Multiple classification

Part 4 is all about multiples, reflections that bounce more than once before reaching the receiver. They look like primaries on the gather but live at wrong times, wrong velocities, or both. Every one you leave in is a false reflector on the final image, a misleading AVO anomaly, or an artifact that wraps through your interpretation. The tools for killing them each target a different multiple type, so the first job is learning to tell the types apart.

1. Why multiples happen

A primary is a reflection that travels down, reflects once off a subsurface interface, and comes back up to the receiver. A multiple is a reflection that has bounced more than once. The free surface (the sea surface for marine data, the ground for land data) is a near-perfect reflector: anything traveling up and hitting it is reflected back down almost in full, with reflection coefficient $R \\approx -1$, so the multiple arrives with its polarity flipped. That is where most multiples come from.

2. Four families you must recognize

The figure below builds every event, primary or multiple, from the legs of its own ray path through one layered earth. Pick an event in its table, switch the families on and off, and compare the gather with the same gather after NMO with the velocities picked on the primaries.

With 225 m of water the seafloor sits at $t\_0 = 0.30$ s and the sediment reflectors at 0.80, 1.40 and 2.20 s. The figure opens on the peg-leg of Sed-1: it arrives at 0.80 + 0.30 = 1.10 s, moves out at about 1820 m/s, 11 % slower than the primaries at its time, and after NMO it curls down 163 ms by 2200 m, the last offset before its critical offset ends it. Every event in the figure ends at its critical offset, past which the reflection would be post-critical. The primaries go flat and the multiples curl down; how far they curl is the diagnostic you use on real data.

• Water-bottom (WB) multiple. The seafloor reflection bouncing between the sea surface and the seafloor. It appears at exactly $2t\_0$, $3t\_0$, $\\dots$ of the seafloor primary with the water’s velocity, and each order flips polarity. It is the most obvious family: a train of water-velocity hyperbolae stepping down at the seafloor’s two-way time. In the figure, with 225 m of water, the first order curls down 70 ms by 800 m after primary NMO, where its critical offset ends it, and the third order curls down 261 ms by 1700 m.
• Peg-leg multiple. A primary with one extra short round trip, here through the water layer. It appears at $t\_0 = t\_0^{\\mathrm{P}} + t\_0^{\\mathrm{WB}}$, the primary time plus one water round trip; the extra bounce can come before or after the deeper reflection, so two paths of equal time add. Part of its path is in slow water, so it moves out a little slower than the primaries around it: a delayed, more curved copy of its primary, with reversed polarity.
• Free-surface multiple of a deeper reflector. A sediment reflection that bounced once off the free surface and made the trip again. It appears at $2t\_0^{\\mathrm{P}}$ with the primary’s own velocity and reversed polarity; the primaries at twice its time are faster, so it curls down after NMO (239 ms by 3000 m for Sed-1 in the figure).
• Inter-bed (internal) multiple. A reflection that bounces only between subsurface reflectors and never returns to the surface in between. It appears at $t\_0 = t\_0^{R2} + (t\_0^{R2} - t\_0^{R1})$, 1.40 + 0.60 = 2.00 s in the figure, with a velocity only slightly below the primary trend at that time (about 5 %): its extra legs are in fast rock, and it never samples the deeper, faster rock. That small difference, about 45 ms of curl at 3000 m, makes it the hardest family to remove, and SRME cannot predict it.

3. The kinematic tells

Each family has a signature that, once you have seen enough gathers, you recognize instantly:

• At exactly $k\\,t\_0$ of the water-bottom primary, at water velocity? Water-bottom multiple train.
• Same velocity as a shallower primary, at twice its time? Free-surface multiple of that reflector.
• Trailing a primary by exactly $t\_0^{\\mathrm{WB}}$, a little more curved? Peg-leg.
• Only slightly slower than the primary trend, and not at a surface-multiple time? Inter-bed (internal) multiple.

4. Which tool kills which

• Predictive deconvolution (Section 2.7): WB multiple trains. Cheap, reliable for periodic water-bottom multiples.
• SRME (Section 4.2): All surface-related multiples: water-bottom trains, peg-legs and free-surface multiples of deeper reflectors. Data-driven, no subsurface model needed. Standard for marine processing.
• Radon demultiple (Section 4.3): Any multiple whose residual moveout after NMO differs from the primary at the same $t\_0$. Fast and model-free; works on NMO-corrected CMP gathers.
• Adaptive subtraction (Section 4.4): Combines a PREDICTED multiple train (from any method above) with a least-squares matched filter to produce a better subtraction. Almost always the final clean-up step.
• Inter-bed prediction (Section 4.5): Internal multiples. Predicted from a model or from the data themselves (Jakubowicz’s generator-horizon method, the inverse scattering series), at a much higher cost than SRME.

5. When multiples dominate

Multiples are most damaging when:

• Hard seafloor. Limestones, chalks, and cemented seafloors reflect strongly, and order $k$ of the water-bottom train scales with $R\_{\\mathrm{wb}}^{k+1}$, so multiple amplitudes approach primary amplitudes. At $R\_{\\mathrm{wb}} = 0.5$ the first order in the figure is 50 % of the seafloor primary.
• Shallow water with deep target. Short-period reverberations and peg-legs trail every deep reflector at nearly its own velocity, so Radon sees little residual moveout, and the missing near offsets weaken SRME. With 75 m of water in the figure the peg-leg trails Sed-1 by 0.10 s and curls only about 33 ms before the mute.
• Strong shallow reflector (e.g., volcanic). Peg-legs from the reflector bury primaries directly below it.
• Carbonate platform. A hard, fast platform top generates strong multiples with periods shorter than the section beneath, so every reflector below it is overprinted.

In each case, multiple attenuation moves from “clean up” to “make or break.” Skip or under-apply and the imaging fails.

6. When multiples are tolerable

For deep water, where the first water-bottom multiple arrives below the target and the multiples are well separated in time, or for land data, where near-surface absorption weakens surface multiples, a moderate SRME pass followed by Radon clean-up is enough. You do not always need the heaviest tools, but you do always need to know which family you are fighting before picking the tool.

Where this goes next

Section 4.2 introduces SRME, the data-driven method that predicts every surface-related multiple from the data itself. It does not distinguish the sub-families; it treats them all as one problem, which is exactly why it is the most widely used multiple attenuation tool in marine processing.

References

• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.
• Verschuur, D. J., Berkhout, A. J., Wapenaar, C. P. A. (1992). Adaptive surface-related multiple elimination. Geophysics, 57, 1166.