# Diff of /branches/doubleplusgood/doc/inversion/ForwardMagnetic.tex

revision 4344 by jfenwick, Wed Feb 27 03:42:40 2013 UTC revision 4345 by jfenwick, Fri Mar 29 07:09:41 2013 UTC
# Line 32  is proportional to the known geomagnetic Line 32  is proportional to the known geomagnetic
32  Values for the magnetic flux density can be obtained by the International  Values for the magnetic flux density can be obtained by the International
33  Geomagnetic Reference Field (IGRF)~\cite{IGRF}  Geomagnetic Reference Field (IGRF)~\cite{IGRF}
34  (or the Australian Geomagnetic Reference Field (AGRF)~\cite{AGRF}).  (or the Australian Geomagnetic Reference Field (AGRF)~\cite{AGRF}).
A rough approximation at latitude $\theta$ is given by
\label{ref:MAG:EQU:5}
\begin{array}{rcl}
B^b_{\theta}  & = & \displaystyle{ \frac{ \mu_0 \cdot m_{earth}}{4 \pi \cdot R_{earth}^3} sin(\theta) }  \\
B^b_r & = & \displaystyle{ \frac{\mu_0 \cdot  m_{earth}}{2 \pi \cdot R_{earth}^3} cos(\theta) }
\end{array}

with the vacuum permeability\index{vacuum permeability} $\mu_0 = 4 \pi \cdot 10^{-7} \frac{Vs}{Am}$,
the magnetic dipole moment of Earth $m_{earth}=8.22 \cdot 10^{22} Am^2$ and
earth radius $R_{earth}= 6378137m$.
$B^b_r$ and $b^b_{\theta}$ denote the radial and latitudinal component of the
geomagnetic flux density.
Notice that convention~(\ref{REF:EQU:INTRO 9}) applies if Cartesian
coordinates\index{Cartesian coordinates} are used.
35  In most cases it is reasonable to assume that that the background field is  In most cases it is reasonable to assume that that the background field is
36  constant across the domain.  constant across the domain.
37
# Line 121  derivative of the density with respect t Line 107  derivative of the density with respect t
107
108  \begin{classdesc}{MagneticModel}{domain, w, B, background_field,  \begin{classdesc}{MagneticModel}{domain, w, B, background_field,
109          \optional{, useSphericalCoordinates=False}          \optional{, useSphericalCoordinates=False}
110            \optional{, fixPotentialAtBottom=False},
111          \optional{, tol=1e-8}}          \optional{, tol=1e-8}}
112  opens a magnetic forward model over the \Domain \member{domain} with  opens a magnetic forward model over the \Domain \member{domain} with
113  weighting factors \member{w} ($=\omega^{(s)}$) and measured magnetic flux  weighting factors \member{w} ($=\omega^{(s)}$) and measured magnetic flux
114  density anomalies \member{B} ($=B^{(s)}$).  density anomalies \member{B} ($=B^{(s)}$).
115  The weighting factors and the  measured magnetic flux density anomalies must be vectors.  The weighting factors and the  measured magnetic flux density anomalies must be vectors.
116  \member{background_field} defines the background magnetic flux density $B^b$  \member{background_field} defines the background magnetic flux density $B^b$
117  as a vector.  as a vector with north, east and vertical components.
118  If \member{useSphericalCoordinates} is \True spherical coordinates are used.  If \member{useSphericalCoordinates} is \True spherical coordinates are used.
119  \member{tol} sets the tolerance for the solution of the PDE~(\ref{ref:MAG:EQU:8}).  \member{tol} sets the tolerance for the solution of the PDE~(\ref{ref:MAG:EQU:8}).
120    If \member{fixPotentialAtBottom} is set to  \True, the gravitational potential
121    at the bottom is set to zero in addition to the potential on the top.
122  \end{classdesc}  \end{classdesc}
123
124  \begin{methoddesc}[MagneticModel]{rescaleWeights}{  \begin{methoddesc}[MagneticModel]{rescaleWeights}{

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