Editing Revisiting SEP tour with Madagascar and SCons (section)

==Processing exercises==
===Windowing and plotting===
Our next task is to window and plot a significant portion of the data. Add the
following line to the <tt>SConstruct</tt> file:
<syntaxhighlight lang="python">
Flow('windowed','Txx.HH','window n2=10 min1=0.4 max1=0.8')
</syntaxhighlight>

The window command selects the first ten traces and the time window between
0.4 and 0.8 seconds.
We will plot the windowed data with three different plotting programs.
<syntaxhighlight lang="python">
plotpar = '''
transp=y poly=y yreverse=y pclip=100 nc=100 allpos=n
'''

for plot in ('wiggle','contour','grey'):
    Result(plot,'windowed',plot + plotpar)
</syntaxhighlight>

For convenience, plotting parameters are put in a string called
<tt>plotpar</tt>. A Python string can be enclosed in single, double,
or triple quotes. Triple quotes allow the string to span multiple
lines. In this case, we use triple quotes for convenience. Next, we
loop (using Python's <tt>for</tt> construct) through three different
programs (<tt>wiggle</tt>, <tt>contour</tt>, and <tt>grey</tt>). For
each program, the command portion of <tt>Result</tt> is formed by
concatenating two strings with Python's addition operator.
Try running <tt>scons -Q wiggle.view</tt>. You should see something like the
following output in your terminal:
<pre>
bash&#36; scons -Q wiggle.view
< Txx.HH /path/to/RSF/bin/sfwindow n2=10 n1=200 f1=200 > windowed.rsf
< windowed.rsf /path/to/RSF/bin/sfwiggle transp=y poly=y yreverse=y 
pclip=100 nc=200 > Fig/wiggle.vpl
/path/to/RSF/bin/sfpen Fig/wiggle.vpl
</pre>
and a figure similar to Figure~(fig:wiggle) appearing on your
screen. The <tt>-Q</tt> switch tells SCons to run in a quiet mode,
suppressing verbose comments. We will use it from now on to save
space. You can dismiss the figure by using the "q" key on the
keyboard or by hitting the "quit" button.
Run <tt>scons -Q view</tt>, and you should see simply
<pre>
bash&#36; scons -Q view
/path/to/RSF/bin/sfpen Fig/wiggle.vpl
</pre>
Since the <tt>wiggle.vpl</tt> figure is up to date, SCons does not rebuild
it. After quitting the figure, SCons will resume processing with
<pre>
< windowed.rsf /path/to/RSF/bin/sfcontour transp=y poly=y yreverse=y 
pclip=100 nc=200 > Fig/contour.vpl
/path/to/RSF/bin/sfpen Fig/contour.vpl
</pre>
and a figure appearing on your screen. Quitting the figure, produces
<pre>
< windowed.rsf /path/to/RSF/bin/sfgrey transp=y poly=y yreverse=y 
pclip=100 nc=200 > Fig/grey.vpl
/path/to/RSF/bin/sfpen Fig/grey.vpl
</pre>
and the next figure.
[[Image:wiggle.png|frame|center|To see this figure on your screen, run <tt>scons~wiggle.view</tt>]] 
[[Image:contour.png|frame|center|To see this figure on your screen, run <tt>scons~contour.view</tt>]]
[[Image:grey.png|frame|center|To see this figure on your screen, run <tt>scons~grey.view</tt>]]

===Resampling===
The next example demonstrated simple signal processing using the Fast Fourier
Transform. We will first subsample the original data and then recover the data
using Fourier interpolation.
Subsampling is accomplished with <tt>sfwindow</tt>.
<syntaxhighlight lang="python">
# decimate time axis by two
Flow('subsampled','windowed','window j1=2')
</syntaxhighlight>

Running <tt>scons -Q subsampled.rsf</tt> produces
<pre>
< windowed.rsf /path/to/RSF/bin/sfwindow j1=2 > subsampled.rsf
</pre>
We can verify that the size of the first axis has decreased by running
<pre>
sfin windowed.rsf subsampled.rsf. 
</pre>
Try also <tt>sfwiggle < subsampled.rsf | sfpen</tt> to quickly inspect the subsampled data on the screen.
To interpolate the data back to the original sampling, the following sequence
of steps can be applied:
  
