Preliminary geoid mapping results by Fugro s improved Micro-g LaCoste turnkey airborne gravity system

Transcription

1 J. Geod. Sci. 2015; 5:80 96 Research Article Open Access D. Zhong* and R. W. Kingdon Preliminary geoid mapping results by Fugro s improved Micro-g LaCoste turnkey airborne gravity system DOI /jogs Received January 26, 2015; accepted May 22, 2015 Abstract: In this paper, we introduce the Micro-g LaCoste Turnkey Airborne Gravity System (TAGS) with Fugro s improved gravity processing and geoid modeling software package for regional gravity field mapping and geoid determination. Three test areas with different topographic characteristics under the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project of the US NOAA National Geodetic Surveys (NGS) were used for case studies and determine the available accuracy of the system. The preliminary results of all these test cases show that the system with Fugro s improved gravity and geoid processing software package is able to achieve a comparable geoid mapping result to traditional terrestrial methods. Keywords: Airborne gravimetry; geoid and quasigeoid; geoid determination; geoid mapping software data collected at a variety of moderate altitudes from 6 to 7.5 km, but is challenging because of the presence of mountains up to about 4 km in height. The third test area is over New Hampshire, USA and Quebec, Canada with a mixed topography up to about 1.8 km in height. The data were collected at a flight altitude about 5.5 km. This paper presents preliminary geoid mapping results for all three test cases, and compares them to traditional geoid determination results based on terrestrial gravity surveys. First, an overview of the Micro-g La- Coste TAGS airborne gravity system for geoid mapping is given with discussions of Fugro s improvements in gravity data processing. Then the geoid mapping approach is summarised, and test results are presented with a processing diagram from the raw gravity calculation to final geoid mapping results. Finally, conclusions drawn from the study are presented. 1 Introduction Since 2008, Fugro has been actively developing airborne geoid mapping capability. Its first generation airborne geoid mapping system based on the Micro-g LaCoste Turnkey Airborne Gravity System (TAGS) is now ready to serve clients. In order to determine the accuracy of Fugro s improved system, three test areas observed under the US NOAA National Geodetic Surveys (NGS) GRAV-D project NOAA NGS (2007) were chosen for case studies. The first test area is in Louisiana and has relatively low topography less than 500 meters in height, but data collected at a high flight altitude about 10 km. The second test area in California has *Corresponding Author: D. Zhong: Fugro Geospatial Inc., 7320 Executive Way Frederick, MD USA, dzhong@fugro.com R. W. Kingdon: Department of Geodesy and Geomatics Engineering, University of New Brunswick. P.O. Box 4400, Fredericton, New Brunswick E3B 5A3, Canada 2 Fugro s improved TAGS airborne gravity system for geoid mapping 2.1 Overview of the system Fugro s airborne gravity system for regional gravity field mapping and geoid determination is built upon the Microg LaCoste TAGS with an improved gravity data processing and geoid modelling software package. The survey instrument of the system is the TAGS s AIR III gravimeter, a beam-type, zero-length spring gravity sensor on a gyrostabilized platform Micro-g LaCoste (2010a). This modern gravimeter measures to 0.01 mgal resolution, has a computerized user-friendly interface, and provides digital data files including horizontal accelerometer output. The software package consists of following 3 programs: GravGNSS a specialized airborne GNSS data processing program for accurate position, velocity and acceleration solutions D. Zhong et al., licensee De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

