Published

2018-07-01

An alternative method to improve gravity field models by incorporating GOCE gradient data

Método alternativo para mejorar los modelos de campo gravitacional al incorporar información del satélite Explorador de la Circulación Oceánica y de Gravedad

DOI:

https://doi.org/10.15446/esrj.v22n3.64666

Keywords:

Gravity gradients, Model modification, Radial gravity gradient, Noise processing (en)
gradiente gravitacional, modificación de modelos, gradiente gravitacional radial, procesamiento de ruido (es)

Downloads

Authors

  • Xiaoyun Wan
  • Jiangjun Ran

The aim of this paper is to present an alternative method that can be used to improve existing gravity field models via the application of gradient data from Gravity field and Ocean Circulation Explorer (GOCE). First, the proposed algorithm used to construct the observation equation is presented. Then methods for noise processing in both time and space domains aimed at reducing noises are introduced. As an example, the European Improved Gravity model of the Earth by New techniques (EIGEN5C) is modified with gradient observations over the whole lifetime of the GOCE, leading to a new gravity field model named as EGMGOCE (Earth Gravitational Model of GOCE). The results show that the cumulative geoid difference between EGMGOCE and EGM08 is reduced by 4 centimeters compared with that between EIGEN5C and Earth Gravitational Model 2008 (EGM08) up to 200 degrees. The large geoid differences between EGMGOCE and EIGEN5C mainly exist in Africa, South America, Antarctica and Himalaya, which indicates the contribution from GOCE. Compared to the newest GOCE gravity field model resolved by direct method from European Space Agency (ESA), the cumulative geoid difference is reduced by 7 centimeters up to 200 degrees. 

El objetivo de este trabajo es presentar un método alternativo que sea usable para mejorar los modelos de campo gravitacional existentes a través de la aplicación de la información de gradiente ofrecida por el satélite Explorador de la Circulación Oceánica y de Gravedad (GOCE, del inglés Gravity field and Ocean Circulation Explorer). Primero, se presenta el algoritmo propuesto para la construcción de la ecuación de observación. Luego se introducen los métodos para el procesamiento y reducción del ruido tanto en el tiempo como en el espacio. Por ejemplo, el Modelo Europeo Mejorado de Gravedad a través de Técnicas Nuevas (EIGEN5C, del inglés European Improved Gravity model of the Earth by New techniques) se modificó con las observaciones de gradiente del satélite GOCE, en órbita desde marzo de 2009, lo que condujo a un nuevo modelo gravitacional llamado EGMGOCE (Modelo Gravitacional Terrestre del GOCE). Los resultados muestran que la diferencia geoidal acumulada entre el modelo EGMGOCE y el Modelo Gravitacional Terrestre de 2008 (EGM08) se reduce en cuatro centímetros a comparación de la diferencia geoidal entre el EIGEN5C y el EGM08, por encima de los 200 grados. Las mayores diferencias geoidales entre el EGMGOCE y el EIGEN5C se presentan principalmente en África, Suramérica, la Antártica y el Himalaya, lo que muestra la contribución del GOCE. Comparado con el más reciente modelo gravitacional GOCE resuelto a través del método directo por la Agencia Espacial Europea (ESA), la diferencia geoidal se reduce en 7 centímetros por encima de 200 grados.

References

Baur, O., Sneeuw, N., & Grafarend, E.W. (2008). Methodology and use of tensor invariants for satellite gravity gradiometry. Journal of Geodesy, 82(4-5), 279-293.

Bouman, J., Ebbing, J., Fuchs, M., Sebera, J., Lieb, V., Szwillus, W., Haagmans, R., & Novak, P. (2016). Satellite gravity gradient grids for geophysics. Scientific Reports, 6, 21050. DOI:10.1038/srep21050

Bruinsma, S. L., Marty, J. C., Balmino, G., Biancale, R., Foerste, C., Abrikosov, O., & Neumayer, H. (2010). GOCE Gravity Field Recovery by Means of the Direct Numerical Method. ESA Living Planet Symposium, 27th June - 2nd July 2010, Bergen, Norway.

