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Performance estimate of some prototypes of inertial platform and strapdown marine gravimeters
Earth, Planets and Space volumeÂ 72, ArticleÂ number:Â 89 (2020)
Abstract
Marine gravimeter has been proved to be the primary technique to efficiently obtain middletoshort wavelength signals of the earthâ€™s gravity field in geodesy, geodynamics and marine sciences research. In recent years, some prototypes of inertial platform and strapdown marine gravimeters have been developed, where the inertial platform gravimeter systems include CHZII and ZL11, and strapdown gravimeter systems include SAG2M and SGAWZ. In order to validate the performance of these marine gravimeter prototypes, a synchronous test with the widely used gravimeters GT2M and LCR arranged on the same vessel was carried out in the north of South China Sea. All the data are processed according to the survey standard flow, and the performance is estimated by analyzing the errors of the repeat lines and the crossover points under the same environment. The compared results show that all the six gravimeters can meet the precision requirement of marine gravity survey. Meanwhile, the precision results of the improved gravimeters can get close to the precision of gravimeter GT2M, higher than the precision gravimeter LCR.
Main text
Introduction
Global ocean area accounts for 71% of the total area of the earth. The marine gravity anomaly survey plays an important role in the fields of geodesy, geodynamics and marine sciences (Ebbing et al. 2013; Sandwell et al. 2013). Marine gravimeter is the main tool for acquiring the marine gravity anomaly with the movingbased platform, which had been proved to be the primary technique to efficiently obtain middletoshort wavelength gravity anomalies (Sandwell et al. 2013).
At present, several marine gravimeters had been widely used around the world to provide accuracies better than 2 mGal for spatial resolutions down to 2Â km (Liu et al. 2017; Hu et al. 2017), such as twoaxis stable platform gravimeter system LCR (Lacoste and Romberg Airâ€“Sea Gravimeter), KSS31M, MGS6 (Marine Gravity System 6), and gimbaled inertial navigation gravimeter system, GT2M, AIRGrav (Airborne Inertially Referenced Gravimeter), BGM3, ChekanAM. They show up different precision levels in real applications, due to the difference in the measuring principles. A synchronized comparison test on the same platform is the most direct method to evaluate the performance of them. Studinger et al. (2008) had evaluated the relative performance and suitability of airborne gravimeters AIRGrav and GT1A with the BGM3 and LCR from the flight test over the Canadian Rocky Mountains near Calgary, which showed that AIRGrav and GT1A could get higher resolution and precision than the others. Forsberg et al. (2015) compared the gravimeters LCR and ChekanAM in Nepal, and found that two systems can obtain a good agreement result. Ouyang et al. (2013) tested 5 seaâ€“air gravimeters with 4 different types equipped onboard the same Y8 fixed wing aircraft by repeat lines and crossover points, which shows that airborne gravimeter GT1A of Russia has the best technical index of comprehensive performance. Zhang et al. (2015), (2017) test the gravimeters GT2M, KSS31M and ZLS in the same vessel, and pointed out that the results of three marine gravimeters are quite different when the vessel speed and heading change or under the bad sea condition, with the gravimeter GT2M having the best precision. By comprehensive analysis, the gravimeter GT2M by Canadian Micro Gravity was recognized as the best to get the highest precision result in the same measuring environment.
In recent years, some prototypes of inertial platform and strapdown marine gravimeters have been developed, where the inertial platform gravimeter systems include CHZII and ZL11, and strapdown gravimeter systems include SAG2M (Seaâ€“Air Gravimeter2Â Marine) and SGAWZ. They were made by Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Tianjin Navigation Instrument Research Institute, Beijing Institute of Aerospace Control Devices, and National University of Defense Technology, respectively. All of these gravimeters have undergone many sea trials to validate their precision by crossover point and repeat lines alone (Cai et al. 2012, 2013, 2017; Luo et al. 2017; Tu et al. 2015; Wang et al. 2018; Yu et al. 2015; Zhang 2007; Zhang et al. 2019; Zhao et al. 2015; 2020). However, all these gravimeters are not compared together to validate their performance under the same sea conditions. The compared results can be useful for the users of marine gravity survey to make a choice in real applications.
In order to validate the performance of the marine gravimeters CHZII, ZL11, SGAWZ and SAG2M, this paper shows a synchronous comparison test of them with widely used commercial gravimeters GT2M (No. 39) and LCR (No. S129) arranged on the same vessel was carried out in the north of South China Sea.
