Solution of the altimetry-gravimetry problem

Svensson, S. Leif

doi:10.1007/bf02520937

Cited by 25 publications

(20 citation statements)

References 3 publications

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“…Further results for the simple AGP-I,II are due to Svensson (1983Svensson ( , 1988. This new approach made heavy use of the modern concept of pseudo-dierential operators (PDOs).…”

Section: Evolution Of the Theory Of Agpsmentioning

confidence: 99%

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Boundary-value problems in the complex world of geodetic measurements

Lehmann

1999

Journal of Geodesy

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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.

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“…Further results for the simple AGP-I,II are due to Svensson (1983Svensson ( , 1988. This new approach made heavy use of the modern concept of pseudo-dierential operators (PDOs).…”

Section: Evolution Of the Theory Of Agpsmentioning

confidence: 99%

“…(Note that compatibility in this sense is dierent from Arnold's notion of compatibility; see above.) Moreover, Svensson (1988) demonstrated numerically that ill-posed cases exist for AGP-I,II, i.e. the boundary operator may have a non-trivial nullspace.…”

Section: Evolution Of the Theory Of Agpsmentioning

confidence: 99%

Boundary-value problems in the complex world of geodetic measurements

Lehmann

1999

Journal of Geodesy

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“…In reality, irregularities exist on the coastline because different types of data with different observation procedures, accuracy and resolution are used. According to Svensson (1988), unless the compatibility conditions are recognized, the mixed problems cannot be solved with a higher degree of smoothness. Additional constraints on the data for the regularization of the solution across the coastline were derived in Sacerdote and Sanso (1987).…”

Section: Introductionmentioning

confidence: 98%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Grebenitcharsky

Sideris

International Association of Geodesy Symposia

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Abstract. The paper presents numerical results for the solution of the altimetry-gravimetry boundary value problem with compatibility conditions along the coastline. The solution is based on the application of spherical Shannon wavelets based on the AbelPoisson kernel and pseudo-diffferential operators. The orthogonality of Shannon wavelets can be used for the numerical solution overcoming some technical problems with generally non-orthogonal spherical wavelets.A numerical experiment has been conducted in eastern Canada and the results have been compared with the geoid heights computed from gravity anomalies by applying ID FFT spherical Stokes convolution with 50 km integration radius. The effect of compatibility conditions along the coastline on the solution are discussed and the following conclusions are drawn: spherical Shannon wavelets can be very successfully applied in the numerical solution of the AGBVP II and the smoothing effect of spherical wavelets is much more effective than the classical planar type of wavelets.

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