Transpetro's geodetic network transformation from SAD69 to SIRGAS2000: Methodology & results

Abstract

This paper presents the main activities of the project Transpetro Geodetic Network transformation to SIRGAS2000, carried out by R&D project between Petrobras CENPES and the UNESP Cartography Department of Presidente Prudente. The changing of the geodetic reference model causes impacts of diverse nature, such as operational, legislative, computational and mathematical. The change in the procedures related to the adoption of a new coordinate system can affect the operational mode from the direct tracking of a GNSS (Global Navigation Satellite System) receiver, without the need to refer to another point of the network. The alteration of the geometry (shape) of the network due to the inclusion of new observations and new adjustment of coordinates is a mathematical aspect that can be considered as network distortion. The definition of procedures and studies aimed to model the distortions associated with the coordinate transformation process is necessary to ensure the relationship of the coordinates between the achievements of the old coordinate frame and the new realizations. The Transpetro geodetic network was established in 2000, using the GNSS techniques and composed by 1740 geodetic stations and 9 subnets according the Brazilian geographic region. With the development of the referential changing project, it was verified that these subnets could be grouped in three main networks due to the techniques used in the survey and coordinate system transport. These networks, however, have no connection to each other. Each network is independent, composed of one set of points per region, and often the residues are not well determined and usually not distributed between points in the network. As first approach it was verified the used of Thin Plate Spline (TPS) model to transform the coordinates applying a unique transformation, similar to the one realized for the SGB points in the conversion SAD69/96 and SIRGAS2000 (MAGNA Jr. et al, 2014). However, when Transpetro presented requirements of accuracy mapping in guidelines, as the geodetic transformation with the error equivalent to 1 s (sigma) or 20 cm, in several cases important extrapolations would occur, something not very appropriate for the use of TPS, i. e., due to the Transpetro network geometry that is, in most part, linear in terms of point distribution. Regarding this issue, we chose to evaluate the IDW method (inverse distance weighted). The IDW method has the following aspects: 1) be less vulnerable to extrapolations; 2) the systematic behavior of distortions by geographic regions has homogeneous characteristics; 3) allow variations in the number of neighboring points, a fact relevant to the characteristics of the set of Transpetro stations. Magna Junior (2009) applied the IDW model for transformation based on the Shepard method and later applied to this project. Using the method the maximum error in some points was 0.4 m in the southern region, attending to the accuracy required to the network.