2 Preliminary geoid mapping results 81 GravPRO a specialized airborne gravity data processing program developed by Fugro Zhong et al. (2015) GravGEOID an improved and specialized geoid mapping suite based on two well-known academic software packages SHGeo Vaníček et al. (2009) and GRAVSOFT Forsberg and Tscherning (2008) for regional gravimetric geoid or quasigeoid determination, modified for use with airborne gravity surveys (more details in section 3). To achieve the best results possible for regional gravity field mapping and geoid determination with the system, Fugro has been tuning and improving these programs for the past 5 years under a cooperation and partnership program between Fugro Geospatial and the US National Geodetic Surveys (NGS) GRAV-D project. The main research and development results include improvements to the airborne gravity processing and specialization of geoid mapping software. 2.2 Improvements to the airborne gravity processing The final gravity calculation formula of the TAGS gravimeter is as follows GRAV-D Science Team (2012a); Zhong et al. (2015) g = g raw a vertical + δg tilt δg drift + g basetie (1) where g raw is a raw gravity measurement from the gravimeter, a vertical is the the vertical acceleration of the moving aircraft including the Eötvös corrections Harlan (1968), δg tilt is the instrument platform tilt or off-level correction, δg drift is the drift correction of the gravimeter and g basetie is the reference gravity at the basetie. From the Eq. (1) and practical surveys, we recognized that the following four factors will influence the final gravity results significantly the instrument parameters used for calculating the raw gravity g raw, the determination method of the vertical acceleration correction a vertical = a GPS δg Etvs, the modelling method for the platform tilt correction δgtilt, and the low pass filter used to filter out high frequency noises from the final gravity observations. To improve the results, Fugro has been intensively investigating each of these factors. First of all, a specialized GNSS data processing program, GravGNSS, was developed. With GravGNSS, the vertical acceleration corrections can be calculated not only from the post-processed positions from commercial GNSS data processing software for a so-called position-based acceleration solution, but also from raw carrier phase observations such as GPS L1 and L2 phases for a so-called carrier phase-based acceleration solution Jekeli and Garcia (1997); Kennedy (2002). The position-based acceleration can also be calculated from a GNSS/IMU integrated position solution if a high grade IMU is installed with the gravimeter. With these different GNSS acceleration solutions, the corresponding gravity solutions can be compared and optimized Zhong and Kingdon (2013). Secondly, we optimized the platform tilt or offlevel correction models from different researchers and developers LaCoste (1967); Swain (1996); Valliant (1992); Peters and Brozena (1995); Olesen (2002). Thirdly, we developed effective and efficient instrument calibration methods based on repeat line surveys, the crossover error adjustment, and the gravity values from accurate terrestrial gravity surveys or from a high quality Global Gravity Model (GGM) such as EGM2008 Pavlis et al. (2008). With these methods, the gravimeter instrument parameters can be calibrated to remove some systematic biases of the instrument Zhong et al. (2015). Fourthly, we developed a low pass filter design tool based on repeat line analysis or comparison with accurate gravity values from terrestrial gravity surveys. Finally, we designed a solution optimization procedure based on minimization of crossover errors. Through this procedure, the quality of the final gravity solution is not only evaluated but also optimized from multiple GNSS acceleration solutions Zhong and Kingdon (2013). 3 Geoid mapping software and solutions Fugro s geoid mapping software is developed from two well-known academic software packages: SHGeo from University of New Brunswick Vaníček et al. (2009) and GRAVSOFT from the Danish Space Institute Forsberg and Tscherning (2008). Based on these two software packages, we developed two solutions adapted to use airborne gravity data observation as an input. One is the SHGeo based geoid mapping solution (GMS) and another is the GRAV- SOFT based quasigeoid mapping solution (QGMS). The Geoid Mapping Solutions (GMS) follows a variation of the Stokes-Helmert technique Vaníček and Martinec (1994) called the "three space scenario" Yang (2005). Following this scenario, gravity anomalies observed at flying height are first converted into the no-topography (NT)

3 82 D. Zhong et al. space (where they are called NT anomalies) by removing all effects of topography. The gravity anomalies are smoother in the NT space than in the real or Helmert space. As with the anomalies in the Helmert space, the NT anomalies are harmonic between the geoid and the observation points, and so can be downward continued to the geoid using the inverse Poisson integral approach as described by Vaníček et al. (1996). The Poisson downward continuation is solved in a least squares sense, transforming gravity anomalies at flying height, observed at scattered points, to a grid of gravity anomalies on the geoid. The aliasing effects that gridding is normally susceptible to are minimized by use of the smooth NT anomaly field. The NT anomalies, once downward continued to the geoid, are converted to the Helmert space by adding to them the effects of the topographical masses flattened ("condensed") onto the geoid. The resulting Helmert gravity anomalies are not significantly affected by variations in topographical density, and so are ideal for conversion to geoidal undulations via the Stokes s integration process. At this stage, a reference field based on a global geopotential model (GGM) (converted into the Helmert space) with a resolution of about 220 km at the equator (spherical harmonic degree/order 90) is subtracted from the Helmert gravity anomalies, creating residual Helmert gravity anomalies. Stokes s integration is applied to the residual anomalies, using a modified spheroidal kernel to filter out any longwavelength (below degree/order 90) components of the gravity field not removed when the reference field was subtracted. This converts the residual Helmert gravity anomalies into geoid-ellipsoid separations in the Helmert space. The resulting residual geoid is called the residual Helmet cogeoid. A GGM is again used to determine components of the Helmert cogeoid, corresponding to those of the subtracted reference field, and these are added to the residual Helmert cogeoid to create a complete Helmert cogeoid. This is then transformed into the actual geoid in the real space by subtracting the effects on the geoid of condensed topography, and adding back the effects of the actual topography Vaníček et al. (2009). Since we care about long wavelengths for the reference field with GMS, we can usually use a satellite-based GGM up to degree and order 90 or 120 for the reference field computation. For this study, we took simply EGM08 Pavlis et al. (2008) up to degree and order 90 for the reference field of GMS. Quasigeoid Mapping Solutions (QGMS) uses a "remove-compute-restore" technique Forsberg and Tscherning (2008). In this method, gravity values on the topographical surface are used as input. Before processing, airborne gravity data, are downward continued to the topographical surface by calculating the change in gravity with height using a high-resolution GGM such as EGM08 Pavlis et al. (2008) or by least squares collocation Forsberg (2002). For this study, EGM08 was used. Having obtained gravity anomalies on the topographical surface, the "remove" step is performed, in two parts. First, the gravity given by a high-resolution GGM, which includes topographical effects up to the wavelength of the GGM used, is subtracted from the gravity observations. Second, effects of the topography not included in GGM gravity, ie. the residual terrain model (RTM) effects, are also subtracted from the input gravity anomalies. The remainder when these components have been removed is called the residual gravity anomaly, and is both smooth and small in magnitude. In the "compute" step, the residual gravity anomaly is gridded by a least squares collocation (similar to Kriging) method Forsberg and Tscherning (2008), and then Stokes s integration is applied to transform the residual gravity anomalies to their corresponding residual quasigeoid heights or height anomalies. Once the residual quasigeoid heights are computed, the contributions to the quasigeoid of the high-resolution GGM plus the residual topographical effects, which were subtracted before, are added back to the solution. This is the "restore" step, and its result is a determination of the regional quasigeoid. For this study, we used the EGM08 up to its highest degree and order 2190 as the high-resolution GGM. It is worth pointing out here that, theoretically, the geoid and the quasigeoid can be converted to one another to a high degree of accuracy Flury and Rummel (2009, e.g.). However, in practice the quality of such conversions depends on the accuracy of the Bouguer anomalies used for the conversions. If the Bouguer anomalies are derived from the gravity observations, the observation errors have direct influences on the converted geoid or quasigeoid. To remove part of the conversion errors, a Gaussian filter can be used to smooth the converted geoid or quasigeoid. In the direct geoid or quasigeoid calculations, the gravity observation errors are largely filtered out during Stokes s integration. This is why the GravGEOID software includes both GMS and QGMS for direct geoid and quasigeoid calculations. Further, comparisons between the GMS and the converted QGMS results, or the QGMS and converted GMS results, provide additional solution validation by independent computation methods. To make the QGMS comparable with the GMS and other geoid models available for the test areas in this study, we converted the quasigeoid to geoid by the program N2ZETA of the GRAVSOFT software package. The Bouguer anomalies used for the conversion are derived from the gridded residual gravity anomalies by restoring

