## Optimization of the Shape of Gaussian Beams
in the smoothed Marmousi model

This is an example how to calculate the optimum initial parameters
of Gaussian beams in the smoothed Marmousi model. The calculation
is based on the paper by Zacek (2006).
The example shows computation for zero offset configuration
(source and receiver are at the same place) and cannot be used
for non-zero offsets.
To calculate the optimum initial parameters of Gaussian beams
launch history file 'mgb-inv.h'.

History file 'mgb-inv.h' calculates optimum initial parameters of
Gaussian beams in the smoothed Marmousi model. The position of
the coincident source-receiver is set according to Zacek (2006)
at 5975 m at a depth of 12 m.
Parameter *CPAR1* controls the position of the source.
History file 'mgb-inv.h' launches another history file
'mgb-opt.h', which is designed to calculate
the optimum initial parameters of Gaussian beams transformed
to initial surface. The first step in 'mgb-opt.h' is ray tracing
from the coincident source-receiver (zero offset).
Multivalued travel times are then computed.
Calculation of the optimum initial parameters
of Gaussian beams is performed by program
'gbopt.for'.
The program 'gbopt.for' is located in the directory '/data/mar'.
To compile the program use command 'perl f.pl gbopt'.

After that, the optimum initial parameters of Gaussian beams
are smoothed (in this case with two iterations).
Smoothing is controled by parameter
*SOBMUL*. The values of parameter *SOBMUL*
correspond to factors *s*_{Y} and
*s*_{R} (see eqs. 82, 89 and 90 in Zacek, 2006).
The values of *SOBMUL* are set according to Zacek (2006):

*SOBMUL*=5E9 m^{3}/s for the initial parameter
*R*_{0} ,
the real part of *M*_{0} , that defines
the curvature of the Gaussian beam (see eq. 57 in Zacek, 2006);

*SOBMUL*=5E10 m^{3}/s for the initial parameter
*Y*_{0} ,
the imaginary part of *M*_{0} , that defines
the Gaussian beam width.

Then, history file 'mgb-test.h' is launched
to calculate and plot the widths of Gaussian beams. The output file
'mar-gb.ps' should be the same as Figure 2b in Zacek (2006). Commented
values of *SOBMUL* in 'mgb-inv.h' should correspond to Figure 3b.
Output files 'r0a.ps' and 'y0a.ps' show distribution of the optimum
initial parameters
*R*_{0} and *Y*_{0} before
smoothing and files 'fgbr22.ps' and 'fgbr22.ps' are plots of smoothed
initial parameters.

### References

Zacek, K. (2006):
Optimization of the Shape of Gaussian Beams.
Stud. Geophys. Geod., 50, 346-366.