SSP -> SSP: Multiples into Primaries Lab: Part I





Figure 1. Computed and theoretical trace g(\ba,t|\bd) 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, corrsum.m, forward.m, xcorr.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. Why don't you see 2nd-order multiples in the redatumed data?
  4. The correlation-summation is a far field approximation to the exact equations discussed in Chapter 2. Decrease the thickness d of the layer and show that the errors become worse.
  5. The data aliasing condition is such that the geophone spacing should be less than half the wavelength. For a 20 Hz wavelet and a layer velocity of 1 km/s, what is the wavelength? Adjust the geophone sampling interval dx so that it violates the anti-aliasing criterion. Do the errors increase or decrease?
  6. Decrease the aperture of the data. What happens to the error?
  7. After reading Chapter 2, replace one of the monopoles by a dipole. Does the noise decrease?
  8. Incorporate the direct wave into the forward data. How does this affect the redatumed result?
  9. If A was at one end of the model and B at the other end of the model, why would you expect the redatuming not to work? (Hint: correlating a primary with a 1st-order multiple transforms into a primary. Is there such a multiple available in the data for this wide aperture primary?)