Matrix polynomial representation of the anisotropic magnetotelluric impedance tensor

A formalism based upon the equal penetration depth stratification assumption is extended to a layered anisotropic medium, yielding a recursive algorithm for the computation of the magnetotelluric impedance tensor elements. The development of this new procedure requires an appropriate layer-discretization as well as an extension of the reflection coefficient definition for the anisotropic layered model.This method transfers the differential problem into an algebraic one, and is independent of the electric and magnetic field vectors. The technique is a recursive process which gives a rational matrix polynomial representation for the magnetotelluric impedance tensor.The procedure involves the use of second-order matrices, rather than the fourth-order ones normally used for such a case. Using this representation, a separation of the contribution of the model parameters from that of the frequency is achieved. Consequently the elements of the magnetotelluric impedance tensor are computed, for each frequency, using coefficients which are evaluated just once for a given model.