Resumo. Abstract. Prudente - SP,

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1 IBP1570_14 INVESTIGATION THE ACCURACY OF THE TRANSPETRO GEODETIC NETWORK AND ITS TRANSFORMATION TO SIRGAS000 João Fracisco G. Moico 1, Paulo de O. Camargo 1, Maurício Galo 1, Leoardo C. de Oliveira, João P. Maga Juior 3, Lis M. L. Rabaco 4, Fábio O. Fagudes 5, João R. P. Obrego 6 Copyright 014, Istituto Brasileiro de Petróleo, Gás e Biocombustíveis - IBP Este Trabalho Técico foi preparado para apresetação a Rio Oil & Gas Expo ad Coferece 014, realizado o período de 15 a 18 de setembro de 014, o Rio de Jaeiro. Este Trabalho Técico foi selecioado para apresetação pelo Comitê Técico do eveto, seguido as iformações cotidas o trabalho completo submetido pelo(s) autor(es). Os orgaizadores ão irão traduzir ou corrigir os textos recebidos. O material coforme, apresetado, ão ecessariamete reflete as opiiões do Istituto Brasileiro de Petróleo, Gás e Biocombustíveis, Sócios e Represetates. É de cohecimeto e aprovação do(s) autor(es) que este Trabalho Técico seja publicado os Aais da Rio Oil & Gas Expo ad Coferece 014. Resumo O propósito deste trabalho é avaliar a acurácia de um cojuto de estações, deomiada de rede geodésica da Traspetro, que é refereciada ao SAD69 (Datum Sul Americao de 1969) e forecer alterativas para a trasformação de coordeadas de SAD69 para SIRGAS000 (Sistema de Referêcia Geocêtrico para as Américas), jutamete com a estimativa da acurácia das coordeadas após a aplicação da trasformação. A comparação foi realizada cosiderado a solução oficial forecida pelo IBGE, ou seja, a partir do software ProGriD, que é baseado o NTv, e o TPS Thi- Plate Splie, que é um modelo que pode ser usado para iterpolar dados irregularmete distribuídos. A trasformação com base o TPS fomplemetada o espaço tridimesioal e os resultados foram avaliados em termos de discrepâcias usado o mesmo cojuto de dados utilizados o ProGriD. Embora estes resultados sejam prelimiares, foi possível observar que a trasformação com base o TPS proporcioou melhores resultados, quado comparados com a solução do ProGriD, uma vez que a primeira solução foreceu discrepâcias com meores RMSE e valores médios. Estes idicadores permitem cocluir que o TPS é uma alterativa viável para trasformar as coordeadas obtidas a partir de diferetes realizações dos sistemas de referêcia geodésicos. Abstract This ivestigatio aims to assessig the accuracy of the so called Traspetro Geodetic Network which is refereced to SAD69 (South America Datum of 1969) ad providig methodologies for coordiate trasformatio from SAD69 to SIRGAS000 (Geocetric Referece System for the Americas i Portuguese) together with the estimatio of the accuracy of the trasformed coordiates. The compariso was performed cosiderig the official solutio provided by IBGE, i.e. ProGriD software, that is based i the NTv solutio ad the TPS Thi-Plate Splie that is a model that ca be used to iterpolate irregularly distributed data. The trasformatio based o TPS was implemeted i 3D space ad the results were evaluated i terms of discrepacies usig the same data set. Although these results are prelimiary it was possible to observe that the trasformatio based o TPS provides better results whe compared to the ProGriD solutio sice the former solutio provided lower discrepacies i RMSE ad average values, allowig to coclude that TPS is a potetial alterative for trasformig coordiates betwee geodetic referece frames. 1 Uiversidade Estadual Paulista UNESP/FCT, Dep. de Cartografia, Campus de Presidete Prudete - SP, {galera, paulo, galo}@fct.uesp.br Istituto Militar de Egeharia IME, Seção de Egeharia Cartográfica, Rio de Jaeiro RJ, leoardo@ime.eb.br 3 Istituto Federal de Educação, Ciêcia e Tecologia de Goiás, Campus de Goiâia GO, joao.paulo@ifg.edu.br 4 Petrobras Petróleo Brasileiro S.A. / CENPES, Rio de Jaeiro RJ, lismaria@petrobras.com.br 5 Petrobras Trasporte S.A. - Traspetro, Rio de Jaeiro - RJ, fabio.fagudes@petrobras.com.br 6 Graduado de Egeharia Cartográfica, Uiversidade Estadual Paulista UNESP/FCT, Campus de Presidete Prudete - SP, jrafael.obrego@gmail.com

