The problem
We have sparse 2D seismic lines crossing a region where no 3D seismic exists. An interpreter has picked horizons on each line, giving us dense observations along the lines and nothing between them. We want to reconstruct what a 3D survey would have shown — and, just as importantly, how confident we should be about each reconstructed location.
Classical interpolation methods — RBF, Gaussian process regression — produce smooth surfaces that honor the observed picks. They are excellent at the long-wavelength regional structure and reliably wrong about everything shorter. They miss the channels, the fault-related folding, the subtle closures. They produce a surface where, for any given point between the lines, we have no idea how much to trust the answer.
The key insight: residual learning
The breakthrough is recognizing that the problem decomposes into two parts, best handled by different methods. RBF handles the smooth regional trend it was designed for. A learned prior handles the short-wavelength geological character — channels, faults, lateral texture — that classical interpolation misses.
Full horizon = RBF smooth prior + geological residual Step 1 ─ Fit RBF to the 2D picks → smooth surface Step 2 ─ Compute residual = truth − RBF Step 3 ─ Train network to predict residual from sparse line observations Step 4 ─ At inference: RBF + predicted residual = full reconstruction
The three-stage framework
The method is built and validated in stages of increasing generality. Each stage is independently demonstrable and answers a specific question. Each stage builds on the last.
Horizon workflow
Sparse 2D picks → 3D horizon surface with feature completion from partial observations
Penobscot experiment
2D lines → full 3D seismic volume, with ground-truth validation on a known 3D survey
Commercial deployment
Calibrated synthetic generator + self-supervised fine-tuning — no 3D ground truth required
Uncertainty quantification — the differentiator
Every reconstruction we deliver is an ensemble, not a point estimate. The Gaussian process realizations used as input channels naturally produce a distribution of reconstructions. The spread across realizations — largest between lines, collapsing to zero at line locations — gives explicit P10 / P50 / P90 estimates of the reconstruction at every point in the volume.
This is the genuine commercial differentiator. Conventional methods give one answer. ORCA gives a calibrated range of answers, each geologically plausible, with the spread quantifying the irreducible uncertainty from limited observations. That reframes the deliverable from "here is our best estimate" to "here is the range of structures consistent with your 2D data, and here is how a 3D survey would reduce that range."
Storage site regulators require explicit uncertainty quantification on structural closure. A single deterministic horizon surface does not answer the regulator's question. A P10–P90 envelope does.
Honest about limits
The credibility of any reconstruction method lives or dies on what the team is willing to say it does not do. Here is what we are and are not claiming.
What the framework does
- Reconstructs between-line structure with geological character
- Produces calibrated P10 / P50 / P90 envelopes
- Honors 2D picks and well constraints exactly
- Validates against ground truth where available
What it does not do
- Replace a real 3D survey where the resolution matters
- Generalize to geology unlike its training set without recalibration
- Invent features unsupported by the 2D observations
- Hide assumptions behind a single point estimate
What's next
The Penobscot experiment lands at EAGE 2026 as the flagship technical case study. Generalization to other geological provinces — passive margin clastics, carbonate platforms, salt basins — proceeds via the model zoo described in the commercial deployment work.