slight improvement on intro / background and second attempt at fixing the math

This commit is contained in:
Lindsey Heagy
2014-04-05 11:59:16 -07:00
parent 9779457448
commit b7bff90c47
+7 -5
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@@ -9,11 +9,13 @@
Frequency Domain Electromagnetics
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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
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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}