Concept of effective density: Key to gravity depth determinations for sedimentary basins

Abstract

The gravity anomaly observed over a layered sedimentary basin is close to that calculated over a basin with the same configuration and depth but filled by homogeneous sediments with density equal to the effective (weighted average) density of the real layered basin. Therefore, it is possible to calculate the effective density contrast of a basin from the residual gravity anomaly over it, if the depth of the basin is known at least at one point. Assuming a mathematical function for density‐depth dependence, an expression for the gravity‐depth dependence using the infinite slab (Bouguer) formula can be developed. This expression makes it possible to calculate the depth of a basin or an isopach map from gravity data. An exponential function and a new hyperbolic density‐depth function and their gravity‐depth functions are analyzed and implemented for determining the depths of basins from gravity data for the San Jacinto graben, California, and the Tucson basin, southern Arizona. The hyperbolic functions are more reliable and realistic than exponential ones. The effective density contrast of sediments filling the Tucson basin and density‐depth dependence were calculated using the infinite‐slab formula from residual gravity data over the deepest borehole, which entered pre‐Eocene bedrock at a depth of 3.66 km. The hyperbolic density‐depth dependence for the Tucson basin is also assumed to be effective for all other basins in the Basin and Range Province, southern Arizona and southwestern New Mexico. The density‐depth function is easily converted into a gravity‐depth function, using the infinite‐slab formula. The residual gravity map of each basin in this Province can then be transformed into a map of basin depth contours, using the hyperbolic gravity‐depth function. Comparison of depths of basins calculated from gravity data with available borehole information (19 wells) showed that the proposed simple and fast method has an error in the range of about 13 percent of the actual depth.