European Space Agency. (1999). Gravity Field and Steady-State Ocean Circulation Mission – The Four Candidate Earth Explorer Core Missions. Technical Report, ESA SP-1233(1), European Space Agency Publications Division, Noordwijk, The Netherlands.

Förste, C., Flechtner, F., & Schmidt, R. (2008). EIGEN-GL05C – a new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. In: General Assembly European Geosciences Union, Vienna, Austria 2008 (Geophysical Research Abstracts, vol. 10, Abstract No. EGU2008-A-06944).

Flechtner, F., Schmidt, R., Meyer, U., Schoene, T., Esselborn, S., Foerste, C., & Rothacher, M. (2006). The benefit of EIGEN gravity field models for altimetry and vice versa. Proceedings of the Symposium on 15 Years of Progress in Radar Altimetry, by Danesy, D. ISBN:92-9092-925-1. Noordwijk, Netherlands: European Space Agency.

Fuchs, M., Bouman, J., Broerse, T., Visser, P., & Vermmersen, B. (2013). Observing coseismic gravity change from the Japan Tohoku-Oki 2011 earthquake with GOCE gravity gradiometry. Journal of Geophysical Research, 118, 5712-5721. DOI:10.1002/jgrb.50381

Gatti, A., Reguzzoni, M., Migliaccio, F., & Sanso, F. (2014). Space-wise grids of gravity gradients from GOCE data at nominal satellite altitude. Presented at the 5th International GOCE User Workshop, 25-28 November 2014, UNESCO, Paris, France

Gilardoni, A., Reguzzoni, M., Sampietro, D., & Sansò, F. (2013). Combing EGM2008 with GOCE gravity field models. Bollettino di Geofisica Teorica ed Applicata, 54(4), 285-302.

Gruber, T., Rummel, R., & Abrikosov, O. (2010). GOCE Level 2 Product Data Handbook, ESA.

Hashemi, F., Ditmar, P., & Klees, R. (2013). The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value. Journal of Geodesy, 87(9), 843-867.

Holota, P. (1989). Boundary Value Problems and Invariants of the Gravitational Tensor in Satellite Gradiometry. Lecture Notes in Earth Sciences, 25, 447-457.

Marchenko, A. N. (2003a). Regional gravity field model from satellite altimetry, gravimetry, and GPS-leveling data in the Black Sea area. Bolletino di Geodesia et Scienze Affini, LXII(4), 246-259.

Marchenko, A. N. (2003b). A note on the eigenvalue – eigenvector problem. In: N. Kühtreiber (Eds,) Festschrift dedicated to Helmut Moritz on the occasion of his 70th birthday (143-154). Institute for Geodesy, Graz University of Technology.

Marchenko, A. N., Marchenko, D. A., & Lopushansky, A. N. (2016). Gravity field models derived from the second degree radial derivatives of the GOCE mission: a case study. Annals of Geophysics, 59(6), 1-11.

Martinec, Z. (2003) Green's function solution to spherical gradiometric boundary-value problems. Journal of Geodesy, 77(1-2), 41-49, DOI: 10.1007/s00190-002-0288-z.

Meng, X. C., Wan, X. Y., Yu, J. H., Zhu, Y. C., & Feng, W. (2016). Optimization method for computing radial gravity gradient using gravity gradient observations. Acta Geodaetica et Cartographica Sinica, 45(7), 775-781.

Pail, R., Bruinsma, S., Migliaccio, F., Förste, C., Goiginger, H., Schuh, W. D., Höck, E., Reguzzoni, M., Brockmann, J. M., Abrikosov, O., Veicherts, M., Fecher, T., Mayrhofer, R., Krasbutter, I., Sansó, F., & Tscherning, C. C. (2011). First GOCE gravity field models derived by three different approaches. Journal of Geodesy, 85, 819-843. DOI: 10.1007/s00190-011-0467-x.

