Abstract
Shipborne gravimetry is an essential method to measure the Earth’s gravity field in the coastal and offshore areas. It has the special advantages of high-accuracy and high-resolution measurements in coastal areas compared to other techniques (e.g., satellite gravimetry, airborne gravimetry, and altimetry) used to obtain information about the gravity field. In this paper, we present the data processing strategies of shipborne gravimetry in GFZ. One key point is that the most suitable filter parameters to eliminate disturbing accelerations are determined by studying the GNSS-derived kinematic vertical accelerations and the measurement differences at crossover points. Apart from that, two crucial issues impacting on shipborne gravimetry are the seiches in some harbors and the squat effect in the shallow water. We identified that inclusion of GNSS-derived kinematic vertical accelerations can help to improve the shipborne gravimetry results at these special cases in the Baltic Sea. In the absence of the GNSS-derived vertical accelerations, the cutoff wavelength of the low-pass filter should be large enough to filter out these disturbing acceleration signals which causes a coarser spatial resolution of the gravity measurements. Therefore, the GNSS-derived kinematic vertical accelerations are very useful for optimum shipborne gravimetry. Finally, our shipborne gravimetry measurements are successfully used to verify the previous gravimetry data and improve the current geoid models in the Baltic Sea.
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References
Akaike H (1968) Low pass filter design. Ann Inst Stat Math 20(1):271–297
Barthelmes F (1986) Untersuchungen zur Approximation des äußeren Gravitationsfeldes der Erde durch Punktmassen mit optimierten Positionen. Veroffentlichungen des Zentralinstituts Physik der Erde 92
Bernoulli D (1968) Hydrodynamica (1738). Translated from Latin by T Carmody and H Kobus, Dover pub, p 128
Bilker-Koivula M, Mononen J, Saair T, Förste C, Barthelmes F, Lu B, Ågren J (2017) Improving the geoid model for future GNSS-based navigation in the Baltic Sea. In: Proceedings FIG (international federation of surveyors) working week 2017 surveying the world of tomorrow—from digitalisation to augmented reality, Helsinki, Finland
Blazhnov B (2002) Integrated mobile gravimetric system-development and test results. In: 9th Saint petersburg international conference on integrated navigation systems, St. Petersburg, pp 223–232
Bruton A, Glennie C, Schwarz K (1999) Differentiation for high-precision GPS velocity and acceleration determination. GPS Solut 2(4):7–21
Cannon ME, Lachapelle G, Szarmes MC, Hebert JM, Keith J, Jokerst S (1997) DGPS kinematic carrier phase signal simulation analysis for precise velocity and position determination. Navigation 44(2):231–245
Childers VA, Bell RE, Brozena JM (1999) Airborne gravimetry: an investigation of filtering. Geophysics 64(1):61–69
Darwin GH (1898) The tides and kindred phenomena in the solar system. Houghton Mifflin Harcourt, Boston
Denker H, Roland M (2005) Compilation and evaluation of a consistent marine gravity data set surrounding Europe. In: Sansò F (ed) A window on the future of geodesy. Springer, New York, pp 248–253
Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Technical report, DTIC document
Förste C, Bruinsma S, Abrikosov O, Lemoine J, Marty J, Flechtner F, Balmino G, Barthelmes F, Biancale R (2014) EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services. https://doi.org/10.5880/icgem.2015.1
Google Maps (2018) The Harbor Trelleborg. https://www.google.de/maps/@55.3666474,13.1565697,2893m/data=!3m1!1e3. Accessed 12 Jul 2018
Grossmann A, Morlet J (1984) Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15(4):723–736
Harlan RB (1968) Eotvos corrections for airborne gravimetry. J Geophys Res 73(14):4675–4679
Hàrting A, Reinking J, Ellmer W (2004) Ship squat in hydrography: a study of the surveying vessel Deneb. Int Hydrogr Rev 5(3):41–47
He K (2015) GNSS kinematic position and velocity determination for airborne gravimetry. Ph.D. thesis, Berlin, Technische Universität Berlin, Diss., 2014
He K, Xu T, Förste C, Petrovic S, Barthelmes F, Jiang N, Flechtner F (2016) GNSS precise kinematic positioning for multiple kinematic stations based on a priori distance constraints. Sensors 16(4):470
Hunegnaw A, Hipkin R, Edwards J (2009) A method of error adjustment for marine gravity with application to mean dynamic topography in the northern North Atlantic. J Geod 83(2):161
Jachowski J (2008) Assessment of ship squat in shallow water using CFD. Arch Civil Mech Eng 8(1):27–36
Jekeli C (2001) Inertial navigation systems with geodetic applications. Walter de Gruyter, Berlin
