Inversion of magnetotelluric soundings using a new integral form of the induction equation

Electromagnetic inverse problems can be formulated using exact non-linear integral equations similar to the traditional linearized equations. It has been suggested by other workers that, while these exact equations are correct, they are not an appropriate basis for general inversion algorithms, in particular for magnetotelluric soundings. In this paper we present a general inversion algorithm based on the exact equation for magnetotelluric soundings. The integral equation is derived directly from the 1-D electromagnetic induction equation using elementary operations, and it is solved numerically by iterations using linear programming techniques. At each iteration the equation is approximated by a linear relationship similar to that of traditional linearization, except that the data and the conductivity profile are not referred to as perturbations, although a reference model is still needed for computing derivatives. It is argued that the method is a natural extension of the Niblett-Bostick transformation for magnetotelluric soundings. The performance of the method is illustrated using numerical experiments and applications to field data.