Migration artifacts & QC

Every migration is an approximation of the earth, and every approximation leaves traces. Production interpreters learn to read migration output for two things at once: the geology underneath, and the artefact pattern that tells them whether the image is trustworthy. This section catalogues the main artefact fingerprints each migration method can produce, and the QC workflow that catches them before they mislead an interpretation. The figure below lets you cause each one yourself: migrate one diffractor with the wrong velocity, too narrow an aperture or traces too far apart, and read the shape each mistake leaves in the image.

1. The figure: four canonical artefacts

Plate (a) is the ideal. One diffractor sits at $x$ = 1000 m, $z$ = 900 m in a 2000 m/s earth, so its apex arrives at $t\_0$ = 0.90 s. Migrated with that velocity, the full 1000 m half-aperture and 12.5 m traces, it collapses to a focus 32 m wide. Plate (b) migrates the same data with your settings and draws it on the same amplitude scale, and plate (c) shows the recorded hyperbola with the curve the migration sums along. The figure opens with $V\_{\\mathrm{mig}}$ = 1700 m/s, 15 % slow: the focus is 3.8 times as wide as the ideal's and 13.3 dB weaker. Each defect leaves its own fingerprint:

• Under-migrated ($V\_{\\mathrm{mig}} \\lt V$). The summing hyperbola is narrower than the data hyperbola, so the sum only partly collapses it. A flatter residual hyperbola, a frown, survives below the focus: at 15 % slow the focus is 3.8 times as wide as the ideal's. On a production section this looks like diffraction tails that never collapsed.
• Over-migrated ($V\_{\\mathrm{mig}} \\gt V$). The summing hyperbola is wider than the data, so the sum overshoots and spreads the focus into an upward-curving arc, the classic migration smile: at 2300 m/s, 15 % fast, the focus is 4.1 times as wide as the ideal's. Smiles that cluster near fault edges or truncations flag over-migration.
• Narrow aperture. Each output point sums only the traces within a half-aperture $A$ of it, so dips steeper than $\\theta\_{\\max} = \\arctan(A/z)$ are never summed and are lost. The focus smears sideways and weakens: at $A$ = 150 m (\\theta\_{\\max} \\approx 9^\\circ) it is 4.4 times as wide as the ideal's and 14.1 dB weaker. The flanks left unsummed stay as a weak arc that bends down below the focus, like a mild frown, but the image gather stays flat, and that is how you tell a narrow aperture from a slow velocity. Near the edges of a survey the available aperture shrinks in the same way.
• Coarse trace spacing. The steep flanks of a diffraction are spatially aliased once $f \\gt V/(4\\,\\Delta x \\sin\\theta)$, about 13 Hz for 48° dips at $\\Delta x$ = 50 m. The arcs that single traces contribute no longer cancel and leave a cross-hatch of dipping swings around a focus that is still in place and as sharp: at 50 m, 17 % of the image energy lies off the focus against 7 % in the ideal. An anti-alias filter in the operator trims that to 9 %, at the cost of steep-dip bandwidth (the focus widens from 32 m to 58 m). At 100 m no filter helps; only finer sampling, recorded or interpolated, removes the aliasing.

2. Common-image gathers (CIGs): the velocity QC

Pre-stack migrations (PSTM, PSDM, beam, RTM) preserve the offset (or angle) axis. For each CMP position, gather the migrated image over offset: that is a common-image gather. If the migration velocity is correct, the event is flat across offset. If $V\_{\\mathrm{mig}}$ is too high, the event curves down at far offsets (residual over-migration). If $V\_{\\mathrm{mig}}$ is too low, it curves up (residual under-migration). For small errors the curvature is proportional to the velocity error. Plate (d) of the figure is such a gather for a flat reflector: at 15 % slow it curls up by 80 ms at 1200 m, and it is flat only at the velocity that gives the narrowest focus. CIGs are the single most important QC and the driver of the iterative velocity update in Section 5.9.

3. Angle gathers: the anisotropy QC

Angle gathers are a different rearrangement of the pre-stack migration output: for each image pixel, plot amplitude as a function of the angle between the ray and the normal to the reflector. Angle gathers should be flat with a smooth amplitude vs angle curve. Anomalies at specific angles, systematic lows or flips, reveal anisotropy, thin-bed tuning, or AVO anomalies that an offset gather would smear together.

4. Stack power and S/N

Migration should make the image sharper. Diffractions collapse, so the peak amplitude and lateral coherence of real events rise. If the coherence falls, or focused events come out weaker and smeared into arcs, suspect a wrong velocity or an over-aggressive anti-alias filter. Production QC always compares pre- and post-migration amplitude spectra and coherence.

5. RTM-specific QC

• Low-frequency backscatter. Strong low-wavenumber content near high-velocity boundaries is the tell. Remove with a Laplacian filter (high-pass the image wavenumbers) or use a Poynting-vector imaging condition.
• Boundary reflections. Imperfect absorbing boundaries reflect energy back into the model, and it is imaged as spurious events near the model edges. Use thicker PML or CPML padding.
• Wavefield-storage artefacts. Lossy compression of saved source wavefields, or applying the imaging condition only every $N$th time step below the wavefield's temporal Nyquist, leaves faint banding and noise. Store with more precision or image more often.

6. Migration stretch

Time-migrated far-offset data shows the same frequency-dependent stretching as NMO-corrected gathers (Section 3.2): shallow, far-offset samples are stretched toward lower frequencies, hurting stack quality at the top of the section. Solutions: apply a stretch mute (zero samples stretched past some threshold, typically 30-50 %) or migrate in the shot-domain to avoid NMO. Depth migration avoids the NMO-style offset stretch, but its image still stretches by $1/\\cos\\theta$ at large reflection angles, because $k\_z = 2\\omega\\cos\\theta/V$. Far angles are usually muted before stacking.

7. The QC workflow

1. Look at the stacked image. Look for smiles, remnant hyperbolas, edge artefacts, crossing aliased swings, and low-frequency banding. Map the geometry of each: are smiles where velocities change abruptly? Do crossing, dipping swings point to traces too far apart for the steepest dips?
2. Compare common-image gathers. For a handful of representative CMPs, plot the image as a function of offset or angle. Look for systematic curvature.
3. Check the migration parameters. Is the velocity updated? Is the aperture broad enough? Is the anti-alias filter in the Kirchhoff operator active? Is the dip limit of the one-way scheme honoured?
4. Iterate the velocity. Residual moveout on CIGs drives the next velocity model (Section 5.9). A single pass of migration is rarely enough; 2-5 iterations are typical.
5. Compare methods. Run both PSTM and PSDM (or beam and RTM) on a subset. Where they disagree, find out why. The more complete method is usually right in complex geology, but first check that both used the same velocity model and parameters. Where they agree, the image is more trustworthy.

Where this goes next

Section 5.9 closes Part 5 with velocity model building, the iterative loop that takes the residual moveout measured on CIGs, updates the velocity field, re-runs the migration, and repeats until the CIGs are flat. Everything in Sections 5.2-5.7 depends on getting that loop to converge.

References

• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Etgen, J., Gray, S. H., Zhang, Y. (2009). An overview of depth imaging in exploration geophysics. Geophysics, 74, WCA5.
• Stolt, R. H., Benson, A. K. (1986). Seismic Migration: Theory and Practice. Geophysical Press.
• Claerbout, J. F. (1985). Imaging the Earth’s Interior. Blackwell.