4 Preliminary geoid mapping results 83 The airborne gravity data over all test areas were collected by a similar procedure, using the Micro-g TAGS airborne gravity system GRAV-D Science Team (2012a). The data processing from the raw gravity calculation to the final geoid or quasigeoid determination is done by Fugro s software GravPRO v6.0, GravGNSS v2.4, and GravGEOID v2.0. Fig. 1 shows an overview of all data processing steps for the airborne gravity preparation, as well as, the GMS and the QGMS solutions in this study. For the geoid determination in all three test cases, we used the new collected airborne gravity data only as input observations and the following supplemental data: the EGM08 global geopotential model Pavlis et al. (2008), the global topographical model DTM2006 and the 3 ACE2 DTM Smith and Berry (2010) for the GMS, and the 3, 30 and 5 DTM generated from the NASA SRTM3 DTM Rodriguez (2005) for the QGMS. Figure 1: Overview of data processing steps for airborne gravity, geoid (GMS) and quasigeoid (QGMS). the RTM gravity effects and EGM2008 contributions. No Gaussian filter was used to smooth the converted geoid. 4 Geoid mapping results In order to examine the available accuracy of Fugro s improved TAGS airborne gravity system for regional gravity field mapping and geoid determination, three test areas under the US NOAA NGS GRAV-D project NOAA NGS (2007) were chosen for case studies. The first test area is in Louisiana and has relatively low topography (less than 500 meters in height), but data collected at a high flight altitude of about 10 km. The second test area in California has data collected at a variety of moderate altitudes from 6 to 7.5 km, but is challenging because of the presence of mountains up to about 4 km in height. The third test area is over New Hampshire, USA and Quebec, Canada with a mixed topography up to about 1.8 km in height. The data were collected at a flight altitude of about 5.5 km. We didn t use the same DTM for both GMS and QGMS solutions for convenience. However, both products can use either DTM if it is converted into the correct format. As our purpose in this study is to examine the available accuracy of the improved TAGS airborne gravity system for regional geoid mapping, we limited our result evaluations to the GMS or the converted QGMS results based on the airborne gravity only. All evaluations are based on comparing the calculated results to geoid undulations determined by GPS and levelling at benchmarks, or to other geoid models which are determined by different modelling techniques and data sources such as the US gravimetric geoid model 2012 (USGG12), Canada gravimetric geoid model 2013 (CGG13) Natural Resources Canada (2013) and a geoid derived from the global geopotential model EGM08 Pavlis et al. (2008). The main quantity used to discuss accuracy will be the standard deviation of result differences, as this is the most common metric of geoid accuracy. It is recognized, however, that range and bias of the results are also relevant accuracy metrics. 4.1 Louisiana test case The Louisiana test area covers part of the data block CS02 under the NOAA NGS GRAV-D project, which is located in the Central Time Zone, south of 40 latitude. This was the second (02) block of data completed in that region. Block CS02 is 430 km by 460 km in the Gulf of Mexico, covering coastal areas of Texas and Louisiana and ocean areas from 200 to 300 km offshore GRAV-D Science Team (2012b).

