In-depth 3D magnetic inversion of basement relief

Abstract

We have developed an iterative, efficient, and stable 3D magnetic inversion method to estimate the depth to the basement of a sedimentary basin, the volume of which is approximated by a grid of rectangular prisms with tops at an arbitrary surface and thicknesses estimated iteratively. To compute the thicknesses corrections at the kth iteration, we first compute an approximate sparse sensitivity matrix in which the nonnull elements of a given line are obtained by differentiating the fitting function at the observation position (which occupies the center of a small moving data window) relative to the thicknesses of the prisms situated inside the window. By moving the data window around, all nonnull elements of all lines are computed. This sparse matrix is used to calculate an approximate Gauss-Newton gradient and an approximate diagonal Gauss-Newton Hessian matrix. Finally, by dividing each element of the gradient vector by the corresponding diagonal element of the approximate Hessian matrix, we obtain the corrections of all parameters at a given iteration. The solution is stable because of (1) the small parameter corrections inherent to the method, combined with the initial estimate at the surface and (2) the application of a moving average operator to the solution. Any magnetization orientation, except horizontal (and parallel to any vertical side of the prisms), yields good results. In the case of magnetization inclinations of approximately 45°, the rectangular prisms may induce spurious ripples on the surface of the estimated relief, which can be eliminated by simultaneously reducing the horizontal dimensions of the prisms and applying an appropriate moving average to the solution. Application of our method to real data in a rift area discloses a confined basin with steep and asymmetric borders, confirming the practical utility of the method.