Kaariainen J, Makinen J (1997) The 1979–1996 gravity survey and results of the gravity survey of Finland 1945–1996 NASA (19980024670)
Krasnov A, Sokolov A (2015) A modern software system of a mobile Chekan-AM gravimeter. Gyroscopy Navig 6(4):278–287
Krasnov A, Sokolov A, Usov S (2011) Modern equipment and methods for gravity investigation in hard-to-reach regions. Gyroscopy Navig 2(3):178–183
Krasnov A, Sokolov A, Elinson L (2014) Operational experience with the Chekan-AM gravimeters. Gyroscopy Navig 5(3):181–185
Lequentrec-Lalancette MF (1992) Les sources d’erreur en gravimétrie marine. Rapport Technique Didacticiel du BGI
Lequentrec-Lalancette M, Salaűn C, Bonvalot S, Rouxel D, Bruinsma S (2016) Exploitation of marine gravity measurements of the mediterranean in the validation of global gravity field models. In: International symposium on earth and environmental sciences for future generations. Springer, pp 63–67
Li M, He K, Xu T, Lu B (2018) Robust adaptive filter for shipborne kinematic positioning and velocity determination during the Baltic Sea experiment. GPS Solut 22(3):81
Lu B, Barthelmes F, Petrovic S, Förste C, Flechtner F, Luo Z, He K, Li M (2017) Airborne gravimetry of GEOHALO mission: data processing and gravity field modeling. J Geophys Res Solid Earth. https://doi.org/10.1002/2017JB014425
Okihiro M, Guza R, Seymour R (1993) Excitation of seiche observed in a small harbor. J Geophys Res Oceans 98(C10):18201–18211
Petrovic S, Barthelmes F, Pflug H (2016) Airborne and shipborne gravimetry at GFZ with emphasis on the GEOHALO project. In: Rizos C, Willis P (eds) IAG 150 years: proceedings of the 2013 IAG scientific assembly, Potsdam, Germany, 2013. Springer, pp 313–322. https://doi.org/10.1007/1345_2015_17
Pinkster J (2009) Suction, seiche, and wash effects of passing ships in ports. Trans Soc Naval Archit Mar Eng 117:99
Prokoph A, Barthelmes F (1996) Detection of nonstationarities in geological time series: wavelet transform of chaotic and cyclic sequences. Comput Geosci 22(10):1097–1108
Rabiner LR, Gold B (1975) Theory and application of digital signal processing. Prentice-Hall Inc, Englewood Cliffs, p 777
Schwabe J, Liebsch G, Schirmer U (2016) Refined computation strategies for the new German combined quasigeoid GCG2016. In: Proceedings the “international symposium on gravity, geoid and height systems 2016 (GGHS 2016), Thessaloniki, Greece
Serrano L, Kim D, Langley RB (2004) A single GPS receiver as a real-time, accurate velocity and acceleration sensor. In: Proceedings of the the 17th international technical meeting of the satellite division of the institute of navigation (ION GNSS 2004), Long Beach, CA, USA, vol 2124
Sokolov A (2011) High accuracy airborne gravity measurements. Methods and equipment. In: IFAC proceedings volumes (IFAC-PapersOnline), proceedings 18th IFAC world congress, pp 1889–1891
Varyani K (2006) Squat effects on high speed craft in restricted waterways. Ocean Eng 33(3):365–381
Wessel P, Watts AB (1988) On the accuracy of marine gravity measurements. J Geophys Res Solid Earth 93(B1):393–413
Zheleznyak L (2010) The accuracy of measurements by the CHEKAN-AM gravity system at sea. Izv Phys Solid Earth 46(11):1000–1003
Zheleznyak L, Koneshov V, Krasnov A, Sokolov A, Elinson L (2015) The results of testing the Chekan gravimeter at the Leningrad gravimetric testing area. Izv Phys Solid Earth 51(2):315–320
Acknowledgements
Thanks for the constructive comments and beneficial suggestions from the anonymous reviewers and editors, which help us a lot for improving this manuscript. The measurement campaigns onboard the vessels DENEB, AIRISTO and JACOB HÄGG have been accomplished within the FAMOS project which has been supported by the European Commission within the Connecting Europe Facility (CEF)—Transport Sector under Grant No. INEA/CEF/TRAN/M2014/1027106. Shipborne gravimetry data were provided by the German Research Centre for Geosciences (GFZ). This study is also supported by the Chinese Scholarship Council (201506270158), the Key Laboratory of Geospace Environment and Geodesy, Ministry Education, Wuhan University (16-02-07), the State Key Laboratory of Geo-information Engineering (SKLGIE2017-Z-1-2) and the Natural Science Foundation of China (41374023, 41474019, 41604027).
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Lu, B., Barthelmes, F., Li, M. et al. Shipborne gravimetry in the Baltic Sea: data processing strategies, crucial findings and preliminary geoid determination tests. J Geod 93, 1059–1071 (2019). https://doi.org/10.1007/s00190-018-01225-7
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DOI: https://doi.org/10.1007/s00190-018-01225-7