ISSN:
1432-1394
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
Notes:
Abstract In this paper we investigate the behaviour of Newton's kernel in the integration for topographical effects needed for solving the boundary value problem of geodesy. We follow the standard procedure and develop the kernel into a Taylor series in height and look at the convergence of this series when the integral is evaluated numerically on a geographical grid, as is always the case in practice. We show that the Taylor series converges very rapidly for the integration over the "distant zone", i.e., the zone well removed from the point of interest. We also show that the series diverges in the vicinity of the point of interest when the grid becomes too dense. Generally, when the grid step is smaller than either the height of the point of interest, or the difference between its height and those of the neighbouring points. Thus we claim that the Taylor series version of Newton's kernel cannot be used for evaluating topographical effects on too dense a topographical mesh.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00867153
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