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Modeling of free-surface multiples

Modeling of free-surface multiples. Using the data as modeling operator: Tutorial Case study example Discussion. sea surface. = receiver. = shot. reflector. D( ) = P ( ) + D ( ) ( r W( ) -1 )P ( ).  : frequency D = Data

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Modeling of free-surface multiples

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  1. Modeling of free-surface multiples • Using the data as modeling operator: • Tutorial • Case study example • Discussion

  2. sea surface = receiver = shot reflector

  3. D() = P () + D ()( r W()-1 )P () •  :frequency • D = Data • P = Primaries (data in experiment without free surface) • W = Acquisition wavelet • r = Reflection coefficient at free surface

  4. = receiver = shot sea surface reflector

  5. D() = P () + D ()( r W()-1 )P () Pi(,s,g) = D (,s,g) - ( r W()-1 ) Sx D(, s,x)P i-1(,x,g) x1 x2

  6. Prepare two-sided shot gathers at locations S and G interpolate gaps use reciprocal traces from common receiver gathers at locations S and G Model of free-surface multiples at location SG

  7. Prepare two-sided shot gathers at locations G andS interpolate gaps use reciprocal traces from common receiver gathers at locations S and G Model of free-surface multiples at trace GS

  8. Prepare two-sided shot gathers at locations G andS interpolate gaps use reciprocal traces from common receiver gathers at locations S and G Convolve the two-sided shot gathers trace by trace Model of free-surface multiples at trace GS

  9. Prepare two-sided shot gathers at locations G andS interpolate gaps use reciprocal traces from common receiver gathers at locations S and G Convolve the two-sided shot gathers trace by trace Model of free-surface multiples at trace GS

  10. Prepare two-sided shot gathers at locations G andS interpolate gaps use reciprocal traces from common receiver gathers at locations S and G Convolve the two-sided shot gathers trace by trace here convolution in x-t other options after transforms time to frequency offset to ray-parameter offset to wavenumber Model of free-surface multiples at trace GS

  11. Prepare two-sided shot gathers at locations G andS interpolate gaps use reciprocal traces from common receiver gathers at locations S and G Convolve the two-sided shot gathers trace by trace Apply tapers, mutes, interpolation, etc Sum traces to obtain the multiple model trace Model of free-surface multiples at trace GS

  12. Repeat the previous procedure for all traces in the shot gather Model of free-surface multiples for shot gathers at location S

  13. Case study example – 2-D, East of Faroes Islands • Acquisition (1999): • Single vessel, towing 11.4 km long streamer • Shot interval 25 m • Group interval 12.5 m • 10 sec records • Grid of eleven 2-D lines • One 120 km long line available at SEP

  14. is an issue for SRME Source locations 3 km Receiver locations Feathering

  15. East of Faroe Islands (ten 2-D lines, 1700 km total)

  16. 12 km Pre-stack time migration

  17. LMO 4 km/sec Input Model Output SRME applied to data from the 1999 survey(offsets up to 9 km)

  18. WBM TBM TB WBM WBM SRME in Shot Gather Domain WB TB TBM WBM TBM Input Input-Predicted multiples Predicted multiples

  19. Requirement for sources and receivers at the same locations … • Heuristics: • Don’t convolve traces which are ``too far apart’’ • Bandpass and dip-filter traces as function of their distance • Estimate ``plane-wave components” from the data and use these to compute the multiple model • Sx D(, s,x)P(,x,g)~Sp D(, s,p)P(,p,g) • x : space coordinate • p : spatial wavenumber or ray-parameter (ps or pg)

  20. Gathers as function of offset (left) and ray-parameter (right)

  21. Models before summation along offsets (left) andray-parameter (right)

  22. Further work • Effect of position errors (non-coincident sources and receivers) on synthetics: • Use source and receiver positions from the field data; • Specifications for maximum feathering during acquisition • Display/Filter intermediate results when computing the multiple model • Investigate computing the multiple model by convolving plane wave components • Local plane-wave decompositions within CRG/CSG gathers? • Could handle also interpolation of missing near-offsets?

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