# SSP -> SSP: Multiples into Primaries Lab: Part II

Figure 1. Computed and theoretical trace g(B,t|A,0) for the two-layer model. This result computed by MATLAB program in exercise 13 of Chapter 1.

Objective: Learn to model synthetic seismograms and interferometrically transform SSP 1st-order multiples into primaries.

Lesson learned

1. Interferometric redatuming works under far field approximation but has errors.
2. Errors increase as reflector approaches free surface.

Procedure:

1. Make a directory, and load into it the files twod.m, xcorr.m, corrsum.m, forward.m, and ricker.m.
2. Type "twod" in Matlab to run the program to forward model SSP (surface seismic profile) shot gathers in a 2-layer model. Only the primaries, 1st- and 2nd-order multiples are generated. These data are also correlated and summed to produce redatumed data on the surface. In this case 1st-order multiples turn into primaries and 2nd-order multiples become 1st-order multiples.
3. Change depth of layer interface and assess how this affects the ability to reconstruct the primaries from the multiples. Does the reconstruction become more accurate or less accurate as the interface depth increases?
4. Change aperture width. Does the reconstruction become more accurate or less accurate as the aperture increases?
5. Insert a near-offset gap in the shot gathers and assess the effects on the reconstruction accuracy. Use gap widths that are integer multiples of a Fresnel zone width on the surface.
6. Adjust model so that there are two reflectors, one at depth d and the other at depth 3d. The shallowest reflector might be a water bottom interface so it can generate strong multiples up to the 3rd order. Numerically assess the sensitivity of the gap width, geophone spacing, aperture width to reconstruction accuracy.
7. Heroic MATLAB exercise: Repeat previous exercise except use a 3D layer cake model with a typical marine survey geometry consisting of a swath of towed hydrophone lines. The swath consists of eight parallel lines, each separated by 10 m and each having a line length of 6 km long. The hydrophone spacing is 20 m and the near-offset source-receiver gap is 120 m.