Lantmäterirapport 2019:3 Reports in Geodesy and Geographical Information Systems RG 2000 – a comprehensive overview on the new gravity reference frame of Sweden Andreas Engfeldt Gävle 2019 Copyright © 2019-12-30 Author Andreas Engfeldt Typography and layout Rainer Hertel Total number of pages 328 Lantmäterirapport 2019:3 ISSN 0280-5731 RG 2000 – a comprehensive overview on the new gravity reference frame of Sweden Andreas Engfeldt Gävle 2019 Preface The author would like to thank all observers who have participated in one or the other way in this project. Especially, the author would like to send some thoughts to the late Swedish relative gravity experts Lars Åke Haller (1938-2001) and Lennart Pettersson (1918-1998). The author would also in particular like to thank Ludger Timmen and Olga Gitlein who performed many gravity measurements with the FG5-220 in Sweden during 2003-2008 and Holger Steffen for valuable comments and remarks on an earlier version of this report. 5 6 Abstract This report is about the new Swedish national reference frame and system for gravity, RG 2000. It contains detailed information about how the frame and the system was developed, like point information, how the points were observed, how the calculations and adjustment were performed and more. RG 2000 is based on time series of absolute gravity observations with the instrument FG5 on 18 points (Class A points) at 14 different stations. It also includes 95 points (Class B points) observed with an A10 instrument. These absolute gravity points are connected with observations from the relative gravimeter types Scintrex CG5 and LaCoste & Romberg model G to each other and/or 230 Class C points. The Class C points are connected to a number of other Class C points with relative gravimeter observations. 148 additional points, observed only with relative gravimeters, are classified as Class D and were included in a second order adjustment. In order to harmonize the Swedish reference frames, the postglacial epoch of RG 2000 is set to 2000.0. The post glacial gravity change model NKG2016LU_gdot has been used to transform all data to this epoch. NKG2016LU_gdot is based on the land uplift model NKG2016LU_abs and has used the factor -0.163 µGal/m to convert the metres into mGal. Furthermore, transformations have been developed to the two previous gravity systems of Sweden, RG 82 and RG 62. The first realization of RG 2000 was finished in February 2018 and a second improved realization with extended and slightly corrected data was finished in October 2019. The realization from 2019 is the valid realization today. If improved absolute or relative data become available in the future or improved land uplift models are developed, new realizations may be provided. 7 Sammanfattning Den här rapporten handlar om det nya svenska nationella referenssystemet och referensnätet för tyngdkraft, RG 2000. Rapporten innehåller detaljinformation om det mesta angående hur systemet togs fram, såsom vilka punkter som ingår, hur de mätts, hur beräkningen och utjämningen gått till m.m. RG 2000 baseras på tidsserier från 18 punkter (Klass A) på 14 olika stationer som mätts med absolutgravimetern FG5. Det innehåller även 95 punkter (Klass B) som mätts med absolutgravimetern A10. Klass A och B punkterna har bundits ihop med varandra och/eller 230 Klass C punkter med hjälp av mätningar med relativa gravimetrar av typen Scintrex CG5 och/eller typen LaCoste & Romberg modell G. Dessa Klass C punkter är i sin tur ihopbundna med ett antal andra Klass C punkter genom mätningar med relativa gravimetrar. Ytterligare 148 punkter mätta med enbart relativa gravimetrar är klassificerade (Klass D) och ingick i en andra ordningens utjämning. För att harmonisera de svenska referenssystemen har RG 2000 fått landhöjningsepoken 2000.0 och i arbetet har konverteringsmodellen NKG2016LU_gdot använts. Den modellen är baserad på landhöjningsmodellen NKG2016LU_abs och använder faktorn -0.163 µGal/m för att konvertera meter till mGal. För referenssystemsbyte från något av de två tidigare svenska tyngdkraftssystemen, RG 82 och RG 62, har transformationer utvecklats. Den första realiseringen av RG 2000 var klar i februari 2018 och en andra bättre realisering med utökade och något korrigerade data var klar i oktober 2019. Realiseringen från 2019 är den som gäller idag, men ifall bättre absoluta data eller relativa data eller bättre landhöjningsmodeller tas fram kan det i framtiden skapas nya realiseringar. 