1. Free Surface Multiple Elimination
Is a single series term enough?
Bee Bednar and Jon Downton
Core Laboratories
A popular approach to multiple elimination is based on suppressing free surface energy using only the first term in the scattering series. When coupled with pattern recognition or matched filter technology this approach has has shown tremendous promise in providing a solution to the complete elimination of free surface reverberations. In contrast, little or no effort has been focused on determining the degree to which utilization of additional terms might improved the quality of the suppression. In order to make some assessment of the degree of improvement that might be expected by using additional series terms this short presentation restricts its attention to a simple synthetic data set (Pluto) and then briefly visually compares the difference between using one and up to four terms of the series in the normal wavelet-estimation based methodology.

2. The series in all its glory
U0=Properly deghosted no first arrivals
P = Primaries without the multiples
The basic equation we sue are from Ikelle, Robert’s, and Weglein , Geophysics, 62, no. 6., The implementation here included the obliquity term.
W = Wavelet Inverse

3. Suppression – Method 1
Use Conjugate Gradients to minimize as a function of W
For some n
Basic idea is to iterate the standard wavelet estimation approach with data that has has the first arrival muted and a “deghost” operator applied to the data. Wavelet is estimated using an iterated conjugate gradients algorithm. Both n and the number of iterations are user settable. For the following graphics, the order n ranged from 1 to 4 and the number of wavelet iterations was held constant at 2. That is, for an nth order demultiple, n terms of the series was used, and a second pass through the entire algorithm was performed using the multiple-suppressed data.
Normal practice:
Hold n =1 and iterate the process
Better practice?
Set n > 1 and iterate

4. Suppression – Method 2 Use match filter to subtract:
Where M = match filter
For some n
Basic idea is to iterate the standard wavelet estimation approach with data that has has the first arrival muted and a “deghost” operator applied to the data. Wavelet is estimated using an iterated conjugate gradients algorithm. Both n and the number of iterations are user settable. For the following graphics, the order n ranged from 1 to 4 and the number of wavelet iterations was held constant at 2. That is, for an nth order demultiple, n terms of the series was used, and a second pass through the entire algorithm was performed using the multiple-suppressed data.
Normal practice:
Hold n =1 and iterate the process
Better practice?
Set n > 1 and iterate

5. Distributed Implementation
Data Read
First arrival
DeGhost
FFT
Node 0
Data Write
Node 1
Node 2
Output all orders or
suppressed data
Fully populated data set in
Node 3
Data is distributed over frequency. The basic sequence can use as many CPU’s as one has frequencies. Otherwise the data is distributed frequency block by frequency block. All calculations are done in the wavenumber domain as per the Ikelle et. al. paper mentioned earlier. On 48, 700 MHZ, CPU’s estimating a 2th order multiple on the Pluto data set takes about 2 hours. Data passing is via a chain to optimize throughput, so data transmission runs at disk read speed. Adding the conjugate gradients suppression increases the overall run time by about 50 %. For matched-filter approaches, distributed prediction outputs to distributed match filter subtraction. As many terms as necessary can be used in either scenario.
Node 4
Node n

6. Pluto Velocity Model
This is the Pluto velocity field from the Smaart Joint Venture.

7. Raw vs. Demultipled Zero Offset
Zero Offset Data without multiple suppression
The zero offset section from the Pluto data. Note the significant multiple energy.

8. 1st order multiples vs. Raw Shot
Left hand slide shows the predicted 1st order multiples while the right hand side represents the raw input shot at the same location. I shifted the multiples on the left up to roughly match arrival times. One can clearly match event-to-event. Multiple clearly have a different phase. These are normalized plots. I did not try to ascertain strength differences.
Shifted up approx .75 sec

9. 1st Order Multiples vs. Raw Shot
Same as previous figure, just a different shot location. Left hand slide shows the predicted 1st order multiples while the right hand side represents the raw input shot at the same location. I shifted the multiples on the left up to roughly match arrival times. One can clearly match event-to-event. Multiple clearly have a different phase. These are normalized plots. I did not try to ascertain strength differences.
Shifted up approx .75 sec

10. Raw Shot vs. Demultipled Shot
Demultipled shot on the left. Input data on right. Arrow points to a significant multiple suppression. Slide is here just to indicate that the process as implemented works.

11. Raw vs. Demultipled Zero Offset
Zero Offset Data without multiple suppression
Zero offset raw data again. Arrows indicate areas of interest with regard to the multiple suppression process.

12. Zero Offset Data with 1st order multiple suppression
First order multiple suppression.

13. Zero Offset Data with 2nd order multiple suppression
Second order multiple suppression

14. Raw vs. Demultipled Zero Offset
Zero Offset Data with 3rd order multiple suppression
Zero Offset Data with 3rd order multiple suppression
Third order multiple suppression.

15. Zero Offset Data with 4th order multiple suppression
Fourth order multiple suppression. Note that although subtle, the process is still suppresses multiple energy.

16. Raw vs. 3rd order Demultipled Zero Offset
Zero Offset Raw Data
Zero Offset 3rd order multiple suppression
Side-by-side of the 3rd order multiple suppression.

17. Input zero offset section
Input zero-offset section in color.

18. First match-filter iteration
First order multiple suppression using match-filter/pattern based approach. One iteration of the process. That is, the 1st order multiples were predicted and then subtracted using a match filter technique. No additional iterations using the suppressed data.

19. 2nd match-filter interation
Second order multiple suppression using the matched-filter approach. Flipping back and forth between this and the previous slide shows that the process has again suppressed additional multiple energy. In this case it appears that the second order effect is just that, but even at this level, it does not appear to be ignorable. If we are to every reach the point of doing imaging without the velocity we will have to do an almost perfect job here.

20. Conclusions
Using higher order terms does indeed help with both wavelet and matched filter based approaches.
Clear improvement in higher order bounces.
Visually the using only the first order term appears to do quite well.
Higher order bounces not as well suppressed but generally better than the wavelet method.
Additional terms still improve the suppression.

21. Thank you for your support!