# Diff of /branches/doubleplusgood/doc/inversion/Mapping.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 6  onto a physical parameter such as densit Line 6  onto a physical parameter such as densit
6  \section{Density Map}\label{Chp:ref:mapping density}  \section{Density Map}\label{Chp:ref:mapping density}
7  For density we use the form  For density we use the form
8  \label{EQU:MAP:1}  \label{EQU:MAP:1}
9  \rho =  \rho_{0} + \Delta \rho \cdot \left( \frac{x_2 - z_0}{l_z} \right)^{\frac{\beta}{2}}  \cdot m  \rho =  \rho_{0} + \Delta \rho \cdot \left( \frac{z_0-x_2}{l_z} \right)^{\frac{\beta}{2}}  \cdot m
10
11  where $\rho_{0}$ is the reference density, $\Delta \rho$ is the density scaling, $z_0$ an offset, $l_z$ vertical expansion  where $\rho_{0}$ is the reference density, $\Delta \rho$ is the density scaling, $z_0$ an offset, $l_z$ vertical expansion
12  of the domain and $\beta$ is a suitable exponent.  of the domain and $\beta$ is a suitable exponent.
# Line 41  returns the value level set function $m$ Line 41  returns the value level set function $m$
41  \section{Susceptibility Map}\label{Chp:ref:mapping susceptibility}  \section{Susceptibility Map}\label{Chp:ref:mapping susceptibility}
42  For the magnetic susceptibility $k$ the following mapping is used:  For the magnetic susceptibility $k$ the following mapping is used:
43  \label{EQU:MAP:2}  \label{EQU:MAP:2}
44  k=  k_{0} + \Delta k \cdot \left( \frac{x_2 - z_0}{l_z} \right)^{\frac{\beta}{2}}  \cdot m  k=  k_{0} + \Delta k \cdot \left( \frac{z_0-x_2}{l_z} \right)^{\frac{\beta}{2}}  \cdot m
45
46  where $k_{0}$ is the reference density and $\Delta k$ is the density scaling.  where $k_{0}$ is the reference density and $\Delta k$ is the density scaling.
47

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