5 84 D. Zhong et al. Table 1: Synopsis of survey layout and execution for Louisiana test area Survey Name LA08 (Louisiana 2008) Airport Base of Operations Louis Armstrong New Orleans Intl (MSY), New Orleans, LA Geographic Location Louisiana, Mississippi, Gulf of Mexico Dates of Airborne Operations Oct. 20 Nov. 23, 2008 Aircraft NOAA Cessna Citation II (N52RF) Engines, Number and Type 2, Jet Gravity Instrumentation Micro-g LaCoste (MGL) TAGS S-137 (relative), MGL FG (absolute), MGL G-157, G-81, and D-43 (relative) GPS Instrumentation NovAtel DL-4 Plus, Applanix POS AV 510 (GPS + IMU) Line Spacing Data Lines: 10 km, Cross Lines: ~40 km Type of Layout Regular data lines & regular cross lines Nominal Survey Altitude 10,606 m (35,000 ft) Nominal Aircraft Ground Speed 280 knots Number of Lines Data Lines: 34, Cross Lines: 9 Number of Crossovers 306 Figure 2: Data coverage of Louisiana test area plotted in Google Earth Airborne gravity data in Block CS02 were collected through 18 flights that include 34 data lines and 9 cross tie lines. All data and cross flights were done at about 10,600 m with the same aircraft and instrument suite. Table 1 gives a synopsis of survey layout and execution for the data. Fig. 2 shows the data coverage, plotted in Google Earth. The NOAA Cessna Citation II was used for data acquisition. This aircraft had two GPS antennas available for scientific measurements and both were used at different times during the survey. Three geodetic-quality GPS receivers shared the antennas: two NovAtel DL-4 Plus (included as part of the TAGS gravimeter timing unit) and a Trimble (inside the Applanix POS AV 510 system). The No- Figure 3: Topographical heights in the Louisiana test area from SRTM 30 data in 10 m contours. The height range within the target geoid area is from 0 to 170 m. vatels had a data rate of 1 Hz and the Trimble of 10 Hz. The Applanix POS AV 510 system also contained an Inertial Measurement Unit (IMU) that recorded aircraft orientation information at 200 Hz during the flight, including pitch, roll, yaw, and heading. On the ground, one backup NovAtel DL-4 Plus (TAGS timing unit) recorded at 1 Hz and one Ashtech Z-Surveyor also recorded at 1 Hz served as GPS base stations throughout the survey.

6 Preliminary geoid mapping results 85 Table 2: Statistics of the differences between the different geoids for the Louisiana test area. Unit is in cm Statistic GMS GMS QGMS GMS QGMS USGG12 QGMS USGG12 USGG12 EGM08 EGM08 EGM08 Min Max Range Std. dev Bias * * the bias was removed from the minimum and maximum differences. This applies to all following comparisons between different models. resolution of 6.5 km at the nominal flight speed 280 knots as shown in Fig. 4. The variation of observed gravity values ranges from 40 to +40 mgal. In total there are free-air gravity anomaly observations covering the region (27.33 < ϕ <31.15 ) and ( < λ < ). The estimated RMS accuracy from 339 crossover errors is 0.8 mgal after a crossover adjustment GMS and QGMS vs. EGM08 and USGG12 Figure 4: Observed free-air gravity anomalies in the Louisiana test area ranges from 40 to 40 mgal. A Micro-g LaCoste TAGS gravimeter with serial number 137 was used for the data acquisition. The TAGS records data at 1 Hz and has a NovAtel timing unit mounted on the gravimeter. The gravimeter also records an environmental file at 0.1 Hz. For more information about the instrument, refer to its user manual Micro-g LaCoste (2010a). To transform the GPS position from the phase center of the GPS antenna to meter s sensor position, the lever arm between the TAGS and GPS antennas were measured and used to correct the lever arm effect with the attitude determined by the Applanix POS AV 510 system. The topographic heights in this test area range from 0 m to about 170 m, as shown in Fig. 3, with target geoid area shown as a grey rectangle. The observed free-air gravity anomalies were filtered using a low pass filter of 90 seconds duration, corresponding to a half-wavelength spatial The geoids computed from GMS directly and converted from the QGMS solution are shown in Fig. 5(a) and 5(b). In comparison to EGM08 and USGG12 geoid which are shown alongside the GMS and the QGMS geoid in Fig. 5(c) and 5(d), their differences and comparison statistics are given in Table 2. From the comparisons between the different geoids above, we can see that significant biases exist in all models except the GMS and EGM08 models, which differ by only about 5 cm. After the biases are removed, all of them, i.e. the GMS, the QGMS, EGM08 and USGG12, match each other very well. The comparison between the GMS and the QGMS shows a standard deviation 1.7 cm. In comparison to USGG12, the model comparison accuracy is 1.4 and 2.0 cm for the QGMS and the GMS respectively. In comparison to EGM08, the model accuracies are similar. Since USGG12 was based on terrestrial and marine gravity data and determined by a different method, we may conclude that Fugro s airborne geoid mapping technology is reliable and a model agreement accuracy of 2 cm is achievable for flat areas. Since the Louisiana test area is very flat, the plots of the different geoids don t show significant differences in their spatial resolution: they all look the same or similar. To compare the airborne and terrestrial gravimetric geoids in more detail, we plotted the differences between the two airborne geoids from the USGG12 geoid in Fig. 6(a)

