## Building the 2-D model Pluto 1.5 for ray tracing

This is an example of fitting gridded velocities
by a 2-D model with interfaces, suitable for ray tracing.

For more information about the Pluto 1.5 synthetic dataset refer to
web site of
SMAART JV.

We take the gridded P-wave velocities
of the model Pluto 1.5, display the data
in PostScript, prepare the data to be inverted, and build
a 2-D model with interfaces suitable for ray tracing
using packages MODEL and CRT.
We perform several numerical tests in the inverted model.

This file is a brief manual describing the computations.
For details refer to Bulant (2001).

### Memory requirements

The dimension of array RAM in file
'ram.inc'
must be at least 15200000 for the calculations.

### Order of execution of the history files

- 'plu-grd.h'
- displays the original gridded velocity in PostScript
- 'plu-inv.h'
- prepares the data for inversion, builds the model by inversion
- 'plu-test.h'
- performs numerical tests of the inverted model

All three history files require file 'plu-vp.grd' to be extracted from
ZIPped file 'plu-vp.zip'.

History file 'plu-grd.h' displays the original gridded P-wave velocity
stored in file 'plu-vp.grd' in PostScript.
History file 'plu-inv.h' builds
a 2-D model Pluto 1.5 with interfaces suitable for ray tracing
using packages MODEL and CRT.
The model is built by inversion
of given data with minimization of Sobolev norm of the model.

The data for inversion of interfaces are obtained as points
at isosurfaces of the given data cube. Sparse velocity grid
to be used as data for inversion of velocities is obtained
by choosing the velocities from the original dense grid.
The model is built by inversion
of given data with minimization of Sobolev norm of the model.
After the inversion, Sobolev norm of the velocity field
in the inverted model is calculated.

History file 'plu-test.h' performs numerical tests of the inverted
model.

The numerical tests cover the visualization of the data for inversion,
visualization of the velocity in the inverted model, calculation
and visualization of velocity deviations from the original data grid,
calculation of Lyapunov exponents for the inverted model and
five simple tests of initial-value ray tracing in the inverted model
using history file 'plu-ray.h'.

### References

Bulant, P.:
Sobolev scalar products in the construction of velocity models ---
application to model Hess, to SEG/EAGE Salt Model, and to model Pluto 1.5.
In: *Seismic Waves in Complex 3-D Structures, Report 11*,
pp. 133-159,
Dep. Geophys., Charles Univ., Prague, 2001.