2 Rio Oil & Gas Expo ad Coferece Itroductio The evolutio of geodetic positioig techiques for the coordiate s determiatio suffered great developmet, maily after that the NAVSTAR-GPS (NAVSTAR - Global Positioig System) was declared operatioal i To keep i pace with the evolutio, several coutries updated their geodetic referece system or tured to adoptig ew oes, usually geocetric, more directly compatible with the moder satellite based positioig techiques. Brazil adopted sice the resolutio R. PR. º 1/005 (IBGE, 005), the SIRGAS000 (Geocetric Referece System for the Americas) as the preset official plaimetric referetial. The process of referetial chagig is complex ad studies about the impact of the adoptio of the ew referece system to the users are relevat. Oe of the most importat factors is related to the procedure of referetial coversio. Such procedure cosists i estimatig the coordiates from oe poit or from a set of poits, i the referetial of destiy by usig the coordiates from the referetial of origi ad applyig a mathematical model. I Brazil, durig the year 008 was made available by IBGE (Istituto Brasileiro de Geografia e Estatística) oe system of trasformatio based i the ProGriD software (IBGE, 009). This software performs the referetial coversio by applyig trasformatio grids i the NTv (Natioal Trasformatio Versio ) format. The NTv was developed ad used i Caada ad is applied also i other coutries as Australia ad Uited States of America. Other methods of referetial coversio have bee studied, as the oes preseted by Oliveira et al. (008) ad Maga Júior (01). By the study of ew methods, it is iteded to adjust the peculiarities of each Geodetic Network ivolved i the coversio process, i terms of patter ad magitude of the distortios, quatity ad homogeeity of the poits, etc. Petrobras Trasporte S.A. Traspetro, a itegrated subsidiary of Petrobras, has a set of geodetic statios, here stated as a Geodetic Network, composed of ie sub etworks that guide all the geodetic surveys coducted by the compay atiowide. All these etworks were deployed after the year 000, ad the GNSS (Global Navigatio Satellite System) techology was largely employed. To perform the coversio ad update the existig geodetic etwork to SIRGAS000 a process of coordiates trasformatio is eeded. Aimig to a better quality trasformatio, some experimets were performed with statios from the Traspetro Network, applyig the official Brazilia model for referetial coversio (i.e., ProGriD) ad also the Thi-Plate Splies 3D solutio (TPS3D) developed by Maga Júior (01) ad Maga Júior et al (014). I these experimets homologous poits from the Traspetro Network were used, with coordiates i two referece systems: SAD69 (South America Datum of 1969), the previous plaimetric referetial, ad i SIRGAS000.. The Traspetro Geodetic Network The Traspetro Geodetic Network is materialized by a set of 1740 geodetic statios ad is divided ito ie sub etworks: Maceio AL; Southeast pipelies (RJ, SP, MG); West pipelies (SP, MG, DF); Souther pipelies (PR, SC, RS) pipelies; Northeast termials (BA, AL, SE, PE, RN, CE, MA); Cacimbas-Catu pipelies; Marahão-Fortaleza pipelies; ad Amazo Basi (Urucu-Maaus) pipelies. The geodetic statios from the etwork are used maily for pipelie projects ad accordig to Petrobras (005) are classified i the followig types: a) statios type B i umber of 60 to be used, i priciple, i the implatatio stage of the defiitive project areas or to be located i the mai termials ad edge poits of right-of-way, piggig lauch ad gas treatig statios; ad b) statios type C which should be pre-molded ad as oe optio to the B type, of lighter weight, for sites of difficult access or i the middle of right-of-way pipelies. Figure 1 shows the distributio of a sample of statios liked to the Traspetro Geodetic Network project, extedig across the coutry. This sample ivolves 831 statios of a estimated total of more tha 1700 statios. As stated before, most these sub etworks were deployed after the year 000, ad the GNSS techology has bee largely employed. Therefore, at least i priciple, the official trasformatio used i Brazil should be suitable to meet the Traspetro requiremet i terms of accuracy. We have to call attetio that such etworks are a set of statios ad ot a etwork i the real meaig, because they are ot coected amog them.

