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.

3D Gravity Inversion by Growing Bodies and Shaping Layers at Mt. Vesuvius (Southern Italy)

“…This is a traditional use of gravity inversion (e.g., studies of sedimentary basins). Considering only one irregular discontinuity surface, the inversion process is not hard to detect, and many studies that have been providing suitable procedures to obtain inversions for just one discontinuity surface are available (e.g., RADHAKRISHNA MURTHY and JAGANNADHA RAO, 1989;RAMA RAO et al, 1999;GALLARDO-DELGADO et al, 2003). A more problematic question is to obtain a non-subjective inversion model when several discontinuity layers are simultaneously considered.…”

Gravity effects of polyhedral bodies with linearly varying density

“…In perfect analogy with the case of constant density mass distributions the case of prisms has been first considered and increasing degrees of complexity in the modelling of the density variation have been taken into account, ranging from linear (Chai and Hinze 988), to quadratic (Garcìa-Abdeslem 1992; Gallardo-Delgado et al 2003), to cubic (Garcìa-Abdeslem 2005), and exponential (Chai and Hinze 988).…”

Joint inversion of gravity and magnetic data for a two-layer model

“…Zhang et al (1993) used BG theory to study an approach to inverting gravity and magnetic data of the same layer with density and magnetism and developed a general linear integral inversion system. Gallardo-Delgado et al (2003) extended the 3D approach to include a continuous density variation with depth and the magnetization direction as unknown parameters. A damped least-squares method was used for joint inversion of gravity and magnetic data by Pilkington (2006) to determine the topography of an interface having a constant density and magnetization contrast.…”