System description
In this section, the measuring principles of the marine gravimeter prototypes CHZII, ZL11A, SAG2M, SGAWZ developed from Chinese research institutes and the commercial gravimeters GT2M and LCR are described.
The gravimeter CHZII in Fig.Â 1a is based on Hookeâ€™s law, which uses a vertical zerolength spring mounted on a twoaxis stabilization platform. The gravity sensor uses an axisymmetric structure design, consisting of a vertical main spring and a tube quality, which has only one degree of freedom along its own axis of vertical movement (Tu et al. 2015).
The gravimeter ZL11 in Fig.Â 1b consists of a twoaxis Schulertuned inertial stabilized platform with three fiberoptic gyroscopes and three acceleration sensors. A gravity sensor replaces the vertical accelerometer. The gravity sensor is an axial system with a reference mass on a flexible support and an electromagnetic feedback. This design minimizes the crosscoupling effect caused by horizontal acceleration and obtains the gravity anomaly in real time (Zhao et al. 2020; Zhang et al. 2019).
The strapdown gravimeters SAG2M in Fig.Â 1c and SGAWZ in Fig.Â 1d are both based on Newtonâ€™s second law, which obtains gravity acceleration and carrier attitude information through triaxial accelerometers and gyroscopes, and then realizes gravity anomaly extraction from a combination of accelerometers and a kinematic navigation system DGPS in inertial reference frame (Cai et al. 2012, 2013, 2017; Luo et al. 2017; Wang et al. 2018; Yu et al. 2015).
The gravimeter GT2M in Fig.Â 1e is a new marine gravimeter, which has evolved from the highly successful GT1A and GT2A airborne gravimeters. It has a vertically oriented sensor, vertical scalar GPSINS gravimeter with a Schulertuned threeaxis inertial platform. A turntable provides the platformâ€™s azimuth axis control (Gabell et al. 2004; Olson et al. 2011).
The gravimeter LCR in Fig.Â 1f consists of a highly damped, springtype gravity sensor mounted on a gyrostabilized platform with associated electronics for obtaining gravity readings. However, the cablestayed zerolength spring will lead to the crosscoupling effect, which cannot be removed under bad sea conditions (LaCoste et al. 1967; 1982).
Measurement process
Between 4 June 2018 and 25 June 2018, a synchronous comparing test was carried out in the north of South China Sea, with gravimeters CHZII, SAG2M, SGAWZ, ZL11, GT2M (No. 39) and LCR (No. S129) arranged on the same vessel, Xiangyanghong No. 06 Comprehensive Scientific Research Vessel, Fig.Â 2.
The gravimeters were all installed along the central axis of the vessel in the middle part of it, which is the most stable area on the vessel. The maximum deviation distance from the central axis should not exceed 5Â m. During the survey, the navigation position data for all the gravimeters came from the same GNSS (Global Navigation Satellite System) receiver SF3050, installed on the top of the vessel to avoid signal blocking. A vessel coordinate system was constructed to correct the leverarm effects of different gravimeters to make the position of the GNSS coincide exactly with the position of the gravimeters (Jekeli 2000; Li 2013). TableÂ 1 shows the coordinates of the gravimeters and GNSS in the vessel coordinate system.
The survey lasted 22Â days at an average sailing speed of 10 knots. We completed 13 effective gravity profiles, shown in Fig.Â 3, with line L1, L2 and L3 having been roundtrip measured three times, line L6 having been roundtrip measured two times, and getting 39 crossover points. The north to south repeat lines design can reduce the EĂ¶tvĂ¶s effect from the earth rotation, which can better reflect the performance characteristics of the gravimeter itself. However, gravimeter CHZII could get only 11 effective lines without L23 and L4, because of a failure of the temperature control system.
Data processing
In order to compare the performance of the gravimeters fairly, we established a unified process standard. All gravity raw data were processed by zero drift correction, EĂ¶tvĂ¶s correction and normal gravity correction to obtain the freeair gravity anomaly in CGCS 2000 (China Geodetic Coordinate System 2000).
Since the measuring principle of each gravimeter is different, each gravimeter has its own processing mode. The gravimeters CHZII and ZL11 have the same processing flow with LCR, because their measured raw data are only filtered by the lowpass filter without any corrections.