3 Rio Oil & Gas Expo ad Coferece 014 Figure 1. Represetatio of sample of statios of the Traspetro Geodetic Network. 3. Coordiate trasformatio betwee Geodetic Referece Systems The coexistece of several geodetic referece systems ad their realizatios requires mathematical models for coversio of coordiates amog them. The coversio process cosists i fidig the positio of kow statios i a referece system (or realizatio) i aother system (or realizatio) ad vice versa. Several models for referece system coversio are preseted i the literature as, for example: Jukis ad Erickso (1996), Collier et al (1996), Oliveira (1998) ad Collier (00). 3.1 Coordiate trasformatio i the Brazilia Geodetic Network The Brazilia Geodetic System has bee usig several methodologies for trasformatio of coordiates betwee referetials. I IBGE (1983) the simplified differetial Molodeski equatios were suggested. With the adoptio of the SIRGAS000, the IBGE (005) published the parameters for trasformatio from SAD69 to SIRGAS000. I December 008, IBGE released the ProGriD software (IBGE, 009) that uses grids i NTv format for coversio of coordiates. The trasformatio grids are computed by usig the set of homologous statios from Brazilia Geodetic System (SGB). The distortio model used by NTv is composed by oe global model, which uses a complex polyomial for modellig the distortios i latitude ad logitude, ad a local model, that deals idividually with the modellig i each compoet, latitude ad logitude, i fuctio of the global residual distortios (JUNKINS, ERICKSON, 1996). The modelled distortios are available i a NTv patter, compatible to may GIS (Geographical Iformatio System) softwares. 3. Coordiate Trasformatio usig Thi-Plate Splies The Thi-Plate Splie (TPS) model is widely used to model distortios, maily i medical applicatios. The TPS formulatio guaratees some restrictios as that the iterpolatio surface presets miimal deformatio eergy ad is smooth. The TPS fuctio is composed by the liear combiatio of radial base fuctios U(r), where the fuctio values are determied by differeces (or distace) betwee coordiates of cotrol poits (used at the model geeratio). The radial basis fuctio U(r) presets a liear behavior whe the aalyzed poits become more distat from the cotrol poits. Oe applicatio of TPS is i the geeratio of mappig fuctios from R to R, relatig two set of homologous poits. I most of TPS solutios a iterpolatio surface of the type f(x,y) from a D domai (X,Y) is geerated. However, depedig o the applicatio it is possible to develop a tridimesioal solutio i X, Y ad Z compoets, 3

4 Rio Oil & Gas Expo ad Coferece 014 makig some modificatios to the radial base fuctio U ad to the equatio system. The fuctio U(r) depeds o the space of the real umbers to be used. Accordig to Bookstei (1989), i the modellig of coordiates i the D space (R ), the fuctio U is give by the Equatio 1; i the tridimesioal space (R 3 ), U is give by the Equatio. Z(X,Y) Z(X,Y, Z) U(r) r log r (1) U(r) r () where r is the Euclidia distace from the origi of the Cartesia system located at each cotrol poit. From the radial base fuctio it is possible to defie the TPS mappig fuctios i X, Y ad Z, by the followig equatios (MAGNA JÚNIOR, 01; MAGNA JÚNIOR et al, 014): i i 1 i X a0 a1 X1 ay1 a3z1 uiu( r ) Y a4 a5 X1 a6y1 a7z1 viu( r ) Z a8 a9 X1 a10y1 a11z wu i ( r ) (3) where: X, Y Z : Cartesia geodetic coordiates at the destiatio referetial;, X 1, Y1, Z1, a1,..., a11, u1,..., u, v1,..., v, w1 ( r i ) : Cartesia geodetic coordiates at the referetial of origi; a 0,..., w : coefficiets of the TPS fuctio i X, Y e Z; U : the applicatio of the Equatio havig the Euclidia distace at the tridimesioal space (r i ) from a cotrol poit to the others. To determie the TPS coefficiets it is ecessary the resolutio of a equatio system composed by the Equatios 3 ad the followig costraits: u i i i i i w X v i i i i i w Y w i 0 u Z v Z i i (4) The set of Equatios 3 warrats the liear growig of the TPS as the poits are progressively far from the cotrol poits ad the costraists (Equatios 4) assures that the liear system to be solved have the same umber of equatios ad ukows. The system to be solved idividually for each coordiate (X, Y ad Z) is composed by +1 equatios ad +1 