Covariance Expressions for Second and Lower Order Derivatives of the Anomalous Potential.
Scientific rept. no. 2,
OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE
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Auto-and cross-covariance expressions for the anomalous potential of the Earth and its first and second order derivatives are derived based on three different degree-variance models. A FORTRAN 4 subroutine is listed and documented that may be used for the computation of auto- and cross-covariance between any of the following quantities 1 the anomalous potential T, 2 the negative gravity disturbancer, 3 the gravity anomaly delta g, 4 the radial component of the gradient of delta g, 5 the second order radial derivative of T, 6, 7 the latitude and longitude components of the deflection of the vertical, 8, 9 the derivatives in northern and eastern direction of delta g, 10, 11 the derivatives of the gravity disturbance in northern and eastern direction, 12-14 the second order derivatives of T in northern, in mixed northern and eastern and in eastern direction. Values of different kinds of covariance of second order derivatives for varying spherical distance and height are tabulated.