7 86 D. Zhong et al. Figure 5: GMS (a) and QGMS (b) geoid vs. EGM08 (c) and USGG12 (d) geoid for the Louisiana test area in 2 cm contours. Figure 6: GMS (a) and QGMS (b) differences from the USGG12 geoid for the Louisiana test area in 1 cm contours. and 6(b). From these two plots, we can see that both of the GMS and the QGMS airborne geoids match the terrestrial gravimetric geoid USGG12 very well. Overall, the standard deviation of the differences is 2.0 cm and 1.4 cm for the GMS and the QGMS respectively. Only a small area near latitude 29.75, longitude shows some significant difference by 10.0 cm and 7.4 cm. The reason for these big differences is actually due to unavailability of terrestrial and/or marine gravity data for modelling the USGG12: that area is a small island where no terrestrial gravity ob-

8 Preliminary geoid mapping results 87 Table 3: Statistics of the differences between the different geoids and GPS-levelling benchmarks for the Louisiana test area. Unit is in cm Statistic GMS QGMS USGG12 EGM08 GPS-Levelling GPS-Levelling GPS-Levelling GPS-Levelling No of Benchmarks Min Max Range Std. dev Bias * Figure 7: Data coverage of California test area plotted in Google Earth servations were available, and so the difference there represents an improvement due to the availability of airborne gravity data GMS and QGMS vs. GPS-Levelling Assessments by NGS of the GPS-levelling benchmarks in this area indicate that 8 of the 107 available GPS-levelling benchmarks are of poor quality and are not reliable for geoid evaluation Milbert (1998). Therefore, these 8 GPSlevelling benchmarks are excluded for the result in Table 3. For a comparison, the results of the EGM08 and USGG12 geoid are also given in Table 3 alongside the comparison results of the GMS and the QGMS to the GPS-levelling benchmarks. Figure 8: Topographical heights in the California test area from SRTM 30 data in 200 meter contours. The height range within the target geoid area is from 0 to 4070 meters. From the statistics in Table 3, we can see that all geoid models show an accuracy comparable to the achievable accuracy of GPS height determination at about 3 cm. The discrepancies between the GMS and QGMS geoid and the GPS-levelling results both are comparable to that of the USGG12 results. Because USGG12 was computed from terrestrial and marine gravity data, we may conclude again that Fugro s airborne gravimetric geoid solutions are able to achieve a comparable accuracy with traditional geoid solutions based on terrestrial gravity data. 4.2 California Test Case The California test area covers the data block PN01 under the NOAA NGS GRAV-D project, which is located in the Pa-

9 88 D. Zhong et al. Table 4: Synopsis of survey layout and execution for California test area Survey Name CA11 (California 2011) Airport Base of Operations Sacramento International Airport (SMF), Sacramento, CA Geographic Location California, Oregon, Pacific Ocean Dates of Airborne Operations Jan. 4 Feb. 25th 2011 Aircraft Alaska Fire Services (BLM) Pilatus PC-12 Engines, Number and Type 1, Turboprop Gravity Instrumentation Micro-g LaCoste (MGL) TAGS S-137 (relative), MGL A-10 (absolute) MGL G-6, G-81, and D-17 (relative) GPS Instrumentation NovAtel DL-4 Plus, Applanix POS AV 510 (GPS + IMU) NovAtel SPAN-SE with Honeywell µirs (GPS + IMU) Line Spacing Data Lines: 10 km, Cross Lines: ~80 km Type of Layout Regular data lines & regular cross lines Nominal Survey Altitude 6060 m (20,000 ft) Nominal Aircraft Ground Speed 225 knots Number of Lines Data Lines: 45, Cross Lines: 7 Number of Crossovers 315 Figure 9: Observed free-air gravity anomalies in the California test area ranges from 80 to 90 mgal cific Time Zone, north of 40 latitude. This was the first (01) block of data completed in that region. Block PN01 is 650 km by 450 km, covering coastal areas of California and Oregon as well as ocean areas from 50 to 180 km offshore GRAV-D Science Team (2012c). Fig. 7 shows the data coverage, plotted in Google Earth. Unlike the Louisiana test area, the topographic heights within the target geoid area range from 0 to 4070 meters. Fig. 8 shows the topographic heights in this test area. The grey rectangle indicates the target geoid area. The airborne gravity data collection method for the California test area is very similar to the method used for Louisiana test area. The difference is that an Alaska Fire Services (BLM) Pilatus PC-12 was used for the data acquisition and the flight height was changed from about 10,600 m to about 6000 m. Also, a NovAtel SPAN-SE with Honeywell µirs (GPS + IMU) was also installed for the data collection. Table 4 gives a synopsis of survey layout and execution for the California test area. We used the same methods to post process the airborne gravity survey data including the lever arm corrections for the transformation of GPS position, velocity and acceleration from the phase center of the GPS antenna to meter s sensor position. Fig. 9 shows the free-air gravity anomalies filtered by a low pass filter of 80 seconds that corresponds to a half- wavelength spatial resolution of 4.6 km at the nominal flight speed 225 knots. For the target geoid computation area, there are free-air gravity anomaly observations covering the region (38.30 < φ <43.27 ) and ( < λ < ) available. The estimated RMS accuracy from 315 crossover errors is 2.2 mgal after a crossover adjustment.

