Appreciable changes in elevations of satellite tracks create significant highs, lows, and trends in a map of the residual total magnetic field. In order to remove these features associated with the peculiarities of the satellite path a method has been developed to reduce the observed residual field to a spherical surface at a constant height from the ground. The reduced field is then continued downward to a parallel surface with recursive operators for enhancement of the detailed features of the anomalous field. The residual field obtained by the process of downward continuation is nonharmonic owing to the variation of the direction of the geomagnetic field over the large area usually covered by satellite anomalies. For this reason the components of the field along fixed directions in space are calculated from the residual total field by employing a new method. This method provides expressions for the field components in the form of digital convolutions of the residual field with suitable operators. The components can then be combined, if necessary, to produce the anomalous total field at any fixed geomagnetic latitude.