Pail, R., Goiginger, H., Schuh, W. D., Höck, E., Brockmann, J. M., Fecher, T., Gruber, T., Mayer-Gürr, T., Kusche, J., Jäggi, A., & Rieser, D. (2010). Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophysical Research Letters, 37, L20314. DOI: 10.1029/2010GL044906.

Pavlis, N. K., Holmes, S. A., Kenyon, S. C., & Factor, J. K. (2012). The development and evaluation of the earth gravitational model 2008 (EGM2008). Journal of Geophysical Research-Solid Earth, 117, B04406. DOI: 10.1029/2011JB008916.

Reguzzoni, M., & Tselfes, N. (2009). Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. Journal of Geodesy, 83(1), 13-29. DOI: 10.1007/s00190-008-0225-x.

Reigber, C., Bock, R., Förste, C., Grunwaldt, L., Jakowski, N., Liihr, H., Schwintzer, P., & Tilgner, C. (1996). CHAMP Phase B: Executive Summary; Scientific Technical Report STR96/13; GeoForschungsZentrum Potsdam.

Rummel, R. (1986). Satellite gradiometry. Lecture Notes in Earth Sciences, 7, 317-363.

Rummel, R., & van Gelderen, M. (1992). Spectral-analysis of the full gravity tensor. Geophysical Journal International, 111(1), 159–169.

Rummel, R., van Gelderen, M., Koop, R., Schrama, E., Sansó., F., Brovelli, M., Miggliaccio, F., & Sacerdote, F. (1993). Spherical harmonic analysis of satellite gradiometry. Report no. 39, Publications on Geodesy, New Series, Netherlands Geodetic Commission, Delft, The Netherlands.

Rummel, R., & Gruber, T. (2012). Product Acceptance Review (PAR) – Level 2 Product ReportRep., ESA.

Sacerdote, F., & Sansò, F. (1989). Some problems related to satellite gradiometry. Bulletin of Geodesy, 63, 405-415.

Schuh, W. D. (2003). The processing of band-limited measurements: filtering techniques in the least squares context and in the presence of data gaps. Space Science Reviews, 108(1-2), 67-78.

Stummer, C., Siemes, C., Pail, R., Frommknecht, B., & Floberghagen, R. (2012). Upgrade of the GOCE level 1b gradiometer processor. Advances in Space Research, 49(4), 739–752. DOI: 10.1016/j.asr.2011.11.027.

Tapley, B. D., & Bettadpur, S. (2004). The gravity recovery and climate experiment: Mission overview and early results. Geophysical Research Letters, 31(9), 1-4.

Vermeer, M. (1990). Observable quantities in satellite gradiometry. Journal of Geodesy, 64(4), 347-361.

Van Gelderen, M., & Rummel, R. (2001). The solution of the general geodetic boundary value problem by least squares. Journal of Geodesy, 75(1), 1-11.

Wan, X. Y., & Yu, J. H. (2013). Derivation of the radial gradient of the gravity based on non-full tensor satellite gravity gradients. Journal of Geodynamics, 66, 59-64.

Ye, Z., Tenzer, R., Sneeuw, N., Liu, L., & Wild-Pfeiffer, F. (2016). Generalized model for a Moho inversion from gravity and vertical gravity-gradient data. Geophysical Journal International, 207(1),111–128. DOI: https://doi.org/10.1093/gji/ggw251.

Yi, W. Y. (2012). An alternative computation of a gravity field model from GOCE. Advances in Space Research, 50(3), 371-384.

Yu, J. H., & Wan, X. Y. (2011). The frequency analysis of gravity gradients and the methods of filtering processing. In: Proceedings of ‘4th International GOCE User Workshop’, Munich, Germany (ESA SP-696, July 2011).

Yu, J. H., & Zhao, D.M. (2010). The gravitational gradient tensor’s invariants and the related boundary conditions. Science in China Series D-Earth Sciences 53(5), 781–790.

How to Cite

APA

Wan, X. and Ran, J. (2018). An alternative method to improve gravity field models by incorporating GOCE gradient data. Earth Sciences Research Journal, 22(3), 187–193. https://doi.org/10.15446/esrj.v22n3.64666

ACM

[1]
Wan, X. and Ran, J. 2018. An alternative method to improve gravity field models by incorporating GOCE gradient data. Earth Sciences Research Journal. 22, 3 (Jul. 2018), 187–193. DOI:https://doi.org/10.15446/esrj.v22n3.64666.

