diff --git a/docs/api_FDEM.rst b/docs/api_FDEM.rst index 1336defb..43286e1d 100644 --- a/docs/api_FDEM.rst +++ b/docs/api_FDEM.rst @@ -9,11 +9,13 @@ Frequency Domain Electromagnetics ********************************* -Intro Here +Electromagnetic (EM) geophysical methods are used in a variety of applications from resource exploration, including for hydrocarbons and minerals, to environmental applications, such as groundwater monitoring. + Background ========== -Electromagnetic (EM) geophysical methods are used in a variety of applications from resource exploration, including for hydrocarbons and minerals, to environmental applications, such as groundwater monitoring. + +Electromagnetic phenomena are governed by Maxwell's equations. They describe the behavior of EM fields and fluxes. Electromagnetic theory for geophysical applications by Ward and Hohmann (1988) is a highly recommended resource on this topic. Fourier Transform Convention ---------------------------- @@ -31,7 +33,7 @@ Maxwell's Equations =================== In the frequency domain, Maxwell's equations are given by -.. math:: +.. math :: \curl \vec{E} = - i \omega \vec{B} \\ \curl \vec{H} = \vec{J} + i \omega \vec{D} + \vec{J_s} \\ @@ -54,7 +56,7 @@ Constitutive Relations ---------------------- The fields and fluxes are related through the constitutive relations. At each frequency, they are given by -.. math:: +.. math :: \vec{J} = \sigma \vec{E} \\ \vec{B} = \mu \vec{H} \\ @@ -74,7 +76,7 @@ Quasi-static Approximation -------------------------- For the frequency range typical of most geophysical surveys, the contribution of the electric displacement is negligible compared to the electric current density. In this case, we use the \emph{Quasi-static approximation} and assume that this term can be neglected, giving -.. math:: +.. math :: \nabla \times \vec{E} = -i \omega \vec{B} \\ \nabla \times \vec{H} = \vec{J} + \vec{J_s}