A new covariance model for inertial gravimetry and gradiometry

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Abstract
A self‐consistent covariance model for the earth's anomalous gravity field is presented within the framework of the planar approximation. The model features simple, closed formulas for autocovariances and cross covariances of geoid undulations, gravity anomalies, deflections of the vertical, and second‐order gradients, both at the reference plane and aloft. Furthermore the main spectral decay of the model gravity power spectral density corresponds closely to Kaula's rule, thus yielding good fits to actual gravity field spectral characteristics. The outlined model may be viewed as the planar equivalent to the spherical Tscherning‐Rapp model. The analytical model is characterized by three free parameters: the gravity anomaly variance, a “shallow” depth parameter, and a “compensating” depth. These parameters act as scale factor, high‐frequency attenuation, and low‐frequency attenuation, respectively. The shallow depth parameter corresponds to twice the Bjerhammer sphere depth of spherical harmonic analysis, while the compensating depth is introduced as an arbitrary mathematical convenience, necessary to obtain finite values for gravity and geoid variance.

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