the corrected SG data showed noticeable seasonal variations. By analyzing groundwater-level and ground-deformation data around the comparison site and employing neural network separation of groundwater effects, the peak-to-peak gravity residual decreased from 15 \u0026micro;Gal before correction to 7 \u0026micro;Gal. From 2023 to 2024, the observed ground deformation remained minimal, producing gravity changes within about 2 \u0026micro;Gal. Thus, the seasonal variation of gravitational acceleration at the comparison site is mainly attributed to hydrological factors.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003eCode and data availability\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eInteractive computing environment\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eSample availability\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eVideo supplement\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eSupplement link\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eAuthor contribution\u003c/p\u003e\n\u003cp\u003eAuthor Lishuang Mou:\u0026nbsp;was responsible for the conception and design of the research study, led the planning of the experimental protocol, and played a key role in formulating the core arguments of the article.\u003c/p\u003e\n\u003cp\u003eAuthors Dong Wang and Jinyang Feng:\u0026nbsp;were jointly responsible for performing the experiments, data collection, and validation.\u003c/p\u003e\n\u003cp\u003eAuthor Qiyu Wang:and Jiamin Yao\u0026nbsp;were\u0026nbsp;responsible for the statistical analysis and interpretation of the data and contributed to the creation of the visualizations for the results.\u003c/p\u003e\n\u003cp\u003eAuthor Huijuan Ma:\u0026nbsp;was responsible for writing the initial draft of the manuscript and incorporated revisions and feedback from all co-authors.\u003c/p\u003e\n\u003cp\u003eAuthor Xiaodong Chen:\u0026nbsp;was responsible for literature review, manuscript revision, and language polishing.\u003c/p\u003e\n\u003cp\u003eAuthor Miaomiao Zhang:\u0026nbsp;provided crucial research tools or experimental materials and offered expert interpretation of the research findings.\u003c/p\u003e\n\u003cp\u003eAuthor Chunjian Li\u0026nbsp;as the project leader, was responsible for overseeing the entire research process, acquired the funding, and provided final approval of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;Competing interests\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interest.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDisclaimer\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThank you to the Chinese Academy of Surveying and Mapping and the China Institute of Geo Environment Monitoring for providing data support\u003c/p\u003e\n\u003cp\u003eFinancial support\u003c/p\u003e\n\u003cp\u003eThis work is supported by the Science and Technology on Metrology and Calibration Laboratory (Grant No. JLJK2024001B003), Central-to-Local Science and Technology Development Special Project in Hubei Province (Grant No. 2025CFC006), and the Fundamental Research Funds for National Institute of Metrology, China (Grant No. AKYZZ2403, AKYZZ2501)\u003c/p\u003e\n\u003cp\u003eReview statement\u003c/p\u003e\n\u003cp\u003ethe review statement will be included by Copernicus.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBerrino G, Corrado G, Luongo G, Toro B (1984) Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift. 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J Geodesy 78(7\u0026ndash;8):481\u0026ndash;488. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s00190-004-0415-0\u003c/span\u003e\u003cspan address=\"10.1007/s00190-004-0415-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Superconducting gravimeter, seasonal gravity variation, absolute gravity benchmark points","lastPublishedDoi":"10.21203/rs.3.rs-8305711/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8305711/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo ensure the sustained stability of absolute gravity benchmark points from 2017 to 2024, this work comprehensively examined observational records from superconducting gravimeters (SG) and absolute gravimeters, while quantitatively assessing environmental effects on gravitational acceleration. The annual fluctuation of the SG (iGrav-012k) scale factor reached up to 2.68 nm/s\u003csup\u003e2\u003c/sup\u003e/V, with a weighted average of (\u0026ndash;928.702\u0026thinsp;\u0026plusmn;\u0026thinsp;0.003) nm/s\u003csup\u003e2\u003c/sup\u003e/V (relative accuracy of 0.3\u0026permil;), offering precise calibration parameters for long-term SG monitoring. By eliminating step discontinuities in SG data using FG5-X249 absolute gravimeter measurements, the residual fitting error decreased to 6.3 \u0026micro;Gal. Additionally, SG drift was estimated as 1.0 \u0026micro;Gal/year through international comparison datasets and FG5 measurements, considerably improving time series consistency. Further investigation indicated that SG residuals exhibited clear seasonal oscillations, mainly attributed to local hydrological processes and ground deformation near the benchmark sites. By integrating groundwater level, rainfall, and deformation monitoring data, and applying a neural network model to separate hydrological load components, the peak-to-peak residual amplitude was reduced from 15 \u0026micro;Gal to 7 \u0026micro;Gal. Quantitative analysis revealed that hydrological effects contributed roughly 10 \u0026micro;Gal to the seasonal variation, whereas surface deformation exerted only a minor impact (\u0026lt;\u0026thinsp;2 \u0026micro;Gal). The findings confirm that careful data correction and isolation of environmental effects are effective in sustaining the long-term stability of gravity benchmarks. The developed workflow provides a reproducible framework for high-precision gravity site maintenance and supports future dynamic monitoring of regional environmental load responses.\u003c/p\u003e","manuscriptTitle":"Stability maintenance of gravity comparison sites (2017–2024): Environmental factors and data processing strategies ","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-27 14:16:14","doi":"10.21203/rs.3.rs-8305711/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6e39ee9a-9fee-444b-9f1d-45f766068f58","owner":[],"postedDate":"January 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-12T09:54:28+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-27 14:16:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8305711","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8305711","identity":"rs-8305711","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}