Choice of norm for the density distribution of the Earth |
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Authors: | F Sansò R Barzaghi C C Tscherning |
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Institution: | Politecnico di Milano, Istituto di Topografia, Fotogrammetria e Geofisica, Piazza L. Vinci, 32, I-20133 Milano, Italy;Geodαtisk Institut, Geodαtisk Afdeling I, Gamlehave Alle22, DK-2920 Charlottenlund, Denmark |
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Abstract: | Summary. The determination of the density distribution of the Earth from gravity data is called the inverse gravimetric problem. A unique solution to this problem may be obtained by introducing a priori data concerning the covariance of density anomalies. This is equivalent to requiring the density to fulfil a minimum norm condition. The generally used norm is the one equal to the integral of the square of the density distribution ( L2 -norm), the use of which implies that blocks of constant density are uncorrelated. It is shown that for harmonic anomalous density distributions this leads to an external gravity field with a power spectrum (degree-variances) which tends too slowly to zero, i.e. implying gravity anomalies much less correlated than actually observed. It is proposed to use a stronger norm, equal to the integral of the square sum of the derivatives of the density distribution. As a consequence of this, base functions which are constant within blocks, are no longer a natural choice when solving the inverse gravimetric problem. Instead a block with a linearly varying density may be used. A formula for the potential of such a block is derived. |
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Keywords: | minimum norm inversion mixed collocation |
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