10 Preliminary geoid mapping results 89 Table 5: Statistics of the differences between the different geoids for the California test area. Unit is in cm Statistic GMS GMS QGMS GMS QGMS USGG12 QGMS USGG12 USGG12 EGM08 EGM08 EGM08 Min Max Range Std. dev Bias * Figure 10: The GMS (a) and QGMS (b) geoid vs. EGM08 (c) and USGG12 (d) geoid for the California test area in 10 cm contours GMS and QGMS vs. EGM08 and USGG12 The geoids computed from GMS directly and converted from the QGMS solution are shown in Figs. 10(a) and 10(b). For comparison, the EGM08 and USGG12 geoids are shown alongside the GMS and QGMS geoids, in Figs. 10(c) and 10(d), their differences and comparison statistics are given in Table 5. Like the model comparison results of the Louisiana test case, significant biases exist in most solutions, with a relatively small bias between the GMS and EGM08 geoids. After the biases are removed, all of these geoid models, ie. the GMS, the QGMS, EGM08 and USGG12 geoids, match each other reasonably well. The comparison between the GMS and the QGMS shows a model agreement accuracy 5.3 cm. In comparison to USGG12, the model comparison accuracy is 6.6 and 4.6 cm for the GMS and the QGMS respectively. In comparison to EGM08, the model agreement accuracies look also similar and comparable. These model comparison results show that Fugro s airborne geoid mapping technology is approaching 5 cm model agreement accuracy in high mountain areas. Unlike the Louisiana test case, the spatial resolutions of the different geoid models look significantly different because of the complex topographic effects. In comparison to USGG12, the QGMS looks very close and comparable; the GMS looks a little smoother. This shows that using appropriate techniques, airborne gravimetry is able to

11 90 D. Zhong et al. Table 6: Statistics of the differences between the different geoids and GPS-levelling benchmarks for the California test area. Unit is in cm Statistic GMS QGMS USGG12 EGM08 GPS-Levelling GPS-Levelling GPS-Levelling GPS-Levelling No of Benchmarks Min Max Range Std. dev Bias * Figure 11: Differences between the different geoids (GMS (a), QGMS (b), EGM08 (c) and USGG12 (d)) and the GPS-Leveling benchmarks for the California test area. The color scale is in meters. achieve a comparable spatial resolution to traditional terrestrial methods for geoid determination in high mountain areas. Since EGM08 represents only a 5 x5 spatial resolution, without taking the rough topographic effects into account, it is not comparable with the others GMS and QGMS vs. GPS-Levelling In the California test area there are 139 valid GPS- levelling benchmarks available for quality validation of the calculated geoid undulations. Table 6 shows the statistics of the differences between the measured and computed values at GPS levelling benchmarks, alongside the equivalent results of the EGM08 and USGG12 geoid for a comparison.

