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Question

If we separately add up |H| and |h| over the earth surface, which of the sums come out smaller?

Background

There is a phrase in the tag description of "ellipsoid" that says "... the geoid, the truer figure of the Earth ..." I am not sure "true" here means less absolute error but I am interested in this question nevertheless.

The following passage seems to suggest that the geoid may not approximate the earth surface particularly well in the land areas: "The dominance of the low-harmonic degrees in the geoid power spectrum indicate that the dominant shape of the geoid is controlled by structures deep within the mantle."

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    What are you trying yo achieve?
    – Devdatta Tengshe
    Dec 15, 2013 at 14:29
  • I feel that question is far too broad, and isn't an answerable questions based on actual problems that you face. To get an answer, I'll recommend that you narrow down the question to a practical question.
    – Devdatta Tengshe
    Dec 16, 2013 at 14:22
  • @Devdatta This is a simple clear question that admits an objective answer, although that answer would take some work to obtain. If you look at a map of the EGM96 geoid, it appears that it is lower than WGS84 in mountainous areas like the Himalayas. (Mountains "float" on tectonic plates because they are less dense and as such the gravity is a little weaker there.) That would suggest--but does not yet prove--that the answer to this question is the WGS84 spheroid.
    – whuber
    Dec 16, 2013 at 15:46

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The answer depends on what you are interested in and therefore what you mean by 'earth's surface'. The Geoid is the equipotential surface (in terms of gravitational potential). The ellipsoid is a geometric approximation of the irregular land-sea (physical) surface. Given the irregularities even in the physical surface, no ellipsoid can ever do a perfect job. On the other hand, the definition of a geoid is clear, its measurement can be improved.

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