The interpretation of gravity data often involves initial steps to eliminate or attenuate unwanted field components in order to isolate the desired anomaly (e.g., residual-regional separations). These initial filtering operations include, for example, the radial weights methods (Griffin, 1949; Elkins, 1951; Abdelrahman et al., 1990), the fast Fourier transform methods (Bhattacharyya, 1965; Clarke, 1969; Mesko, 1969, 1984, Botezatu, 1970), the rational approximation techniques (Agarwal and Lal, 1971) and recursion filters (Bhattacharyya, 1976), and the bicubic spline approximation techniques (Bhattacharyya, 1969; Inoue, 1986). The derived local gravity anomalies are then geologically interpreted to derive depth estimates, often without properly accounting for the uncertainties introduced by the filtering process. When filters are applied to observed data, the filters often cause serious distortions in the shape of the gravity anomalies (Hammer, 1977). Thus the filtered gravity anomalies generally yield unreliable geologic interpretations (Rao and Radhakrishnamurthy, 1965; Hammer, 1977; Abdelrahman et al., 1985, 1989.