Joint inversion of magnetic and gravity data using group lasso regularization

Magnetic and gravity inversion has long attracted attention and research. A recent topic in such inversion studies is the magnetic and gravity joint inversion with the constraint that the derived magnetization and density models are similar and correlated. The purpose of this approach is to reduce the non-uniqueness of the individual models, which is an inherent problem of potential-field data inversion, by using the constraints of multiple data. Another point of interest is the introduction of sparse regularization in the magnetic and gravity inversion. If the conventional smoothness promoting inversion is used, the derived model is likely to be blurred. The aim of introducing sparse regularization is to reduce the blurred feature and improve the resolution of the derived model. In this paper, we proposed and developed a new magnetic and gravity joint inversion method by introducing the group lasso regularization. The group lasso is a kind of sparseness promoting regularization method, an extension of the L1 norm regularization. By introducing the group lasso into the magnetic and gravity joint inversion, the derived magnetization and density models are constrained to have a high correlation with each other and at the same time the sparseness of the derived model is promoted. In this way, the incorporation of the group lasso has the advantage that the two recent research trends, the introduction of structural similarity and sparseness in the derived model, can be implemented at once. However, the L1 norm and other sparse regularization methods are known to have a drawback of deriving an over-concentrated model, and this property is carried over to the group lasso, which is confirmed by the synthetic test. Therefore, to overcome this problem, this paper proposes the use of L2 norm and group lasso combined regularization, which leads to derive a correlated magnetic and density model that is not overly concentrated and not too blurred. The implementation of the inversion with this combined penalty can be easily completed by using the Alternating Direction Method of Multiplier (ADMM), a family of Lagrange multiplier methods. The proposed method is applied to synthetic data and magnetic and gravity anomalies observed on the Hiraniwa pluton, Kitakami Belt, North-east Japan, and the validity of our proposed method is confirmed.