ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Isostasy  (1)
  • Key words: Direct effect – Helmert reduction – Stokes' formula – Topographic effect  (1)
  • Key words: Least squares – Modified Stokes' kernel – Truncated Stokes' formula  (1)
  • Remove  (1)
Collection
Keywords
Publisher
Years
  • 1
    Electronic Resource
    Electronic Resource
    The exterior Airy/Heiskanen topographic–isostatic gravity potential, anomaly and the effect of analytical continuation in Stokes' formula (1998)
    Springer
    Journal of geodesy 72 (1998), S. 654-662 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Analytical continuation ; Isostasy ; Stokes' formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. This study deals with the external type of topographic–isostatic potential and gravity anomaly and its vertical derivatives, derived from the Airy/Heiskanen model for isostatic compensation. From the first and the second radial derivatives of the gravity anomaly the effect on the geoid is estimated for the downward continuation of gravity to sea level in the application of Stokes' formula. The major and regional effect is shown to be of order H 3 of the topography, and it is estimated to be negligible at sea level and modest for most mountains, but of the order of several metres for the highest and most extended mountain belts. Another, global, effect is of order H but much less significant
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050205
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the indirect effect in the Stokes–Helmert method of geoid determination (1999)
    Springer
    Journal of geodesy 73 (1999), S. 87-93 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Geoid ; Helmert condensation ; Indirect effect ; Remove ; restore
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The classical integral formula for determining the indirect effect in connection with the Stokes–Helmert method is related to a planar approximation of the sea level. A strict integral formula, as well as some approximations to it, are derived. It is concluded that the cap- size truncated integral formulas will suffer from the omission of some long-wavelength contributions, of the order of 50 cm in high mountains for the classical formula. This long-wavelength information can be represented by a set of spherical harmonic coefficients of the topography to, say, degree and order 360. Hence, for practical use, a combination of the classical formula and a set of spherical harmonics is recommended.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050222
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Some modifications of Stokes' formula that account for truncation and potential coefficient errors (2000)
    Springer
    Journal of geodesy 74 (2000), S. 232-238 
    Details
    ISSN: 1432-1394
    Keywords: Key words: Least squares – Modified Stokes' kernel – Truncated Stokes' formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  Stokes' formula from 1849 is still the basis for the gravimetric determination of the geoid. The modification of the formula, originating with Molodensky, aims at reducing the truncation error outside a spherical cap of integration. This goal is still prevalent among various modifications. In contrast to these approaches, some least-squares types of modification that aim at reducing the truncation error, as well as the error stemming from the potential coefficients, are demonstrated. The least-squares estimators are provided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach) and (2) Stokes' kernel is optimally modified to minimize the global mean square error. Meissl-type modifications are also studied. In addition, the use of a higher than second-degree reference field versus the original (Pizzetti-type) reference field is discussed, and it is concluded that the former choice of reference field implies increased computer labour to achieve the same result as with the original reference field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050281
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Topographic effects by the Stokes–Helmert method of geoid and quasi-geoid determinations (2000)
    Springer
    Journal of geodesy 74 (2000), S. 255-268 
    Details
    ISSN: 1432-1394
    Keywords: Key words: Direct effect – Helmert reduction – Stokes' formula – Topographic effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H 2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is shown that the spherical approximation to power H 2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜2 (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed. The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050284
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...