Electromagnetic fields in planarly layered anisotropic media

This paper presents a method for calculating the electromagnetic field from a dipole source in stratified media with general anisotropy. The formulation can be applied to geophysical applications such as ground-penetrating radar and marine controlled source electromagnetic (CSEM) methods. In stratified media, the propagation of fields can be considered in the frequency-wavenumber domain. The resulting set of ordinary differential equations consists of a field vector, a system matrix, and a source vector. In each piecewise homogeneous region, the system matrix is given by the material properties and the horizontal slownesses. The vertical slownesses are the eigenvalues of the system matrix. A diagonalization of the system matrix transforms the field vector into a mode-field that contains upgoing and downgoing field constituents. For system matrices that account for general anisotropy, it is shown how the electromagnetic field from any of the four basic dipole types can be calculated at any desired position in the stratified medium. It is furthermore shown how the reflection and transmission response from a stack can be calculated by a recursive scheme. Potential numerical instabilities due to using propagators are avoided by using this reflectivity method. Due to an energy-flux normalization of the eigenvector matrices, the reciprocity relations for reflection and transmission of electromagnetic fields in general anisotropic media can be derived. Several other useful relations between the reflection and transmission matrices are obtained as well. The propagator method is dependent on the ability to calculate eigenvalues and eigenvectors of the system matrix for all layers. In simple cases with isotropy or transversal isotropy in the direction of medium variation, the eigenvalue problem can be solved explicitly. These eigenvector matrices have useful properties, e.g. when processing data. The possibility to remove layers above or below the receiver layer follows from the decomposition of a field into upgoing and downgoing polarization modes. The propagator theory was implemented in order to model anisotropy in marine CSEM. A modelling study shows that responses are affected by horizontal, vertical, and dipping anisotropy in different manners. This suggests that when anisotropy is present at a survey site, careful planning and interpretation are required in order to correctly account for the responses.