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
- Interferometric redatuming works under far field approximation
but has errors.
- Errors increase as reflector approaches free surface.
Procedure:
- Make a directory, and load into it the files
twod.m,
corrsum.m,
forward.m,
xcorr.m,
and ricker.m.
- 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.
- Why don't you see 2nd-order multiples in the redatumed data?
- 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.
- 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?
- Decrease the aperture of the data. What happens to the error?
- After
reading Chapter 2, replace one of the monopoles by a dipole. Does the noise decrease?
- Incorporate the direct wave into the forward data. How does this affect the redatumed result?
- 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?)