A New Axial Constraint with Variable Angle for the Inversion of Gravity Data

The axial constraint is an important constraint for the inversion of gravity data with which the dip information of the target geological bodies can be incorporated effectively. However, poor selection of the dip angles would inevitably lead to unreasonable inversion results. To reduce the errors caused by inappropriate angle estimation, this study proposes a new variable angle axial constraint for the inversion of gravity data. Moreover, to extend the utility of this new constraint, a method for employing multi-axial constraint is also introduced. The presented novel multi-axial constraint with a variable angle can be used to solve the inverse problems for complex geological bodies. We present a detailed iterative algorithm to solve the inverse problems with the presented constraints, in which the randomized singular value decomposition (RSVD) is used to solve the total objective function, and the generalized cross-validation (GCV) is utilized to estimate the regularization parameter. Numerous tests on synthetic gravity data with noise demonstrate that the inversion errors induced by inappropriate angle estimation can be greatly reduced by using the new constraints. Moreover, the presented methodology is successfully applied to a field data from the Morro do Engenho complex in the center of Brazil. This application also demonstrates the effectiveness of the proposed constraint.