Boundary-value problems in the complex world of geodetic measurements

Abstract

A review of recent progress and current activities towards an improved formulation and solution of geodetic boundary value problems is given. Improvements stimulated and required by the dramatic changes of the real world of geodetic measurements are focused upon. Altimetry±gravimetry problems taking into account various scenarios of non-homogeneous data coverage are discussed in detail. Other problems are related to free geodetic datum parameters, most of all the vertical datum, overdetermination or additional constraints imposed by satellite geodetic observations or models. Some brief remarks are made on pseudoboundary value problems for geoid determination and on purely gravitational boundary-value problems.

A new ellipsoidal gravimetric, satellite altimetry and astronomic boundary value problem, a case study: The geoid of Iran

“…The idea of using satellite altimetry data in the problem of geoid computations has already been proposed by Svensson (1983), Sanso (1983, 1987), Grafarend and Keller (1995), Jinghai and Xiaoping (1997) and Lehmann (1999). Here, we differ from aforementioned contributions, by the type of the observation equation that we introduce via application of the inverse Bruns' formula.…”

Μελέτη Του Πεδίου Βαρύτητας Και Της Θαλάσσιας Τοπογραφίας Στον Ελλαδικό Χώρο Με Συνδυασμό Επίγειων Δεδομένων Και Δεδομένων Των Νέων Δορυφορικών Αποστολών CHAMP Και GRACE.

“…Στην παρούσα διατριβή αξιοποιείται η κλασσική διατύπωση του προβλήµατος συνοριακή τιµών. Υπάρχει εκτενής βιβλιογραφία σχετική µε τις διατυπώσεις των προβληµάτων συνοριακών τιµών και τον τρόπο επίλυσής τους (π.χ., Arnold 1983;Grbenitcharsky 2004;Heck 1997;Heiskanen and Moritz 1967;Keller 1996;Lehmann 1999aLehmann , 1999bMoritz 1980;Sansò 1981Sansò , 1993Sansò , 1995. ( )…”

A numerical study of solving the altimetry-gravimetry boundary value problem in coastal regions

“…Holota treated both problems in a linearized form in Holota (1983aHolota ( , 1983b. Later, with the availability of GPS/levelling data, a new AGBVP appeared, called AGBPV III (Lehmann, 1999). All AGBVPs consist of two different types of geodetic boundary data sets, one on land and one at sea.…”

“…They are usually used to ensure the well-posedness of the problem (Sacerdote and Sanso 1987, Svensson 1988, Lehmann 1999. The uniqueness and existence of the solution of AGBVPs depend upon the smoothness assumptions along the coastline.…”

“…2 The AGBVP II and the role of compatibility conditions along the coastline -spherical approximation According to Sanso (1993) and Lehmann (1999) the AGBVP II in spherical approximation, will have the form:…”