A versatile algorithm for joint 3D inversion of gravity and magnetic data

Abstract

We describe the implementation of a versatile method for interpreting gravity and magnetic data in terms of 3D structures. The algorithm combines a number of features that have proven useful in other algorithms. To accommodate structures of arbitrary geometry, we define the subsurface using a large number of prisms, with the depths to the tops and bottoms as unknowns to be determined by optimization. Included in the optimization process are the three components of the magnetization vector and the density contrast, which is assumed to be a continuous function with depth. We use polynomial variations of the density contrast to simulate the natural increase of rock density with depth in deep sedimentary basins. The algorithm minimizes the quadratic norm of residuals combined with a regularization term. This term controls the roughness of the upper and lower topographies defined by the prisms. This results in simple shapes by penalizing the norms of the first and second horizontal derivatives of the prism depths and bottoms. Finally, with the use of quadratic programming, it is a simple matter to include a priori information about the model in the form of equality or inequality constraints. The method is first tested using a hypothetical model, and then it is used to estimate the geometry of the Ensenada basin by means of joint inversion of land and offshore gravity and land, offshore, and airborne magnetic data. The inversion helps constrain the structure of the basin and helps extend the interpretation of known surface faults to the offshore.