12 Preliminary geoid mapping results 91 Table 7: Statistics of the differences between the different geoids and the GPS-levelling benchmarks after the removal of systematic slopes by a 3-parameter fitting for the California test area. Unit is in cm Statistic GMS QGMS USGG12 EGM08 GPS-Levelling GPS-Levelling GPS-Levelling GPS-Levelling No of Benchmarks Min Max Range Std. dev Bias and slopes (cm, deg, deg) 19.3, 3.5, , 3.5, , 3.2, , 4.0, 4.1 Figure 12: Data coverage of New Hampshire test area plotted in Google Earth From the statistics in Table 6, we can see that both GMS and QGMS give a result comparable to USGG12 and EGM08. Their difference ranges look a little smaller. This is a benefit from better data coverage with airborne gravity. Since this test area is located in an area of high mountains with topographic heights up to 4070 m, the standard deviations of all models are much larger than the Louisiana test area, ranging from 8.4 to 10.0 cm. This is likely due to some combination of the technical difficulty associated with geoid modeling in mountainous areas (e.g. density variations, high frequency gravity field variations), the inaccuracy of orthometric height computations in these areas, and systematic leveling errors. To estimate the systematic errors, we plotted the differences between the different geoids and GPS-leveling benchmarks in Fig. 11 and tried to remove them by applying corrections based on a 3- parameter (one for shift and two for linear trends) fit. After the removal of the systematic slopes, the new statistics of the differences between the measured and computed values at GPS levelling benchmarks are given in Table 7. Systematic differences between gravimetric geoidal heights and those calculated from the GPS-levelling benchmarks are identified, and given the consistency in slopes of these trends between diverse calculation methods, these are likely associated with systematic levelling errors. If we remove the slopes by applying the corrections based on a 3-parameters fit, the results in Table 7 show us a significant improvement from 45% to 48%, and these new precision levels are, as expected, close to the results of the model comparisons in Table 5, i.e. about 5 cm. Figure 13: Topographical heights in the New Hampshire test area from SRTM 30 data in 10 meter contours. The height ranges from 0 to 1800 meters. 4.3 New Hampshire test case The New Hampshire test area covers the whole data block EN08 under the NOAA NGS GRAV-D project, which is located in the Eastern Time Zone, north of 40 latitude. This was the eighth (08) block of data completed in that region.

13 92 D. Zhong et al. Table 8: Synopsis of survey layout and execution for New Hampshire test area Survey Name NH13 (New Hampshire 2013) Airport Base of Operations Portsmouth International Airport at Pease (KPSM), New Hampshire, NH Geographic Location New Hampshire, Vermont, Quebec Canada Dates of Airborne Operations Sep. 08 Oct. 1, 2013 Aircraft Fugro Earth Data Cessna Conquest N93HC Engines, Number and Type 2, Turboprop Gravity Instrumentation Micro-g LaCoste (MGL) TAGS S-160 (relative), MGL A (absolute), MGL G-6 (relative) GPS Instrumentation NovAtel DL-4 Plus, NovAtel SPAN-SE (GPS + IMU) Line Spacing Data Lines: 10 km, Cross Lines: ~80 km Type of Layout Regular data lines & regular cross lines Nominal Survey Altitude 5,500 m Nominal Aircraft Ground Speed 250 knots Number of Lines Data Lines: 43, Cross Lines: 7 Number of Crossovers 257 Table 9: Statistics of the differences between the different geoids for the New Hampshire test area. Unit is in cm Statistic GMS GMS GMS QGMS QGMS CGG13 QGMS USGG12 CGG13 USGG12 CGG13 USGG12 Min Max Range Std. dev Bias * Table 10: Statistics of the differences between the different geoids and GPS-levelling benchmarks for the New Hampshire test area. Unit is in cm Statistic GMS QGMS USGG12 CGG13 EGM08 GPS-Levelling GPS-Levelling GPS-Levelling GPS-Leveling GPS-Levelling No of Benchmarks Min Max Range Std. dev Bias *

14 Preliminary geoid mapping results 93 to a half-wavelength spatial resolution of 6.4 km at the nominal flight speed 250 knots. For the target geoid computation area, there are 147,361 free-air gravity anomaly observations covering the region (42.00 < φ < ) and ( < λ < ) available. The estimated RMS accuracy from 257 crossover errors is 1.5 mgal after a crossover adjustment GMS and QGMS vs. USGG12 and CGG13 Figure 14: Observed free-air gravity anomalies in the New Hampshire test area from 55 to 35 mgal. Block EN08 is about 450 km by 500 km crossing the border between the USA and Canada, covering part areas of New York, Vermont, New Hampshire in the USA, Quebec and Ontario in Canada. Fig. 12 shows the data coverage, plotted in Google Earth. The topographic height and roughness in the New Hampshire test area are somewhere in between those in the Louisiana and California test areas. Fig. 13 shows the topographic heights in this test area. The gray rectangle is the target geoid area. The airborne gravity data collection method for the New Hampshire test area is similar to the methods used for the Louisiana and California teat areas. The difference is that Fugro Earth Data s Cessna Conquest N93HC and TAGS gravimeter with serial number S-160 was used for the data acquisition. The flight height was also changed to about 5500 m. Table 8 gives a synopsis of the survey layout and execution for the New Hampshire test data. We used the same methods to post process the airborne gravity survey data, but there is a difference in the lever arm corrections for the transformation of GPS position, velocity and acceleration from the phase center of the GPS antenna to meter s sensor position. Because of unavailability of the attitude data determined by the NovAtel SPAN-SE system for this study, and because the gravimeter s lever arm is relatively small (0.769 m, m, m), we used a simple lever arm correction method based on aircraft s orientation Hwang et al (2006); Li (2013). Fig. 14 shows the free-air gravity anomalies filtered by a low pass filter of 100 seconds that corresponds The geoid computed from GMS directly, and that converted from QGMS solution are shown in Fig. 15(a) and 15(b). In comparison to the USGG12 and CGG13 geoids which are shown alongside the GMS and QGMS geoid in Fig. 15(c) and 15(d), the differences and comparison statistics are given in Table 9. From Table 9, we can see that the different model comparison accuracy ranges from 1.5 to 2.5 cm after their biases are removed. In comparison to the previous two test cases, these results are similar to the Louisiana case but much better than the California case. This shows that the current modelling techniques need to be improved for high mountain areas with rough topography. Assuming that the accuracy of the DTMs used for modelling terrain effects is equal in all test cases, the most likely reason for the different geoid determination accuracy is the density variations in areas of rough topography, or the inability for airborne gravity or the processing methods used to capture the effect of high frequency gravity field variations. For a mixed topography up to 1830 m in this test area, the accuracy of around 2 cm is reasonably good. In order to compare the airborne and the terrestrial solutions in more detail, we plotted their differences in Fig. 16. From Fig. 16, we can see that the airborne geoid mapping results are comparable with gravimetric geoids based on terrestrial gravity such as USGG12 and CGG GMS and QGMS vs. GPS-Levelling In this New Hampshire test area there are 167 valid GPSlevelling benchmarks available for quality validation of the calculated geoid undulations. Table 10 shows the statistics of the differences between the measured and computed values at GPS levelling benchmarks, alongside the equivalent results for the EGM08, USGG12 and CGG13 geoid for comparison. Similar to the Louisiana test case, the difference between all geoid models and GPS - Leveling results is about

