A comparative study of spherical and flat-Earth geopotential modeling at satellite elevations
Flat-Earth modeling is a desirable alternative to the complex spherical-Earth modeling process. These methods were compared using 2 1/2 dimensional flat-earth and spherical modeling to compute gravity and scalar magnetic anomalies along profiles perpendicular to the strike of variably dimensioned rectangular prisms at altitudes of 150, 300, and 450 km. Comparison was achieved with percent error computations (spherical-flat/spherical) at critical anomaly points. At the peak gravity anomaly value, errors are less than + or - 5% for all prisms. At 1/2 and 1/10 of the peak, errors are generally less than 10% and 40% respectively, increasing to these values with longer and wider prisms at higher altitudes. For magnetics, the errors at critical anomaly points are less than -10% for all prisms, attaining these magnitudes with longer and wider prisms at higher altitudes. In general, in both gravity and magnetic modeling, errors increase greatly for prisms wider than 500 km, although gravity modeling is more sensitive than magnetic modeling to spherical-Earth effects. Preliminary modeling of both satellite gravity and magnetic anomalies using flat-Earth assumptions is justified considering the errors caused by uncertainties in isolating anomalies.