DETERMINATION OF THE FIRST DERIVATIVES OF THE DISTURBING POTENTIAL BY GREEN'S FUNDAMENTAL FORMULA.
OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE
Pagination or Media Count:
Simplified evaluations of the first derivatives with respect to an arbitrary direction of the potential of a simple layer and a double layer are given. The obtained formulas are used to differentiate Greens fundamental formula, which follows from Greens identities. They are checked by another method of differentiation. An application of the derivative of Greens formula in geodesy leads to a linear integral equation for the derivative of the disturbing potential with respect to the earths normal. Using a method due to Molodensky, the integral equation is transformed into an integral formula. This formula yields the first derivatives of the disturbing potential at the earths surface with respect to an arbitrary direction, if the free-air anomalies and the disturbing potential are known at the earths surface. Author