A regularized magnetotelluric inversion with a minimum support gradient constraint

Magnetotelluric (MT) inversion is an ill-posed problem and the standard way to address it is through regularization, by adding a stabilizing functional to the data objective functional in order to obtain a stable solution. The traditional stabilizing functionals, in which a low-order differential operator is used, yield a smooth solution that may not be appropriate when anomalies occur in block patterns. In some cases the focused imaging of a sharp electrical boundary is necessary. Even though various experiments have used stabilizing functionals that are suitable to obtain a clear and sharp boundary, such as the minimum support (MS) and the minimum gradient support (MGS) functionals, there are still some limitations in practice. In this paper, the minimum support gradient (MSG) is proposed as the stabilizing functional. Under the uniform regularization framework, a regularized inversion with a variety of stabilizing functionals is performed and the inversion results are compared. This study shows that MSG inversion can not only obtain a clearly focused inversion but also a quite stable and robust one.