8 Table of contents Preface 5 Abstract 7 Sammanfattning 8 1 Introduction 15 2 The situation before RG 2000 18 2.1 Base points from 1943-1948 18 2.2 RG 62 19 2.3 The land uplift gravity lines 21 2.4 RG 82 23 2.5 FG5 points 25 2.5.1 Mårtsbo AA and AB 25 2.5.2 Onsala AA, AC, AN and AS 25 2.5.3 Skellefteå AA 26 2.5.4 Kiruna AA 27 2.5.5 Kramfors AA 27 2.5.6 Östersund AA 28 2.5.7 Arjeplog AA 28 2.5.8 Visby AA 29 2.5.9 Smögen AA 29 2.5.10 LMV AA 30 2.5.11 Ratan AA 30 2.5.12 Lycksele AA 31 2.5.13 Borås AA 31 2.5.14 Holmsund AA 32 2.6 Other available gravity points 32 2.7 Reconnoitring the existing points 33 3 Definition and realization of RG 2000 35 3.1 Definition of RG 2000 35 3.2 Realization of RG 2000 35 4 The strategy 36 5 FG5 observations 37 5.1 FG5-233 37 5.1.1 Corrections according to results from ICAG/ECAG/EURAMET 37 5.2 FG5-220 39 5.3 Other instruments 40 9 5.4 FG5 observations used in the RG 2000 realization 41 6 A10 observations 43 6.1 A10-020 43 6.1.1 The campaign in July 2011 43 6.1.2 The campaign in June 2012 44 6.1.3 The campaign in September 2012 45 6.1.4 The campaign in June/July 2013 46 6.1.5 The campaign in May/June 2015 47 6.2 A10-019 49 6.2.1 The campaign in 2012 49 6.3 A10 points 50 6.3.1 Old RG 62 or RG 82 points 50 6.3.2 New points 55 6.4 Chosen observations 63 7 Relative observations 64 7.1 Observations in the main adjustment 64 7.1.1 Observations from the RG 82 Zero Order campaign 64 7.1.2 Observations from the RG 82 First Order campaign 65 7.1.3 Observations from the RG 2000 campaign 66 7.1.4 Additional observations 2003-14 68 7.1.5 Land uplift observation campaigns 1975-2003 70 7.1.6 Additional observations 1972-1979 71 7.1.7 Observations from 2019 71 7.1.8 Instruments used 72 7.1.9 Chosen observations for the first RG 2000 realization (2018) 73 7.1.10 Chosen observations for the new RG 2000 realization (2019) 74 7.2 Observations in the second step adjustment 75 7.2.1 Observations from the 1973 campaign 75 7.2.2 Observations from the 2015 harbour campaign for the FAMOS project76 7.2.3 Additional observations 76 7.2.4 RG 62 observations 77 7.2.5 Chosen observations for the 2018 realization 77 7.2.6 Chosen observations for the 2019 realization 78 7.3 Gradient measurements 78 7.3.1 Gradient measurements for FG5 points 78 7.3.2 Gradient measurements for A10 points 80 7.4 The new RG 2000 realization in 2019 81 7.4.1 Differences in absolute data between the two RG 2000 realizations 82 7.4.2 Differences in relative data between the two RG 2000 realizations 83 7.4.3 Differences in precomputed differences between the two RG 2000 realizations 83 7.4.4 Differences in á priori standard uncertainties between the two RG 2000 realizations 83 7.4.5 Differences in instruments between the two RG 2000 realizations 84 7.4.6 Additional differences between the two RG 2000 realizations 85 7.4.7 Points in the 2019 realization, only observed with relative gravimeters85 10 8 Software for adjustment 110 8.1 Gprep 110 8.1.1 Gred2, for LCR observations 110 8.1.2 LMV Det g, for Scintrex observations 112 8.1.3 Input file for precomputed differences 113 8.1.4 Input files for coordinates 114 8.2 Gad, input files 114 8.2.1 Input file for absolute gravity data 115 8.2.2 Input file for relative gravity data 115 8.2.3 Input file for precomputed differences 117 8.2.4 Input file for instruments 117 8.3 Gad, formulas used 118 8.3.1 Formulas for absolute gravity data 118 8.3.2 Formulas for relative gravity data 118 8.3.3 Formulas for precomputed differences 119 8.3.4 Formulas for sigma 119 8.4 Gad, output files 119 8.4.1 The main result file 119 8.4.2 The result file with the extra name “relative” 122 8.5 Gcross 123 8.5.1 Output file for Gcross 123 9 Calculation and FG5 adjustment 125 9.1 Formulas 125 9.2 Weighting in 2017-18 (for the first realization) 125 9.2.1 Á priori standard uncertainties for FG5 observations 125 9.2.2 Á priori standard uncertainties for A10 observations 125 9.2.3 Á priori standard uncertainties for LCR observations 125 9.2.4 Á priori standard uncertainties for Scintrex observations 126 9.2.5 Á priori standard uncertainties for precomputed differences 126 9.2.6 Á priori standard uncertainties, special cases 127 9.3 Weighting in 2019 (for the new realization) 128 9.3.1 Á priori standard uncertainties for FG5 observations 128 9.3.2 Á priori standard uncertainties for A10 observations 128 9.3.3 Á priori standard uncertainties for LCR observations 129 9.3.4 Á priori standard uncertainties for Scintrex observations 129 9.3.5 Á priori standard uncertainties for precomputed differences 129 9.3.6 Á priori standard uncertainties, special cases 129 9.4 Main adjustment in 2018 130 9.4.1 Details about the main adjustment in 2018 130 9.4.2 Single connected points in the main adjustment in 2018 132 9.5 Main adjustment in 2019 132 9.5.1 Details about the main adjustment in 2019 133 9.5.2 Single connected points in the main adjustment in 2019 133 9.6 Second step adjustment in 2018 134 9.6.1 Weighting 134 9.7 Second step adjustment in 2019 134 9.7.1 Weighting 134 11 10 Results 136 10.1 Main adjustment in 2018 136 10.1.1 Irregularities/anomalies