ACS

(1)
Wan, X.; Ran, J. An alternative method to improve gravity field models by incorporating GOCE gradient data. Earth sci. res. j. 2018, 22, 187-193.

ABNT

WAN, X.; RAN, J. An alternative method to improve gravity field models by incorporating GOCE gradient data. Earth Sciences Research Journal, [S. l.], v. 22, n. 3, p. 187–193, 2018. DOI: 10.15446/esrj.v22n3.64666. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/64666. Acesso em: 20 apr. 2025.

Chicago

Wan, Xiaoyun, and Jiangjun Ran. 2018. “An alternative method to improve gravity field models by incorporating GOCE gradient data”. Earth Sciences Research Journal 22 (3):187-93. https://doi.org/10.15446/esrj.v22n3.64666.

Harvard

Wan, X. and Ran, J. (2018) “An alternative method to improve gravity field models by incorporating GOCE gradient data”, Earth Sciences Research Journal, 22(3), pp. 187–193. doi: 10.15446/esrj.v22n3.64666.

IEEE

[1]
X. Wan and J. Ran, “An alternative method to improve gravity field models by incorporating GOCE gradient data”, Earth sci. res. j., vol. 22, no. 3, pp. 187–193, Jul. 2018.

MLA

Wan, X., and J. Ran. “An alternative method to improve gravity field models by incorporating GOCE gradient data”. Earth Sciences Research Journal, vol. 22, no. 3, July 2018, pp. 187-93, doi:10.15446/esrj.v22n3.64666.

Turabian

Wan, Xiaoyun, and Jiangjun Ran. “An alternative method to improve gravity field models by incorporating GOCE gradient data”. Earth Sciences Research Journal 22, no. 3 (July 1, 2018): 187–193. Accessed April 20, 2025. https://revistas.unal.edu.co/index.php/esrj/article/view/64666.

Vancouver

1.
Wan X, Ran J. An alternative method to improve gravity field models by incorporating GOCE gradient data. Earth sci. res. j. [Internet]. 2018 Jul. 1 [cited 2025 Apr. 20];22(3):187-93. Available from: https://revistas.unal.edu.co/index.php/esrj/article/view/64666

Download Citation

CrossRef Cited-by

CrossRef citations3

1. Xiaoyun Wan, Richard Fiifi Annan, Shuanggen Jin, Xiaoqi Gong. (2020). Vertical Deflections and Gravity Disturbances Derived from HY-2A Data. Remote Sensing, 12(14), p.2287. https://doi.org/10.3390/rs12142287.

2. Yuan Fang, Shuiyuan He, Xiaohong Meng, Jun Wang, Yongkang Gan, Hanhan Tang. (2021). A Fast Method for Calculation of Marine Gravity Anomaly. Applied Sciences, 11(3), p.1265. https://doi.org/10.3390/app11031265.

3. Lijun Zhang, Kecheng Liu, Jinxing Yu, Hesong Han, Qiu Chen, Chongming Chen. (2021). Design of online monitoring system for heavy metal mercury in industrial wastewater based on ZigBee wireless network. Desalination and Water Treatment, 239, p.31. https://doi.org/10.5004/dwt.2021.27811.

Dimensions

PlumX

Plum Print visual indicator of research metrics
  • Citations
  • CrossRef - Citation Indexes: 2
  • Scopus - Citation Indexes: 4
  • Usage
  • SciELO - Full Text Views: 138
  • SciELO - Abstract Views: 16
  • Captures
  • Mendeley - Readers: 4
  • Social Media
  • Facebook - Shares, Likes & Comments: 18
-
see details

Article abstract page views

461

Downloads

License

Copyright (c) 2018 Earth Sciences Research Journal

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Earth Sciences Research Journal holds a Creative Commons Attribution license. 

You are free to:

Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.