Inversion of gravity‐field inclination to map the basement relief of sedimentary basins

Abstract

This paper presents a method to map the basement relief of homogeneous sedimentary basins that does not require the knowledge of the basin density contrast. To reach this task, the proposed method relies on the invariance of the inclination of the anomalous gravity field with the density contrast caused by models constituted by two homogeneous media. This invariance occurs because the density contrast appears as a constant factor in both vertical and horizontal gravity components, therefore being canceled out when these components are divided during the evaluation of the field inclination. For such media, the field inclination is independent of the density contrast, thus allowing the source geometry reconstruction even when the density contrast is unknown. As the inclination is rarely measured, the gravity anomaly (i.e., the field vertical component) is initially used to compute the horizontal component of the gravity field by applying a suitable linear transform. The field inclination is estimated from both components and then used to invert the source geometry by fitting the inclination values under the geologic constraints attributed to the causative sources. In this process, the density contrast is not required nor introduced as an unknown parameter in the formulated inverse problem. Moreover, it can be estimated later by solving a new inverse problem where the source geometry determined from the inverted inclination is fixed and the constant density contrast is determined by fitting the gravity anomaly. This paper applies such ideas to map the basement relief of a sedimentary basin and to estimate its density contrast. The inversion is implemented by a random search procedure that excludes extreme models, and imposes constraints that the unknown interface is smooth everywhere and assumes known depth values at isolated points investigated by wells. The proposed technique is tested with synthetic noisy data from homogeneous and heterogeneous basin models and is applied to invert a gravity profile from the Recôncavo Basin, Brazil. The results from the real data application are compared with well data and previously published results.