S U M M A R YThis 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 frequencywavenumber 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.

This paper gives a unified treatment of electromagnetic ͑EM͒ field decomposition into upgoing and downgoing components for conductive and nonconductive media, where the electromagnetic data are measured on a plane in which the electric permittivity, magnetic permeability, and electrical conductivity are known constants with respect to space and time. Above and below the plane of measurement, the medium can be arbitrarily inhomogeneous and anisotropic.In particular, the proposed decomposition theory applies to marine EM, low-frequency data acquired for hydrocarbon mapping where the upgoing components of the recorded field guided and refracted from the reservoir, that are of interest for the interpretation. The direct-source field, the refracted airwave induced by the source, the reflected field from the sea surface, and most magnetotelluric noise traveling downward just below the seabed are field components that are considered to be noise in electromagnetic measurements.The viability and validity of the decomposition method is demonstrated using modeled and real marine EM data, also termed seabed logging ͑SBL͒ data. The synthetic data are simulated in a model that is fairly representative of the geologic area where the real SBL were collected. The results from the synthetic data study therefore are used to assist in the interpretation of the real data from an area with 320-m water depth above a known gas province offshore Norway. The effect of the airwave is seen clearly in measured data. After field decomposition just below the seabed, the upgoing component of the recorded electric field has almost linear phase, indicating that most of the effect of the airwave component has been removed.

Low-frequency electromagnetic (EM) signal propagation in geophysical applications is sometimes referred to as diffusion and sometimes as waves. In the following we discuss the mathematical and physical approaches behind the use of the different terms. The basic theory of EM wave propagation is reviewed. From a frequency-domain description we show that all of the well-known mathematical tools of wave theory, including an asymptotic ray-series description, can be applied for both nondispersive waves in nonconductive materials and low-frequency waves in conductive materials. We consider the EM field from an electric dipole source and show that a common frequency-domain description yields both the undistorted pulses in nonconductive materials and the strongly distorted pulses in conductive materials. We also show that the diffusion-equation approximation of low-frequency EM fields in conductive materials gives the correct mathematical description, and this equation has wave solutions. Having considered both a wave-picture approach and a diffusion approach to the problem, we discuss the possible confusion that the use of these terms might lead to.