Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part II: Non-uniform source field model

Abstract

The Riccati equation approach to the analysis of magnetotelluric impedances in 1-D anisotropic structures is generalized to models with non-uniform source field excitation. The problem is solved in the horizontal wave-number domain. General Riccati matrix equations for the spectral impedances of the medium are derived and their relation to the standard impedance propagation formulae in layered anisotropic models is discussed. Riccati equations give a full solution for the spectral impedances, comprising both the induction and galvanic mode. For a purely inductive excitation of the field, each wave-number harmonics of the magnetic field is strictly linearly polarized on the surface, and only one half of the spectral impedance tensor can be restored. Both induction and galvanic modes generally exist inside the anisotropic conductor and are coupled. A formal similarity between the Riccati equations for a 1-D anisotropic medium with non-uniform sources and those obtained for 2-D laterally inhomogeneous structures is demonstrated, which indicates a possible way of extending the Riccati impedance/admittance equations to multi-dimensional conductors.