ukows, where is the umber of cotrol poits. This formulatio is called TPS3D ad some details i the solutio ca be foud i Maga Júior (01). Oce estimated the ukows, the coordiates at the referetial of destiy are computed usig the Equatios Prelimiary results of the referetial trasformatio o the Traspetro Geodetic Network I order to coduct the experimets, a sample of geodetic statios of types C ad B from the Traspetro Network had its coordiates determied with high accuracy usig GNSS, followig a very well established specificatio. Each statio was idepedetly occupied twice for a period of four hours. Also, some origial files of GNSS observatios were recovered from oe previous campaig ad the data processig was carried out. The methods for data processig ivolved were PPP (Precise Poit Positioig) ad relative positioig (MONICO, 008). Whe both results agreed quite well (at cetimeter level) the statio was selected for use. Statios from the Amazo Basi were ot cosidered ad, from the 8 sub etworks, a total of 94 statios were made available. The coordiates are give i SIRGAS000 with high accuracy (cm). 4

5 Rio Oil & Gas Expo ad Coferece 014 Usig a set of 94 homologous statios kow i both referetials, SAD69 ad i SIRGAS000, some experimets were performed to verify the etwork quality ad the most adequate model to the coordiate trasformatio i the Traspetro etwork. 4.1 Coordiate trasformatio usig the ProGriD To verify the trasformatio quality applied to the Traspetro Network, the first step was to perform the trasformatio of the 94 statios give i SAD69 to SIRGAS000 usig the ProGriD. The trasformatio was performed usig the optio SAD69 Doppler or GPS Techique, optio that performs the trasformatio applyig oly parameters of traslatios. The trasformed coordiates were compared to the coordiates obtaied by positioig ad these discrepacies were used to compute the RMSE (Root Mea Square Error), the mea values ad the extreme absolute errors. Table 1 shows a summary of the obtaied results. Table 1. Statistics of the coordiate s discrepacies after SIRGAS000 to SAD69 Trasformatio. Statistics Discrepacies ProGriD Latitude (m) Logitude (m) RMSE 1,948 1,438 Abs maximum 9,15 7,944 Abs miimum 0,003 0,00 Mea 1,375 0,491 From Table 1 oe ca observe that the discrepacies ca reach more tha 9 m i Latitude ad a little less i Logitude. These values are quite larger tha what is expected by IBGE for those techiques based o spatial techology (maximum value of 46 cm) ad classical etwork for the regio of Traspetro etwork (up to 1m) (IBGE, 006). Therefore, the results have show that is quite importat for Traspetro to apply a specific trasformatio for reachig their aim, oce the ProGriD results did ot meet the Traspetro accuracy requiremets (0 cm). 4. Quality aalysis of the trasformatios with the ProGriD ad the TPS3D i poits of check The alterative solutio ivestigated i this work was based o the TPS3D model, which is used for deformatio iterpolatio i differet applicatios, as metioed. A so called TPS3D program was developed to apply the method i the Traspetro database. From the 94 statios available, 66 were used to determie the coefficiets of the TPS3D model ad 8 statios were used as referece or check poits (Figure ). From Figure it is possible to see how disperse is the distributio of the statios i the etwork. However, this is a characteristic of etworks built to support pipelie projects. Figure. Distributio of cotrol ad check poits i the Traspetro Network. 5

6 Rio Oil & Gas Expo ad Coferece 014 The Table shows the statistic of the results based o the ProGriD ad TPS3D solutios, allowig the compariso of the discrepacies based o the computed ad the adjusted coordiates i the 8 check poits Table. Statistics of the coordiate s discrepacies after SIRGAS000 to SAD69 Trasformatio based o ProGriD ad TPS3D for the 8 statios of checkig Statistics Discrepacies ProGriD Discrepacies TPS3D Latitude (m) Logitude (m) Latitude (m) Logitude (m) RMSE,018 1,380 0,067 0,147 Abs maximum 3,303 1,687 0,344 0,440 Abs miimum 0,003 0,003 0,000 0,000 Mea 1,516 0,51 0,016 0,00 From Table it is quite clear show how better results are redered whe usig TPS3D for trasformatios i the Traspetro database from SAD69 coordiates to SIRGAS000. As ca be observed, the Traspetro requiremets for 0 cm are reached for this sample of statios. It may ot be the case for the complete data set, but it is a quite ethusiastic prelimiary result. 