#Fourier transform from time domain to frequency domain. 
#Pad the frequency axis 
#Inverse Fourier transform from frequency to time. 
All three steps are conveniently combined into one using pipes.
<syntaxhighlight lang="python">
# sinc interpolation in the Fourier domain
Flow('resampled','subsampled',
     'fft1 | pad n1=102 | fft1 inv=y opt=n | window max1=0.8')
</syntaxhighlight>

Why do we pad the Fourier domain to 102? The time length of the original data
is 201 samples. In the frequency domain, it can be represented with 101
positive frequencies plus the zero frequency, which amounts to 102. Note that
the output of <tt>sffft1</tt> does not contain negative frequencies.
Finally, we display the result. The reconstructed data is shown in
the figure. Comparing this result with
the previous plots, we can verify a fairly accurate reconstruction.
<syntaxhighlight lang="python">
Result('resampled','wiggle title=Resampled' + plotpar)
</syntaxhighlight>

[[Image:resampled.png|frame|center|To see this figure on your screen, run <tt>scons resampled.view</tt>]] 

As an exercise, try subsampling the data by a factor of 4 and see if you can
still reconstruct the original data with the Fourier method.

===Normal Moveout===
The next example applies a simple constant-velocity NMO correction to the
windowed data
and pipes the result to a wiggle plotting command:
<syntaxhighlight lang="python">
Result('nmo','windowed',
       '''
       nmostretch v0=2.05 half=n |
       wiggle pclip=100 max1=0.6 poly=y
       ''')
</syntaxhighlight>

Running <tt>scons -Q nmo.view</tt> produces 
<pre>
< windowed.rsf /path/to/RSF/bin/sfnmostretch v0=2.05 half=n | 
/path/to/RSF/bin/sfwiggle pclip=100 max1=0.6 poly=y > Fig/nmo.vpl
/path/to/RSF/bin/sfpen Fig/nmo.vpl
</pre>
Note that SCons does not recreate the
<tt>windowed.rsf</tt> file if that file is up to date. You can
experiment with the NMO velocity (2.05~km/s) or with plotting
parameters to get different results. As Dellinger and T&#225;las (1992<ref>Dellinger, J. and S. T&#225;las,  1992, A tour of SEPlib for new users, ''in''  SEP-73,  461--502. Stanford Exploration Project.</ref>)
point out, the NMO velocity of 2.05~km/s "appears to split the
difference between two distinctly non-hyperbolic shear waves".
[[Image:nmo.png|frame|center|To see this figure on your screen, run <tt>scons nmo.view</tt>]]

===Advanced plotting===
Sometimes, we need to combine different plots either by overlaying
them on top of each other or by putting them side by side. Here is an
example of accomplishing it with RSF and SCons.
Start by creating common plotting plotting arguments and plotting the
data in greyscale. 
<syntaxhighlight lang="python">
plotpar = plotpar+' min1=.4 max1=.8 max2=1. min2=.05 poly=n'

Plot('grey','windowed',
     'grey wheretitle=t wherexlabel=b' + plotpar)
</syntaxhighlight>

Next, plot the wiggle traces twice: the fist time, using thick black
lines (<tt>plotcol=0 plotfat=10</tt>), and the second time, using
thinner white lines (<tt>plotcol=7 plotfat=5</tt>).
<syntaxhighlight lang="python">
Plot('wiggle1','windowed',
     'wiggle plotcol=0 plotfat=10' + plotpar)
Plot('wiggle2','windowed',
     'wiggle plotcol=7 plotfat=3' + plotpar)
</syntaxhighlight>

The plots are combined by overlaying or by putting them side by side.
<syntaxhighlight lang="python">
Result('overplot','grey wiggle1 wiggle2','Overlay')
Result('sidebyside','grey wiggle2','SideBySideIso')
</syntaxhighlight>

The resultant plots are shown in the figures. 
[[Image:overplot.png|frame|center|To see this figure on your screen, run <tt>scons overplot.view</tt>]]
[[Image:sidebyside.png|frame|center|To see this figure on your screen, run <tt>scons sidebyside.view</tt>]]