The effect of crustal density variation on PITE (Primary Indirect Topography Effect)

Abstract

In geoid determination studies, the main goal is to create a geoid model with an accuracy of 1 centimeter. Solving this goal in the fastest and most practical way makes it easier to implement some engineering problems. For this reason, the methods used to determine the geoid are being developed day by day. The Stokes-Helmert approach is one of the classical geoid modeling options. If the topography is not handled carefully in the solution of the boundary value problem, it is an obstacle to achieving the desired goal. In the final stage of the StokesHelmert approach, the exact geoid height is obtained by calculating the PITE (Primary Indirect Topographic Effect). The density change causes a significant difference in the PITE's calculation and, therefore, in the geoid heights. To see this difference, it is enough to use the digital elevation model and the crustal density model. In geosciences studies related to topography, the density value is usually taken as an average of 2.67 g/cm3. However, this value varies in some regions, approaching 20%. Such a ratio, which can be observed in the density change, affects the values obtained from the PITE calculation at the decimetre level. In this study, the effect of density change on PITE will be examined. In this way, an important contribution will be made to the centimeter accuracy geoid determination studies in our country. The PITE values depend on the height and density of the calculation point. As a result of numerical application, the density change gives PITE values between -43 cm and -1 cm, while under constant density these values are between -39 cm and 39 cm.