Knowledge Bank

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 IV 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 disturbance/r, (3) the gravity anomaly Δg, (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 of northern and eastern direction of Δg, (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.