A new objective method is proposed for estimating an average surficial density, Bouguer density, from gravity data, which then may be correlated with the surface and/or near-surface geology in analyzed area. The method assumes that a suitable Bouguer density will lead to smooth Bouguer anomaly. With this assumption, the method fits a two-dimensional curved function to the observed Bouguer anomaly by finding a Bouguer density that gives the optimum trade-off between smoothness and goodness of fit to the Bouguer anomalies. This trade-off is interpreted by an objective Bayesian procedure and determined by minimization of Akaike's Bayesian Information Criterion (ABIC). Further, the distribution of Bouguer density is assumed to be smooth enough to apply our method to any of the spatial windows with an area of 20¿20 km2 in the district, and therefore be obtainable by moving successively the windows. The proposed method is tested against the gravitational data in Kyushu district, southwest Japan. The distribution of Bouguer density which is obtained by this method agrees remarkably well with the geology of the relevant area. ¿ American Geophysical Union 1993