Subsalt imaging: Thunder Horse from Kirchhoff to FWI to QI

How the images of Thunder Horse improved

• Wide azimuth. The first wide-azimuth towed-streamer survey for subsalt imaging in the Gulf of Mexico was BP’s over Mad Dog in late 2004 and early 2005 (Threadgold et al., 2006); it began a broad programme of such surveys over subsalt discoveries.
• Azimuths, offsets and nodes. Rodriguez Castelan et al. (2016) describe data from five towed-streamer surveys over Thunder Horse, with offsets up to 10 km and a broad range of azimuths. Ocean-bottom-node data were recorded over the field too, and that paper uses them with the streamer data to predict and remove multiples. In 2015 BP acquired a long-offset, full-azimuth node survey over the field to improve the subsalt illumination (Elebiju et al., 2022).
• Borehole seismic. From 2015 to 2018 BP acquired six large 3D vertical seismic profiles at its Gulf of Mexico fields, two of them at Thunder Horse (van Gestel et al., 2019).
• Full-waveform inversion. Successes of FWI that updates the salt itself had almost only been seen on synthetic data until the progress at Atlantis (Wang et al., 2019), where BP’s salt FWI gave some of the best subsalt images yet seen at that field (Shen et al., 2017). In January 2019 BP reported that its proprietary algorithms for FWI, which let data that once took a year to analyse be processed in a few weeks, together with reservoir characterization had identified a further 1 billion barrels of oil in place at Thunder Horse, and that ocean-bottom-node surveys with its ultra-low-frequency Wolfspar source, after a trial at Mad Dog, were being planned for Thunder Horse and Atlantis (BP, 2019). FWI of the 2015 node data has since improved the field’s subsalt velocities and images (Elebiju et al., 2022).

The published record gives the steps and the outcome, not the images or the velocity models. The figure below is therefore a model: a section shaped from these descriptions, with the book’s own rocks and physics, built to show why each step was needed.

Exercise, take the image through its history

Figure 9.3 traces rays through a model earth, 16 km across and 9 km deep: 1.85 km of water, sediments compacting from 1,600 to 4,460 m/s, a salt canopy at 4,500 m/s and 2.16 g/cm³ (the halite of Figure 3.5 and the rock library), and beneath it a closure whose crest lies at 7.2 km, with the salt over 76% of its 6.8 km (a choice of the model). Its target is an oil sand of the book’s library, 120 m thick. A part of the closure counts as mapped when it is lit, receiving at least a quarter of the light that offsets to 8 km give it with no salt above (light is measured in the true earth, whatever the velocity model), and imaged within a quarter wavelength of its true depth, $\lambda/4 = 62$ m at 15 Hz in the shale above the sand.

1. Start as a first pass does: Kirchhoff migration, offsets to 8 km, and a velocity model with no salt in it. Read at the slower sediment velocity, the salt’s short traveltime becomes too short a distance, so everything beneath it is imaged too shallow: the target lands up to 1,677 m high in (d). At a constant sediment velocity the shift would be $\Delta z = -h(1 - V_\text{sed}/V_\text{salt})$ for salt of thickness $h$; here the sediments speed up with depth and the shift grows beneath the salt. The light in (b) is as poor: a Kirchhoff migration whose traveltimes are first arrivals misplaces 81% of the 2,246 recorded paths that reach the closure beneath the salt, because there the first arrival has come through the fast salt by another route. Only 6% of the closure, at its east end, is mapped.
2. Put the salt in, with its base smoothed the way an early interpretation might have picked it. The target comes back to within about 200 m of its depth, and (d) stays inside its band over about half the closure; the swells and the keel of the true base that the smoothed base misses are where it does not. The light is unchanged, because the figure measures it in the true earth whatever the model, and only 12% is mapped.
3. Record out to 16 km and switch to reverse-time migration, which solves the wave equation and uses every arrival. The whole closure is lit and the share mapped jumps to 51%. The rest is lit but in the wrong place: light cannot move a target that the velocity model misplaces.
4. Migrate through the FWI model, the true earth seen at the resolution of an inversion run to 8 Hz, half its shortest wavelength (the rule of Figure 8.4.1). Now 94% of the closure is mapped. What remains sits at the salt’s east tip, where a model that resolves 250 m blurs a jump of more than 2,000 m/s and puts the target up to 200 m too deep.
5. Set plate (c) to Inverted, the relative impedance. Integrating the image down each trace is the simplest relative-impedance inversion; at the crest it recovers 91% of the oil sand’s softness at the depth a well would find it. Switch back to no salt: the sand is imaged 1.1 km higher, and at the well’s depth the inversion reads other beds. Quantitative interpretation beneath salt starts only where the image is lit and in place.
6. Drag the shot across (a), which always shows the true earth, with offsets to 8 km. From a shot at 6 km, over the canopy, 17 of the 33 rays reach the target and 6 emerge within 8 km of the shot; the rest are turned back by the salt or emerge beyond it. From a shot at 12 km, east of the salt, 25 reach the target and 18 return.

