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Spherical harmonic expansion of the continents and oceans distribution function

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В эmоŭ сmamъе оnuсывaеmся nроцесс вычuсленuя коэффuцuенmов ¶rt;ля сферuческогогaрмонuческого ря¶rt;a ¶rt;ля функцuu Е(г, φ), коmорaя nозволяеm оnре¶rt;елumъ рaсnре¶rt;еленuе конmuненmов u океaнов nрu nомощu меmо¶rt;a нauменъщuх квa¶rt;рamов. Обсуж¶rt;aюmя некоmорые своŭсmвa сuсmемы номaлънх урaвенuŭ ¶rt;ля случaя, ког¶rt;a uзмерumелъные mочкu рaсnоложены в регулярноŭ сеmu. Полносmъю нормaлuзозовaнные комnлэксные коэффцuенmы ¶rt;o ¶rt;евяmоŭ сmеnенu nрuво¶rt;яmср в maблuце.

Summary

An algorithm is derived to compute the coefficients of a spherical harmonic series for the functionE(г, φ) representing the distribution of continents and oceans with the least-squares method. Some properties of the system of normal equations, when measuring points are distributed in a regular grid, are discussed. The fully normalized complex coefficients to the ninth degree are given in the table.

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Authors and Affiliations

  1. Karl-Marx-Universität, Leipzig

    Uwe Koppelt

  2. Charles University, Prague

    Martin Biegel

Authors
  1. Uwe Koppelt
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  2. Martin Biegel
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Koppelt, U., Biegel, M. Spherical harmonic expansion of the continents and oceans distribution function. Stud Geophys Geod 33, 315–321 (1989). https://doi.org/10.1007/BF01637687

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  • DOI: https://doi.org/10.1007/BF01637687

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