Mass Anomalies of Earth, Venus, and Mars: Initial Estimates

Abstract

Sets of planetary spherical harmonic coefficients, because they depict the gravity potential field from the planet surface into the surrounding space, offer two means for estimating the magnitudes of causative mass anomalies. One is from simple ratios, at anomaly centers, of the vertical derivative of the potential (gravity) by its integral (geoid) anomaly value. That ratio gives an estimate of an equivalent point mass depth, and then using that depth with either of the anomaly values used in computing the ratio, a mass estimate is obtained for the equivalent point mass. The ratio of the depths obtained by the gravity over geoid values, divided by the vertical gravity gradient over gravity values, tests the degree to which contributing mass anomalies are co-centric and at a common depth, by deviation from a value of 1.0. The second method analyzes individual harmonic degree contributions, and their consistency for evaluating causative masses. So far this last method has only rigorously been applied to the Earth, revealing that the greatest mass anomalies (about 9×10²² grams) probably result from topography at the core-mantle boundary. [the corresponding simple ratio mass estimates are 1.4 − 1.8×10²² grams] The largest Venus geoid anomaly features have ratio estimated masses of 1.2×10²² and 8.1×10²¹ grams (with depth ratios of 1.09 and 1.3). Most of Venus’ anomaly features have depth ratio values within 1/10 of 1.0. The three largest Mars geoid anomaly features all correlate with positive topography features and have ratio estimated masses of 5.4, 4.6, and 2.4×10²² grams, but their depth ratio values are 0.71, 0.65, 0.76 (all Mars’ depth ratio values are less than 0.85), indicating more complex structures than on Venus.