Summary for Practical 4 (Tomography, finally! make your own phase velocity map)

- instructions and script files are in     
  data.dir/prac4.dir

We will make phase velocity maps at fixed frequency using two different
techniques. The first one is a direct matrix inversion. In this case,
the model parameterization is spherical harmonics. We will expand our
map up to harmonic degree 36 (i.e. 37^2 = 1369 model parameters).

- script file run.cinv calls two executable routines: cinv3a and trade2p
  cinv3a reads in the phase data, composes the Gram matrix ATA and then
  find its eigenvalues and eigenvectors. trade2p composes the generalized
  inverse and calculates the model vector for a suite of damping parameters.
  There will be two output files: "iterations" has the models while
  "trace.curve" contains the trade-off curve.
  
  You can plot a model by calling the script file domap (call getmodel
  first, then sphmap -- domap reads in a 5x5 degree grid called out.map).

The second technique is a variant of an iterative conjugate-gradient
technique (LSQR). The model parameterization is equal area blocks with
the width of the blocks being 5 degrees at the equator. This gives
1654 block which gives roughly the same number of degrees of freedom 
as the spherical harmonic l=36 expansion.

- script file run.lsqswmat calls a routine that calculates the kernel matrices
  A (one for each phase file). Routine lsqrphs takes these matrices and
  creates models of a number of iterations. Play with the smoothing
  parameter lambda.

  You can plot such a model by calling the script file dolsqmap (needs the
  output file of lsqrphs "tomo.int3" and you need to specify the
  iteration you want to look at).

* After finding a suitable model, we need to find out "how well this model fits
  the data". The routines chiphs and chisqphs will help you.
  Does a rough model fit the data better than a smooth model?

* What is the spectral content of your map and how well do the two maps
  coming from the two different techniques correlated? Routine lcor will
  help you with this.

* Don't forget the geophysical interpretation.