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Boundary-Value Problems for Gravimetric Determination of a by Zdenek Martinec

By Zdenek Martinec

This booklet deals a simultaneous therapy of the idea and numerical program of boundary-value difficulties regarding the choice of an exact geoid from gravimetric information. the subsequent matters are mentioned: topographical results and their computations in certain gravimetric geoid choice, the downward continuation of a harmonic functionality, Stokes' challenge formulated on an ellipsoid of revolution, round Stokes' challenge with ellipsoidal corrections excited by boundary stipulations for an anomalous capability, and the altimetry-gravimetry boundary-value challenge. the reply to a few medical difficulties, raised and mentioned in geodetic literature during the last years, are available right here. The ebook is meant for scientists and complicated graduate students.

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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. 18) Chapter 3 38 The compensation density &(f~) and the depth D(f~) are two free parameters of an isostatic compensation model that must be chosen before computing topographical effects.

In the past, two extremely idealized isostatic compensation models were proposed to cancel the effect of topographical abundances from surface gravity observations. ), the topographical masses are compensated by varying density distribution within the layer of a constant thickness, D(f/) = Do=const. 21) can be approximated by 1. 67 g/cm 3. 23) Topographical effects 39 The Airy-Heiskanen model assumes that the topographical masses are compensated by varying thickness D(f~) of a compensation layer.

This difference depends on a height of the computation point; the larger the height of the computation point, the larger the difference between these kernels, and therefore, the stronger is the indirect topographical effect on potential. ,'" °,, -- E-7 ~ i~.. i ~ ~l/r~-i t~ill i l~t, I 1E-4 1E-3 1E-2 IE-1 1E+0 1E-4 angular distance (degree) 1 E+2 IE+1 ~ 1E-3 1E-2 1E-1 tE+O angular distance (degree) '~,-. ,9. = . ltl] tE-4 1E-3 1E-2 IIIIIII 1E-1 1E+O angular distance (degree) The integration kernels for the indirect and direct topographical effects grid step size rather than that with a sparse grid size.

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