5. Fial cosideratios The prelimiary experimets showed that the trasformatio usig the TPS model has some advatages compared to the ProGriD solutio whe applied to the Traspetro Geodetic Network of poits. The ProGriD solutio trasformatio provides discrepacies of up to 10 m i the plaimetric resultat, with RMSE of,4 m. I the quality test of the trasformatios based o checks poits, the TPS3D model gives a reductio of 85 % i the value of discrepacies whe compared with the ProGriD for the plaimetric resultat. The values of RMSE reduced from,4 m to 0,16 m for the plaimetric resultat. It is importat to poit out that further ivestigatio is still eeded. I the ext steps a boudary aalysis will be carried out to aswer questios related to the extrapolatio of the trasformatio. Due the complexity of Traspetro Geodetic Network, other types of trasformatio must also be tested tryig a compariso betwee local trasformatio ad TPS3D. 6. Ackowledgmets The authors thak the Techological Trasportatio Program (PROTRAN) from Petrobras for supportig this research ad Eg. Leopoldo Machado Pagaelli for the suggestios preseted i this article. 7. Refereces BOOKSTEIN, F. L. Pricipal warps: Thi-plate splies ad the decompositio of deformatios. IEEE Trasactios o Patter Aalysis ad Machie Itelligece, v. 11,. 6, p , ju COLLIER, P.; LEAHY, F. J.; ARGESEANU, V. S. Trasitio to the Geocetric Datum of Australia. The Uiversity of Melboure, Departmet of Geomatics. Cosultats Report to the Office of Surveyor Geeral, Victoria, COLLIER, P. Developmet of Australia s Natioal GDA94 Trasformatio Grids. The Uiversity of Melboure, Departmet of Geomatics. Cosultat s Report to the Itergovermetal Committee i the Surveyig ad Mappig. 00. IBGE INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA ProGriD guia do usuário ftp://geoftp.ibge.gov.br/documetos/geodesia/projeto_mudaca_referecial_geodesico/progrid_guia_do_usuario.pdf IBGE INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA. Ajustameto da Rede Plaimétrica Brasileira em SIRGAS000, 006. ftp://geoftp.ibge.gov.br/documetos/geodesia/rel_sirgas000.pdf. IBGE INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA. Resolução º 1, de 005. Altera a caracterização do sistema geodésico brasileiro, Rio de Jaeiro, 005. ftp://geoftp.ibge.gov.br/documetos/geodesia/projeto_mudaca_referecial_geodesico/legislacao/rpr_01_5fev00 5.pdf. IBGE FUNDAÇÃO INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA. Resolução º, de Especificações e ormas gerais para levatametos geodésicos, Rio de Jaeiro,

7 Rio Oil & Gas Expo ad Coferece 014 JUNKINS, D.; ERICKSON, C. Versio of the Natioal Trasformatio betwee NAD7 ad NAD83 ad its importace for GPS positioig i Caada. Draft Report, Geodetic Survey Divisio, Geomatics Caada, MAGNA JÚNIOR, J. P. O uso de Thi-Plate Splies a trasformação de coordeadas com modelagem de distorções etre realizações de refereciais geodésicos p. Tese de Doutorado. Programa de Pós-Graduação em Ciêcias Cartográficas. FCT/UNESP. Presidete Prudete, SP. MAGNA JÚNIOR, J. P.; CAMARGO, P. de O.; GALO, M. Trasformação de coordeadas com modelagem de distorções etre SAD69 e SIRGAS000 com o uso de THIN-PLATE SPLINES. BCG - Boletim de Ciêcias Geodésicas, v. 0,. 1, p. 19-8, 014. DOI: MONICO, J. F. G. Posicioameto pelo GNSS: Descrição, Fudametos e Aplicações, Editora UNESP, 008. PETROBRAS. Levatameto Topográfico Georrefereciado N-47. Rev. J, CONTEC Comissão de Normalização Técica, 005, SC 04 Costrução Civil. OLIVEIRA, L. C. Realizações do Sistema Geodésico Brasileiro associadas ao SAD69 Um proposta metodológica de trasformação p. Tese (Doutorado em Egeharia) Escola Politécica, Uiversidade de São Paulo, São Paulo. OLIVEIRA, L. C.; SANTOS, M. C.; NIEVINSKI, F. G.; LEANDRO, R. F.; COSTA, S. M. A.; SANTOS, M. F.; MAGNA JÚNIOR, J. P.; GALO, M.; CAMARGO, P. O.; MONICO, J. F. G.; SILVA, C. U.; MAIA, T. B. Searchig for the Optimal Relatioships Betwee SIRGAS000, South America Datum of 1969 ad Córrego Alegre i Brazil. I: SIDERIS, M. G. Observig our Chagig Earth. Itália: Spriger Berli Heidelberg, 008. v. 133,