For gravimeter GT2M, the measured raw data is a freeair gravity anomaly, which has been filtered by three different filter length, 150Â s, 300Â s and 600Â s, and has the EĂ¶tvĂ¶s effect and normal gravity effect to be corrected. However, the normal gravity correction formula of GT2M,
is the Helmert equation in the Potsdam reference ellipsoid, which is different from the normal gravity correction formula in CGCS 2000:
Therefore, in order to obtain the freeair gravity anomaly in CGCS 2000, a transformation is needed (Zhang et al. 2017).
Unlike the other gravimeters, the strapdown gravimeters SAG2M and SGAWZ directly measure the specific force and the angular motion information of the carrier system. Based on the Newtonâ€™s second law, gravity can be extracted from a combination of the measured specific force information and the kinematic acceleration of the carrier measured by GNSS. The gravity anomaly calculation formula of the strapdown gravimeter is
where \( \dot{v}_{D} \) is the down component of acceleration of the carrier, \( f_{D} \) is the down component of the specific force, \( w_{ie} \) is the angular velocity of the Earthâ€™s rotation, \( \varphi \) is the latitude of the carrierâ€™s location, \( R_{M} \) and \( R_{N} \) denotes the meridian radius and the prime vertical radius at the point on the reference ellipsoid obtained by orthogonal projection of the measuring point in the direction of the ellipsoid normal, respectively, \( h \) is the height, and \( v_{E} \) and \( v_{N} \) are the eastbound and northbound speed of the carrier, respectively.
Zhao et al. (2015) and Wang et al. (2018) has pointed that the precision of the gravity anomaly extraction depends on the precision of the specific force, which mainly relies on the measurement precisions of the attitude matrix of the carrier and the specific force in the carrier coordinate system during navigation. Due to the random error of the gyroscope and the accelerometer in the strapdown gravimeter drifts over time, a combined navigation approach with a Kalman filter is adopted to correct for the attitude error caused by the drift of the inertial instrument. A detailed strapdown gravimeter data processing flow is demonstrated by Zhao et al. (2015) and Wang et al. (2018).
Survey data comparison
In order to evaluate the performance of the gravimeters, the root mean square error (RMS), systematic deviation (SD) and mean error (ME) of the repeat lines and the crossover points are the main technology specifications to determine their precision and internal consistency (Guo et al. 2008; Huang et al. 2013; Yu et al. 2015). The root mean square error describes the precision of the observed data. The systematic deviation is the arithmetic mean of the observation error, which reflects the systemic change characteristics of observation error. The mean error is the average of the absolute value of the observation error, which describes the discrete degree of the observation error.
For the multimeasured repeat line, we use a combination of any two of the repeat times to estimate the RMS precision, which can reflect the reliability and stability of the gravimeter more comprehensively. The RMS precision of any two repeat lines can be calculated by Eqs.Â 4, 5:
where \( d_{i12} \) is the difference between two measurement value \( g_{i1} \) and \( g_{i2} \) in the repeat line \( i \), \( n \) is the number of observed points in each repeat line.
The SD of repeat line can be calculated by Eq.Â 6:
The ME of repeat line can be calculated by Eq.Â 7:
For the crossover points, the RMS error can be calculated by Eq.Â 8:
where \( d \) is the discrepancy of intersection point gravity anomaly, and \( m \) is the number of intersection points.
The SD error can be calculated by Eq.Â 9:
The ME error can be calculated by Eq.Â 10:
FiguresÂ 4, 5, 6 compare the measured results of the repeat lines L1, L2 and L3 in different sea conditions, all with three roundtrip measurements. We can see that the measured gravity anomalies of the improved gravimeters CHZII, SAG2M, SGAWZ and ZL11 had a good coincident with the measured gravity anomalies of gravimeter GT2M in every repeat line, with slightly different. The gravimeter LCR had the biggest anomalies from the others, which means that the gravimeter LCR had a worst result in the comparison. The main reason for this is that the gravimeter LCR has a strong crosscoupling effect affected by the horizontal accelerations in the rough sea condition (Ouyang et al. 2011; Wang et al. 2018; Zhang et al. 2007), with large roll and pitch angles, especially when the pitch angle is rough, shown in Figs.Â 4 and 6. Genrich and Minster (1991) pointed that the noise caused by the heave and roll of the vessel due to wave action can be well removed by the lowpass filter of the gravimeter. Therefore, pitch angle is the main reason leading to the poor results of gravimeter LCR. In repeat line L2, the gravimeter CHZII only had two effective measurements in the lines L21 and L22, without the L23, as the failure originates from the temperature control system. This also led to three false anomalies in the line L22 and systematic deviation compared to the others in the lines L21 and L22 in Fig.Â 5.
