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\line{\hskip 3 em\hfill \bigbf LAB 8 \hfill}
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\line{\hskip 3 em\hfill\bigbf FORWARD MODELING \hfill}
\line{\hskip 3 em\hfill\bigbf USING DIPOLE SOURCES\hfill}

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\item{} An isolated magnetic source often looks to first order like a dipole. So dipole modeling is a first step in modeling. It can give you a pretty good idea of depth, physical size (in terms of the dimension along the polarization and orientation.) \it DipoleFieldGui, DipoleFieldScript \rm  and \it DipoleFieldProfile \rm can be used to familiarize yourself with how the shape of an anomaly changes as depth etc change. These are all below \it local \rm in the directory structure I gave you, so make sure you set the path. Run \it DipoleFieldGui \rm it call the other two and brings up an interactive graphic. 



\vskip 1 em \item{1)} In particular, start with a vertical dipole and a
vertical field, ie induced magnetization at the North pole, and
progressively change the inclination of the dipole and the field in steps
of $5^o$. Notice that for large values of inclination there are negative
lows either side of the high, that is, one to the north and one to the
south. At an inclination of about $80^o$ (the inclination at Saskatoon
is about $75^o$) the negative low to the south
disappears. The negative low to the
north increases in amplitude, until at an inclination of $0^o$, ie at the
equator, the low and high are the same magnitude. 

\vskip 1 em \item{2)} Set the inclination of the field and dipole
polarization to
$75^o$ (similar to what it is at Saskatoon), the depth to 5, and the dipole
length to 5. Now increase the depth in steps of 5 and note what happens to
the general shape of the anomaly. What happens to the positions of the
high and low, as the depth increases?

\vskip 1 em \item{3)} Set the inclination of the field and dipole
polarization to
$90^o$, the depth to 1, and the dipole length to 1. Now increase the
dipole length in steps of 5. What happens to the general shape of the
anomaly? Why is this?


\vskip 1 em \item{4)}The matlab function \it DipoleGrid \rm is similar to
\it DipoleFieldGui, \rm
except that it returns a 2D contour map, with 40 contour levels. The grid
can 
be re-displayed with \it mesh \rm or \it surf \rm etc. The call is:  \it
[X,Y,F] = DipoleGrid(source,field,swne) \rm where \it source \rm  is a vector
whose 7 elements define the source parameters, \it field \rm is a vector
whose 2 elements define the parameters of the local field, and \it
swne \rm  is a vector whose four elements define the sw and ne corners of
a rectangular grid.  The grid spacing is 1 m. Do help DipoleGrid for a
description.  If grids X and Y are substituted for the vector swne, then
the output is calculated on these grids. X,Y,F are the arrays of x, y, and the total field anomaly F,
which you can subsequently examine with \it surf \rm etc.  Experiment with this, until you feel confident that
you understand how the various parameters interact to produce a given
contour map. The contour map will have North at the top, East at the
right. Use surf(X,Y,F), view, colormap etc to plot different views of
this. If you want to re-contour this with a fewer number of contour lines
use; $$ contour(X(1,:),Y(:,1),F,N) $$ where N is the number of contour
lines you want. 


\vskip 1 em\item{5)} Try to adjust  the various parameters until you
produce a contour map that looks similar to your field data from the
detailed grid. The best way to do this is to grid your data to create  [X,Y,ZO], the use [X,Y] in \it DipoleGrid \rm so you calculate model anomalies on the same grid as you observed. This is forward modeling, just as you did with GM-SYS,
except you are only dealing with a dipole source, not a source of
arbitrary shape. The xy positions of the maximum and minimum, the peak to
peak amplitude, the extent of the anomaly (full width at half height), and
the shape are important features to match. Once you develop some
experience with this you should find that a few iterations are sufficient
to get a reasonably good fit. \it DipoleGrid \rm has no regional, so you
must have a good regional residual separation on your data before you try
the modeling.

\vskip 1 em \item{} The field school target is not a single dipole, so you
will not get a perfect match, and the recovered parameters will only
approximate the actual conditions. You could of course forward model a second source as well.  How well can a 3D source be
approximated by a single dipole? The best fitting dipole will most likely
be approximately centered in the source, and contained within the source
as well. So the length of the best-fitting dipole can be expected to
approximate  the dimension of the target in the direction of polarization,
and the depth of the N and S poles should be an upper bound on the depth
to top, and a lower bound on depth to bottom. In the case of a thin sheet,
the polarization will lie within the plane of the sheet, so for this
target, the
declination of polarization should define the strike of the source quite
well. The
deeper the source is the better the dipole will fit the observed field, but
in the field school the target is quite shallow, so you should not expect
perfect agreement. Nevertheless, the recovered dipole does supply valuable
information about the source, that can be used as an initial model in 
GM-SYS. You could
improve this modeling by constructing a target from a sheet of dipoles
(execute DipoleGrid many times to construct a sheet of dipoles and add the
results together to form the response from a plane target). 

\vskip 1 em\item{} Use \it profilex.m \rm to extract profiles from the contour map. 
The call is  \it [x,XI,YI,Z1]=profilex(X,Y,sp,Z), \rm where \it X,Y,Z \rm are the usual
grids, and \it sp \rm is the spacing at which a profile will be extracted. x is distance along the profile from start to end, and XI YI are the locations. A second version of the call is \it [x,XI,YI,Zout1,Zout2,Zout3]=profilex(X,Y,sp,Z,Z1,Z2). \rm
 Here Z1 and Z2 are other gridded values on [X,Y], eg Z might be Free air gravity, Z1 topography and Z2 something else. Profilex expects [X,Y,Z] to be contoured in the current figure window when the call is made, and you define a profile to extract by
clicking on beginning and end points. When you do depth estimates from
profiles, or modeling with GMSYS, it
may be helpful to extract  profiles that run across the strike of the
target.




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