Why salt defeats a Kirchhoff image

Two things fail beneath salt, and the figure measures both.

• Light. Halite at about 4,500 m/s sits in sediments of 2,000 to 3,800 m/s. A ray steeper than the critical angle $\theta_\text{c} = \arcsin(V_\text{sed}/V_\text{salt})$ cannot enter the salt, and the rays that do enter are bent hard at its faces, so parts of the target are barely reached (the shadow of Figure 3.5, here with rays rather than vertical paths). Rugose and overhanging faces also bring energy to one point along several paths at different times. Salt itself is nearly lossless: the shadow is geometry, not absorption.
• Arrivals. A Kirchhoff migration sums each trace along one traveltime per image point, or a few. Where fast, rugose salt brings energy to one point along several paths, a single-arrival Kirchhoff images one of them and puts the rest in the wrong place, and migrations that use every path image beneath salt better (Gray et al., 2001). Figure 9.3 makes the textbook simplification: its Kirchhoff takes the first arrival, the time an eikonal solver gives, which beneath fast salt often belongs to a weak path through the salt rather than to the strong reflection; production codes may keep the most energetic arrival, or several, and do better. Reverse-time migration propagates the whole wavefield and needs no choice of arrival.
• Position. Every migration places energy where the velocity model says it came from. Leave the salt out and the subsalt section is imaged hundreds of metres too shallow; pick its base wrongly and the target moves with every error in the base. Wide azimuths and reverse-time migration restore the light, and only a better velocity model restores the position.
• Multiples. The strong salt faces and the sea floor generate multiples that fall among the weak subsalt primaries; removing them, with the help of ocean-bottom data at Thunder Horse, is part of every subsalt workflow (Rodriguez Castelan et al., 2016). The figure does not model them.

Workflow walkthrough, the modern subsalt chain

1. Acquisition for light: wide- and full-azimuth towed streamers, long offsets and ocean-bottom nodes illuminate the subsalt target from more directions than a single narrow-azimuth survey can, and low-frequency sources give FWI the long wavelengths it starts from.
2. Sediment velocities: reflection tomography under a tilted transverse isotropy (Section 8.3) builds the velocities above and beside the salt from picked reflections.
3. Salt geometry: top salt is a strong reflector and is picked first; the base, imaged through the salt, is the hardest surface in the model and is refined over several passes of migration and interpretation.
4. FWI (Section 8.4): starting from low frequencies to avoid cycle skipping, it updates the sediments and, since Atlantis, the salt body itself, so that modelled waveforms match the recorded ones.
5. Reverse-time migration through the final model gives the structural image and the angle gathers for AVO.
6. Quantitative interpretation (Parts 5 to 7): the same inversion and rock-physics workflow as on any image, read with a map of the illumination, because amplitudes in poorly lit areas are less reliable.

Outcomes and lessons

• At Thunder Horse every published step, many azimuths and long offsets, ocean-bottom nodes, borehole seismic and FWI, was aimed at the salt’s distortion of the subsalt image, and BP credits the last of them, with reservoir characterization, for a further 1 billion barrels in place (BP, 2019).
• Light and position are separate problems. The figure’s third and fourth steps show that more light without a better model images the target brightly in the wrong place.
• Imaging is never finished. Each new survey and each better model is a reason to migrate the field again, and each new image moves the maps that wells are planned on.

The lesson that transfers to every subsalt or sub-basalt project: the image limits the interpretation. An inversion of a misplaced or unlit image returns misplaced or unlit answers, so effort goes first to the light and the velocity model.

Where the Thunder Horse story generalizes

• Strong generalization: the other subsalt fields of the deepwater Gulf of Mexico, such as Atlantis, Mad Dog and Tahiti, and salt provinces offshore Brazil, West Africa and Mexico. The physics and the processing chain are the same.
• Adapted application: sub-basalt imaging on the North Atlantic margin (Faroe-Shetland, Rockall), where basalt is faster still and its layering scatters more.
• Pre-salt (Section 9.5 preview): Brazil’s pre-salt carbonates lie beneath thick salt and are imaged with the same chain of salt interpretation, reverse-time migration and FWI.
• Onshore: thrust belts with fast carbonates thrust over slower rocks face the same problems of light and position.
• Where it does not apply: basins with gently varying velocities, where a tomographic model and a Kirchhoff migration image the target well enough.