Partial Derivatives for the One-Dimensional Magnetotelluric Problem

This paper shows methods for calculating the partial derivatives of various components of the impedance tensor observable at the free surface, with respect to several components of the conductivity at different depths within the model, and with respect to the thicknesses of different sublayers, for a structure consisting of a stack of sublayers overlying a homogeneous half-space. The structure may contain isotropic and non-isotropic layers. For illustration we calculated the resolution and information matrices as well as the trade-off curve derived from the partial derivatives for a structure having high conductivity at some depth.