Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media ?
Anisotropy of the electrical conductivity within the Earth has recently provided a significant link between geoelectrical models and the underlying tectonic setting. Interpretation of magnetotelluric data for anisotropic conductivities suffers from inherent ambiguity, and even for theoretically distinguishable parameters the resolution pattern may be rather complex as compared to isotropic models. As a tool for the resolution and sensitivity studies, we present an algorithm for jointly evaluating the magnetotelluric impedances and their partial derivatives with respect to the parameters of a 1-D generally anisotropic layered medium. The algorithm is based on impedance propagation formulas through a stack of anisotropic layers and their direct differentiation with respect to the model parameters. By virtue of an equivalency principle, the situation of a generally anisotropic layered medium can be always reduced in magnetotellurics to a simpler model with horizontally anisotropic layers. By rotating the impedances into the local anisotropy strike, the two wave modes in an anisotropic layer can be quasi-separated, and elimination of the positive exponential wave factors in the impedance formulas is possible, which stabilizes both the impedance and sensitivity calculations. The performance of the algorithm is demonstrated on a simple qualitative sensitivity study for a four-layer model with depth-variable anisotropy parameters.
impedance propagation equivalent horizontal anisotropy matrix propagation parametric partial derivatives frechet derivatives