A new covariance model for inertial gravimetry and gradiometry
Abstract
A selfconsistent 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 secondorder 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 TscherningRapp 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, highfrequency attenuation, and lowfrequency 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.
 Publication:

Journal of Geophysical Research
 Pub Date:
 February 1987
 DOI:
 10.1029/JB092iB02p01305
 Bibcode:
 1987JGR....92.1305F
 Keywords:

 Covariance;
 Geopotential;
 Gravimetry;
 Gravity Gradiometers;
 Inertia;
 Mathematical Models;
 Airborne Equipment;
 Earth Surface;
 Flat Surfaces;
 Geoids;
 Self Consistent Fields;
 Geodesy and Gravity: Geopotential theory and determination;
 Geodesy and Gravity: Local gravity anomalies and crustal structure