The Influence of Buildings in Calculating the Gravitational Effect of Topographic Masses – A Case Study in the City of Porto Alegre - RS (Brazil)

Abstract

One of the goals of Geodesy is to study the geoid and its determination is obtained through knowledge of the gravity field that involves the distribution of masses on the Earth's surface. The classic approach to the solution of the geodetic boundary value problem (GBVP) aimed at determining the geoid assumes that the effects associated with the topography taken into account. The Residual Terrain Modelling (RTM) aims to model the gravity field as a function of the mass distribution associated with topography where, in this type of study, the high frequency content of the spectrum related to gravity is generated through this reduction method associated with a high resolution digital elevation model (DEM). In this contexto the main objective of this research is to calculate the value of the gravitational potential of the topographic masses from buildings in the city of Porto Alegre - RS together with the gravity anomalies associated with the topography. This study was developed from a vector base with more than 200 thousand buildings where the gravitational potential was calculated from an DEM generated through LiDAR (light detection and ranging) data. To assist in the calculations, a density model was estimated according to the dimensions of each building in the database. Thus, the value of the gravitational potential was calculated using the mass element tesseroid, prism and point mass and also the value of gravity for distances of 1 km, 2 km, 5 km, 10 km and 20 km using the RTM modeling technique. The influence of buildings masses, in this study, represented 10.62% of the value of the gravity anomalies compared to its corresponding in relation to the ground.