Upward continuation of gravity disturbance covariance functions

Physics

Scientific paper

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Covariance, Earth Surface, Geoids, Gravity Anomalies, Altitude, Anisotropy, Fourier Transformation, Inertial Navigation, Integral Equations, Isotropism, Markov Processes, Mathematical Models, White Noise

Scientific paper

The paper presents a method for extrapolating covariance functions aloft. Covariance functions for gravity anomalies, vertical deflections, and undulations of the geoid are typically estimated from data that are available on the surface of the earth. One- and two-dimensional integrals are derived for upward continuation of gravity disturbance covariance functions. An upward continuation integral is derived for the disturbing potential autocovariance function, and the gravity anomaly and gravity disturbance autocovariance function are then determined by differentiation. Both spherical earth and flat earth formulas are presented as well as the associated Legendre and Fourier transforms.

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