Surface-related multiple elimination (SRME)

Predictive decon (§2.7) removes water-bottom multiples by picking a single lag. SRME does something more general: it predicts every surface-related multiple — water-bottom, peg-leg, surface-related internal — 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 sea surface. 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, the observed trace satisfies

where d is observed data, p is the primary-only response, and the second term is the multiple series. Rearrange:

— approximating p ≈ d inside the convolution. That single approximation is the SRME trick: predict the multiple by autoconvolving the data, then subtract. It works because the primary is much larger than any individual multiple, so d ≈ p is correct to first order.

2. The 1D widget

The widget shows a trace with a primary at 0.5 s and two WB multiples at 1.0 s and 1.5 s. The middle panel is gain · shift(autoconv(d)). The bottom panel is d − prediction. Play with the sliders:

Drop the gain slider from 1.00 to about 0.80 while keeping the shift at 0 ms and watch the bottom panel — the multiples at 1.0 s and 1.5 s collapse, pushing attenuation past +12 dB. The non-unity gain compensates for the fact that autoconvolving a Ricker with itself produces a slightly wider wavelet with different peak amplitude, so a scalar rescale matches the predicted multiple height to the true one. The shift slider lets you also explore small temporal misalignments; in production SRME both the gain and any residual shift are absorbed by the adaptive-subtraction step of §4.4, so you never tune them 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:

• Starts from dense, fully-sampled shot gathers (sparse geometry gets interpolated first).
• Computes per-trace convolutions of shot gathers and receiver gathers that share a common source-receiver midpoint with the target multiple.
• Sums all convolutions that could produce a multiple at the target location. This is the predicted multiple trace.
• Subtracts adaptively (§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.
• Multiples are reasonably linear combinations of primaries. For strong, multi-generation inter-bed multiples §4.5’s model-based methods are better.
• 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

§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 (τ, p) bins.

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.