Comparison of various methods for modeling gravitational effects of the topography
20/09/2016 | 17:30 | Session 3: Local/regional geoid determination methods and models
Author(s): Miao Lin and Heiner Denker
Miao Lin and Heiner Denker
The computation of gravitational effects (i.e., gravitational potential and its partial derivatives) caused by topographic masses is an important issue for geodetic and geophysical applications, such as high-precision geoid modeling and geophysical exploration of anomalous masses insideth e Earth. With the availability of local to global digital terrain models based on geographical coordinates, the appropriate mass element for the computation of gravitational effects is the tesseroid (spherical prism). In this contribution, the emphasis is on the precise calculation of tesseroid effects for points at or near the Earth’s surface.
Since integrals over tesseroid volumes cannot be completely solved in an analytical way, three approaches are investigated, including numerical integration based on the Gauss-Legendre quadrature, Taylor series expansions, and point mass approximations. As points at or near the Earth’s surface are most critical due to the strong influence of the nearest topographic masses, an automatic subdivision strategy is applied and tested by using analytical results from spherical shell zones. In addition, rectangular prisms are examined and compared with corresponding tesseroid results based on real digital terrain models.