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 one common-shot gather. To calculate the optimum initial parameters of Gaussian beams launch history file 'mgb-opt.h'.

History file 'mgb-opt.h' calculates optimum initial parameters of Gaussian beams in the smoothed Marmousi model. Distributed version of 'mgb-opt.h' performs optimization for the shot 77. It may simply be modified to perform optimization for another shot. The position of the shot 77 is set at a horizontal coordinate of 4.9 km at a depth of 8 m in this example.

History file 'mgb-opt.h' launches another history file 'mgb-opt1.h', which is designed to calculate the optimum initial parameters of Gaussian beams transformed to initial surface. The first step in 'mgb-opt1.h' is ray tracing from the source. Multivalued travel times are then computed. Next step in 'mgb-opt1.h' is ray tracing from initial points of intersections of the central ray of a Gaussian packet with the profile. Positions of initial points and ray parameters are computed in 'mgb-opt1.h' using program 'gprpar.for' and calculation of the optimum initial parameters of Gaussian beams is performed by program 'gbopt.for'. Programs 'gprpar.for' and 'gbopt.for' are located in the directory 'data/mar'. Use commands 'perl f.pl gprpar' and 'perl f.pl gbopt' to compile the programs.

After that, the optimum initial parameters
*R*_{0}
(defines the curvature) and *Y*_{0}
(defines the width) of Gaussian beams
are smoothed in history file
'mgb-smo.h'
(history file 'mgb-opt.h' launches 'mgb-smo.h').
Smoothing is controled by parameter *COEF2*.
The value is set to *COEF2*=19.5, and for this value
the smoothing varies in two orders of magnitude. It is time consuming
to manually find a proper value of smoothing parameter for each
common-shot gather. The values of the smoothing parameter are
in a range of several orders for
the whole Marmousi data set (240 shots).

Then, history file 'mgb-smo.h' plots distributions of the optimum initial parameters before and after smoothing ('r0sxxx.ps', 'y0sxxx.ps' and 'r0m.ps', 'y0m.ps'). The last step is calculation of new discretization steps (program 'gpstep.for') and recomputation of smoothed optimized parameters on the new grid for decomposition and migration (history file 'mgb-opt.h' launches another history file 'mgp-step.h' and this file runs 'mgb-grd.h'). Output files 'r0m077.out' and 'y0m077.out' with real and imaginary part of the optimum initial parameters are used as input in Decomposition of the wave field into optimized Gaussian packets.

To run the history file 'mgb-opt.h' it is necessary to compile program 'matmul.for' and program 'invpts.for' with parameter MRAM=12000000. Include file 'ram.inc' is distributed with MRAM=4000000.

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