Capstone: Marine WAZ FWI project

Wide-azimuth (WAZ) marine acquisition sails one or two streamer vessels with extra source vessels alongside at crossline offsets of several kilometres, repeating the pass in lateral tiles, so each image point is illuminated from a wide range of azimuths rather than along the single sail-line direction of a narrow-azimuth survey. WAZ was developed for sub-salt illumination and 3D multiple attenuation; its long, all-azimuth offsets later proved valuable for FWI, which updates the model better when every region is sampled from many directions. Avoiding cycle skipping still depends on low frequencies and a good starting model, not on azimuth.

Project setup

A 5000 km² WAZ survey in a deep-water frontier basin: 10 km streamers at 120 m separation, with source vessels sailing alongside at crossline offsets of several kilometres, repeated in lateral tiles. Primary deliverable: an FWI $V\_{\\mathrm{P}}(x,y,z)$ volume sampled at 12.5 m laterally and 10 m vertically, calibrated to a dozen regional wells. Secondary deliverable: a pre-stack depth-migrated volume with the FWI velocities.

The pipeline

In the figure the first band starts from the recorded 2.75 Hz with a far-offset error of 221 ms, more than half a period (182 ms), so FWI converges on the wrong cycle: it makes the whole model faster until the far trace in (d) sits one period, 364 ms, off, and the model error grows instead of falling. Put the low-frequency extension back and FWI starts at 1.5 Hz, where half a period is 333 ms; after the 12 to 15 Hz band the far trace is 3 ms off and the model resolves about 100 m.

FWI as deliverable

In many modern workflows the FWI velocity model is itself the deliverable, not just a step on the way to migration. Interpreters use the velocity volume directly to map facies (clastic, carbonate, basalt), identify gas clouds (low-velocity anomalies) and set up reservoir models. A well-calibrated FWI $V\_{\\mathrm{P}}(x,y,z)$ volume, sampled every 12.5 m and resolving features of about $\\lambda/2 \\approx 100$ m at 15 Hz, is a geology-grade product by itself.

The ML acceleration stage

ML-based low-frequency reconstruction (spectral extrapolation of the FWI band, a different problem from the dead-trace interpolation of Section 9.3) is a recent addition to WAZ workflows. Towed-streamer data are usually usable from about 3 Hz (2.75 Hz in the figure); reconstructing plausible 1.5 to 3 Hz content from the recorded band gives FWI nearly one more octave, which nearly doubles the traveltime error the starting model may carry ($T/2 = 1/(2f\_{\\min})$ grows from 182 ms to 333 ms). The networks, usually CNNs trained on synthetic data, need careful QC, but when they work FWI converges from a much more forgiving starting model.

Multi-scale schedule

The cascade in the figure, with typical iteration counts:

1. From the lowest usable frequency (extrapolated or recorded) to 6 Hz: about 20 to 30 iterations; converges from the tomography starting model when it passes the half-period test.
2. 6 to 9 Hz: about 15 to 20 iterations; keeps the long-wavelength structure and adds intermediate-scale features.
3. 9 to 12 Hz: about 10 to 15 iterations; reservoir-scale detail emerges.
4. 12 to 15 Hz: about 10 iterations; boundaries sharpen toward $\\lambda/2 \\approx 80$ to 100 m, still far coarser than thin beds.

Where this goes next

Section 10.4 moves to a 4D monitoring project, where the deliverable is a time-lapse difference rather than a static image.

References

• Virieux, J., Operto, S. (2009). An overview of full-waveform inversion in exploration geophysics. Geophysics, 74, WCC1.
• Pratt, R. G. (1999). Seismic waveform inversion in the frequency domain, Part 1. Geophysics, 64, 888.
• Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49, 1259.
• Etgen, J., Gray, S. H., Zhang, Y. (2009). An overview of depth imaging in exploration geophysics. Geophysics, 74, WCA5.
• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.