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 sY and sR (see eqs. 82, 89 and 90 in Zacek, 2006). The values of SOBMUL are set according to Zacek (2006):
SOBMUL=5E9 m3/s for the initial parameter R0 , the real part of M0 , that defines the curvature of the Gaussian beam (see eq. 57 in Zacek, 2006);
SOBMUL=5E10 m3/s for the initial parameter Y0 , the imaginary part of M0 , 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 R0 and Y0 before smoothing and files 'fgbr22.ps' and 'fgbr22.ps' are plots of smoothed initial parameters.
Zacek, K. (2006): Optimization of the Shape of Gaussian Beams. Stud. Geophys. Geod., 50, 346-366.