Surface-related multiple elimination (SRME)

Predictive decon (Section 2.7) removes water-bottom multiples by picking a single lag. SRME does something more general: it predicts every surface-related multiple (water-bottom multiples and surface peg-legs alike) from the data itself, without needing to know the subsurface velocity or the water depth. It is the standard multiple-attenuation tool for modern marine processing.

1. The central identity

A surface-related multiple is a primary that has bounced at least once off the free surface (the sea surface offshore, the ground surface onshore). Mathematically, that second bounce re-injects the primary as a virtual source, and the multiple is the data convolved with the data at the correct offset. In 1D, once the source wavelet has been removed, the observed trace satisfies

where $d$ is the observed data, $p$ the primary-only response, $r\_0$ the free-surface reflection coefficient, and $r\_0\\,(p \\ast d)$ the whole multiple series. Rearrange:

approximating $p \\approx d$ inside the convolution. That single approximation is the SRME trick: predict the multiples by convolving the data with itself, then subtract. It predicts every first-order multiple exactly and over-predicts the higher orders, so production SRME iterates the prediction, $p\_k = d - r\_0\\,(p\_{k-1} \\ast d)$ from $p\_0 = d$, or subtracts adaptively (Section 4.4).

2. The figure: one line over a sloping seabed

Figure 4.2 applies the 1D identity to every trace of a zero-offset line whose seabed deepens from 200 to 400 m, so the multiple period changes along the line. The prediction in (b) is built from the recorded section (a) alone, with no water depth and no velocity, and (c) is what is left after subtraction. Start with one pass, then raise the passes, leave the source wavelet in, or mis-time the prediction, and read each order of multiple in the table. Plates (e) and (f) build one multiple of the 1500 m trace the way 2D SRME does, as a sum over surface bounce points: open a near-offset gap there and watch the sum lose the multiple:

After one pass the first-order multiples fall to −48.9 dB, but the second-order multiple at 1.20 s is left at full size, 0.0 dB, with its polarity flipped, and the third and later orders grow by 6.7 dB: putting $d$ for $p$ inside the convolution predicts the second order twice and the third three times. Each further pass removes one more order, and after four passes the multiple energy on the 1500 m trace is down to −40.8 dB. Two errors spoil a direct subtraction. With the source wavelet left in, the prediction carries the wavelet twice ($w \\ast w$ instead of $w$), a shape no scalar can fix: even the best gain, 1.14, leaves −14.0 dB after four passes, so the source signature must be removed first. A 4 ms timing error, an eighth of the 30 Hz wavelet’s period, leaves the first-order multiples at −1.8 dB. In production both errors are absorbed by adaptive subtraction (Section 4.4), so you never tune the gain or the timing by hand on real data.

3. Why 2D SRME is the production tool

The 1D derivation above is a pedagogical stand-in. Real SRME operates on shot gathers and receiver gathers. The central convolution becomes a 2D operation across the recording grid, and the prediction requires every possible (source, receiver) pair. Production SRME:

1. Starts from dense, fully-sampled shot gathers (sparse geometry gets interpolated first).
2. For each source $s$ and receiver $r$, convolves the trace from $s$ to every surface point $x$ with the trace from $x$ to $r$: $M(s,r,t) = r\_0 \\sum\_x P(s,x,t) \\ast P(x,r,t)$, where the bounce points near the stationary point add up to the multiple. The sum is the predicted multiple trace.
3. Repeats the prediction from the demultipled data $p\_1$, and so on, as the passes of Figure 4.2 do, until the higher orders are right.
4. Subtracts adaptively (Section 4.4) rather than directly, to absorb small amplitude and phase errors in the prediction.

4. What SRME assumes

• Free-surface reflection coefficient is known (usually taken as −1 for marine surface).
• Data is fully sampled. Gaps in shot or receiver spacing introduce prediction errors that map into the subtracted data as residual multiples. Dense streamers and wide-azimuth marine are SRME-friendly; sparse 2D land lines are not.
• Only free-surface multiples are predicted. Inter-bed multiples never touch the surface and need the methods of Section 4.5.
• Near offsets are present. The missing near-offset traces (the streamer gap) must be extrapolated first, or the shallowest multiples are under-predicted. In Figure 4.2 (f) a gap of only 50 m leaves the sum with 34 % of the first-order seabed multiple, and from 150 m it predicts almost none of it.
• Source signature is deconvolved before SRME. Residual wavelet in $d$ leaks into the prediction’s shape.

5. The advantage: data-driven

Predictive decon needs you to know the multiple period; Radon needs an NMO velocity that separates primary and multiple; model-based methods need a subsurface model. SRME needs only the data. In complex bathymetry (continental shelf edge, canyons, channelized sea beds), where the multiple period changes laterally, SRME works where predictive decon fails and Radon demultiple needs far-offset data it may not have.

6. Computational cost

Production 3D SRME is expensive. For each target sample, you convolve many candidate shot-receiver combinations. A 3D marine volume takes thousands of CPU-hours to run SRME on. Modern implementations use sparse approximations, FFT-based convolutions, and GPU acceleration, but it is still the single most expensive step in many marine processing flows.

Where this goes next

Section 4.3 introduces Radon demultiple, a faster, cheaper alternative that exploits a different property of multiples: they have the wrong NMO velocity and therefore a different residual curvature in a CMP gather. Radon separates primaries from multiples by mapping them to different $(\\tau, q)$ bins, where $q$ measures residual moveout curvature.

References

• Verschuur, D. J., Berkhout, A. J., Wapenaar, C. P. A. (1992). Adaptive surface-related multiple elimination. Geophysics, 57, 1166.
• Berkhout, A. J., Verschuur, D. J. (1997). Estimation of multiple scattering by iterative inversion. Geophysics, 62, 1586.
• Weglein, A. B., Araújo, F. V., Carvalho, P. M., et al. (1997). An inverse-scattering series method for attenuating multiples. Geophysics, 62, 1975.
• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.