TablesÂ 2, 3, 4 describe the RMS, SD and ME errors statistics results of a combination of two of repeat times of different gravimeters in the repeat lines L1, L2 and L3, indicating that all the six gravimeters can obtain the precision requirement within 2 mGal of marine gravity measurement. However, gravimeter GT2M had the minimum RMS, SD and ME statistic results of all the gravimeters in the repeat lines L1, L2 and L3, with the maximum RMS being 0.36 mGal, SD 0.18 mGal and ME 0.29 mGal. The improved gravimeters CHZII, SAG2M, SGAWZ and ZL11 all had the RMS, SD and ME statistics results less than the gravimeter LCR in the repeat lines. Therefore, we can conclude that the gravimeter GT2M showed the best performance in different sea conditions; improved gravimeters CHZII, SAG2M, SGAWZ and ZL11 were better than gravimeter LCR.
Additionally, we also used the crossover points statistic errors to estimate the performance of different gravimeters. FigureÂ 7 shows the crossover points error distributions for the different gravimeters. TableÂ 5 indicates the maximum error, minimum error, RMS, SE and ME statistic results. We can see that the gravimeter LCR had the largest crossover errors than the others, with the maximum error being 3.88 mGal, and the minimum error being âˆ’â€‰1.94 mGal. The crossover point errors of the other gravimeters were between âˆ’â€‰1.5 mGal and 1.2 mGal. From the RMS statistics results, we can see that the gravimeters GT2M, CHZII, SAG2M, SGAWZ and ZL11 all can have a RMS precision better than 0.5 mGal and the gravimeter LCR a RMS precision with 1.11 mGal. From the SD statistics results, we can see that all the gravimeters showed little system observation errors. From the ME statistics results, the discrete degree of the observation error of gravimeters CHZII, SAG2M, SGAWZ, ZL11 and GT2M are more stable than the gravimeter LCR.
Conclusions
In this paper, we have compared the performance of the improved marine gravimeters CHZII, SAG2M, SGAWZ and ZL11 developed in Chinese research institutions with the widely used marine gravimeters GT2M by Canadian Micro Gravity and LCR S129 by LaCoste & Romberg in sidebyside testing. The purpose of the test program was to evaluate the suitability of these improved systems for research applications by designing different profiles, i.e., measurement surveys conducted on repeated lines and crossover points under different sea conditions. The results show that the gravimeter GT2M can get the best performance in the rough sea condition with the minimum RMS, SD and ME in the statistic errors of the repeat lines and crossover points. This test has demonstrated that the homemade marine gravimeter prototypes CHZII, SAG2M, SGAWZ and ZL11 can get similar precision results to the gravimeter GT2M with RMS precision less than 0.5 mGal, better than the gravimeter LCR. The main findings of this study clearly indicate that the gravimeters we have tested can compete with the accuracy standards currently achieved by the best instruments available on the world market for marine gravimetry.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on any request.
Abbreviations
 RMS:

Root mean square error
 SD:

Systematic deviation
 ME:

Mean error
 GNSS:

Global Navigation Satellite System
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Acknowledgements
We express our sincere gratitude to the editors and reviewers in improving the manuscript, and acknowledge the Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Beijing Institute of Aerospace Control Devices, National University of Defense Technology, and Tianjin Navigation Instrument Research Institute in providing the improved gravimeters to the comparison test.
Funding
This study is supported by the Fundamental Research Funds for National Natural Science Foundation of China (41804169), Natural Science Foundation of Zhejiang Province, China (LQ18D040001), Basic Scientific Research Special Fund Project of Second Institute of Oceanography, MNR (JP1902), National key research and development plan (SQ2018YFF020145), Marine/Airborne Gravimeter Research Project (2011YQ12004505), Open Fund of MLR Key Laboratory of Marine Mineral Resources, MNR,(KLMMR2017B03).
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In this study, YY and JG conceived and designed the experiments. YY, ZW and ZS were responsible for the initial maritime data collection. YY processed the data and wrote the main manuscript text. All authors read and approved the final manuscript.
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Yuan, Y., Gao, J., Wu, Z. et al. Performance estimate of some prototypes of inertial platform and strapdown marine gravimeters. Earth Planets Space 72, 89 (2020). https://doi.org/10.1186/s4062302001219w
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DOI: https://doi.org/10.1186/s4062302001219w