--- branches/doubleplusgood/doc/inversion/ForwardMagnetic.tex 2013/03/27 07:58:34 4344 +++ branches/doubleplusgood/doc/inversion/ForwardMagnetic.tex 2013/03/29 07:09:41 4345 @@ -32,20 +32,6 @@ Values for the magnetic flux density can be obtained by the International Geomagnetic Reference Field (IGRF)~\cite{IGRF} (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. In most cases it is reasonable to assume that that the background field is constant across the domain. @@ -121,15 +107,18 @@ \begin{classdesc}{MagneticModel}{domain, w, B, background_field, \optional{, useSphericalCoordinates=False} + \optional{, fixPotentialAtBottom=False}, \optional{, tol=1e-8}} opens a magnetic forward model over the \Domain \member{domain} with weighting factors \member{w} ($=\omega^{(s)}$) and measured magnetic flux density anomalies \member{B} ($=B^{(s)}$). The weighting factors and the measured magnetic flux density anomalies must be vectors. \member{background_field} defines the background magnetic flux density $B^b$ -as a vector. +as a vector with north, east and vertical components. If \member{useSphericalCoordinates} is \True spherical coordinates are used. \member{tol} sets the tolerance for the solution of the PDE~(\ref{ref:MAG:EQU:8}). +If \member{fixPotentialAtBottom} is set to \True, the gravitational potential +at the bottom is set to zero in addition to the potential on the top. \end{classdesc} \begin{methoddesc}[MagneticModel]{rescaleWeights}{