By Zdenek Martinec
This publication bargains a simultaneous therapy of the idea and numerical program of boundary-value difficulties relating to the choice of an actual geoid from gravimetric info. the next topics are mentioned: topographical results and their computations in specified gravimetric geoid selection, the downward continuation of a harmonic functionality, Stokes' challenge formulated on an ellipsoid of revolution, round Stokes' challenge with ellipsoidal corrections serious about boundary stipulations for an anomalous capability, and the altimetry-gravimetry boundary-value challenge. the reply to a few clinical difficulties, raised and mentioned in geodetic literature over the last years, are available the following. The e-book is meant for scientists and complicated graduate students.
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Extra info for Boundary-Value Problems for Gravimetric Determination of a Precise Geoid
We will call Vn(r, f~) the terrain roughness term. It depends chiefly on the behaviour of the difference H ( a ) - Y(a'). 13). When ¢ -+ 0, then ~(f~') -+ ~(f~) and g(f~') -+ H(f~). , that there are no mass-singularities inside the topographical masses and the heights of the Earth's topography are finite). , Z,:R ¢=+on ( r , ¢ , r ' ) L(r,~,~)dr' fR+H(~) sine sin~b= li_+mL(r,¢,r,)r'2dr '. 15) are finite and have the same value; their difference is thus equal to zero. 13). 3). 3 The Pratt-Hayford and the Airy-Heiskanen isostatic compensation models In order to remove the singularity of the isostatic compensation potential V ° (r, f~), cf.
1 P r i n c i p l e of m a s s c o n s e r v a t i o n Let us first consider the case when surface density ~r(~) of the Helmert condensation layer is chosen according to principle of mass conservation. , i c= i t . (~) e(r, fl)r2drdn . 3) Zeroth- and tirst-degreesphericMharmonics 29 in any direction fL Provided that the density of the condensation layer is chosen in agreement with the principle of mass conservation, the residual topographical potential 5V does not include, by definition, zeroth-degree spherical harmonic, but it does include the first-degree spherical harmonics.
5: The real vs. imaginary parts of the eigenvalues of matrix A with (lower branch) and without (upper branch) the ellipsoidat corrections eh and %. 4 (J~l = 20, and jma~ = 1600). ~ = 80 °) (e02= 0 and j~ei = 10000). --~ ¢D 3 . . . 6. act as regularization factors removing the ill-posedness of matrix A. , Cruz, 1985). 3, but now, in contrast with preceeding Stokes's two-boundary-value problem 23 example, we will not multiplied height H(t~) by 10. In this case, it is not possible to carry out the eigenvatue analysis of matrix A starting from degree j~,] = 20 and going up to degrees j m ~ ~ 104 - 10s due to a huge consummation of computer time and memory.
Boundary-Value Problems for Gravimetric Determination of a Precise Geoid by Zdenek Martinec