Abstract

A minimum distance mapping from the physical surface of the earth to the telluroid under the normal filed of Somigliana-Pizzetti is constructed. The point-wise minimum distance mapping under the constraint that actual gravity potential at the a point of physical surface of the earth be equal to normal potential of Somigliana-Pizzetti leads to a system of four nonlinear equations. The normal equations of minimum distance mapping are derived and solved via Newton-Raphson iteration. The problem of the existence and uniqueness of the solution is addressed. As a case study the quasi-geoid for the state Baden-Wurttemberg (Germany) is computed.

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