15 94 D. Zhong et al. Figure 15: The GMS (a) and QGMS (b) geoid vs. USGG12 (c) and CGG13 (d) geoid for the New Hampshire test area in 5 cm contours. 3 cm, which approaches the typical accuracy of GPS height determination. This result confirms that Fugro s airborne geoid mapping technology is reliable and comparable with traditional geoid solutions based on terrestrial gravity data. 5 Conclusions From the presented test results in three different areas with different topographic height characteristic, we can draw following conclusions: 1. For regional geoid determination, Fugro s airborne gravimetric geoid mapping solutions have achieved reasonably good results. In comparison with advanced geoid solutions based on terrestrial gravity surveys, such as USGG12 and CGG13 models, Fugro s airborne geoid mapping solutions are comparable and sometimes appear slightly better. This comparability is not only in the achievable accuracy but also in the spatial resolution of the determined geoid models. 2. In comparison with the most accurate geoid models determined by GPS-levelling, Fugro s airborne geoid solutions have achieved a better than 5 cm relative accuracy (actually around 3 cm) in flat or low mountain areas and a better than 9 cm in mountain areas, as estimated by comparison with terrestrial approaches and with GPS-levelling benchmarks. Apart from likely systematic differences between gravimetric geoidal heights and those calculated from GPSleveling benchmarks, as estimated by a fitted 3- parameter transformation, a better than 5 cm accuracy is also achievable for mountain areas. These achievable accuracies approach the accuracy of GPS height determination, especially in flat and low mountain areas. 3. In comparison with the well-regarded global geopotential model EGM08, Fugro s airborne gravimetric geoid solution presents a better spatial resolution in mountainous areas. Although the spatial resolution

16 Preliminary geoid mapping results 95 Figure 16: Differences between the airborne and terrestrial gravimetric geoids for the New Hampshire test area in 2 cm contours: (a) differences between the GMS geoid and the USGG12 geoid; (b) differences between the QGMS geoid and the USGG12 geoid; (c) differences between the GMS geoid and the CGG13 geoid and (d) differences between the QGMS geoid and the CGG13 geoid. of EGM08 is limited by its maximal model resolution of 5 x5, and is arguably not directly comparable without taking local topographic effects into account, the airborne geoid mapping results in the California test area show us that a global geopotential model such as EGM08 with degree and order up to 2190 is not good enough to represent details of a local geoid in mountain areas. The test results demonstrate also that airborne gravimetry is a good choice for geoid mapping in mountain areas with its data acquisition efficiency, and its results are comparable with the traditional terrestrial method. 4. For high mountain areas with rough topography, the current geoid modelling techniques need to be improved in order to achieve a comparable accuracy in flat or low mountain areas. If we assume that the quality of the applied airborne gravity and DTM data for three different test areas are comparable, given that they are from the same observation technologies, then a very possible reason for the incomparable accuracy is unavailability of detailed and accurate density information required for the computation of terrain effects (both in geoid determination and in determination of the geoid-quasigeoid correction), and/or the limited spatial resolutions of the gravity observations. Acknowledgement: The support of the US NOAA NGS GRAV-D team is gratefully acknowledged. Thanks go to GRAV-D project manager Dr. Vicki Childers for her approval of the survey data released to Fugro, and Dr. Theresa Damiani for her preparing and releasing the data. References Flury J. and Rummel R., 2009, On the geoid- quasigeoid separation in mountain areas, J. of Geod. 83: , doi: /s

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