A Detection Transformer that picks every fracture and bedding plane in an image log is, for all its accuracy, blind in one direction: it sees only the rock the wellbore actually touched. The interpreter's real question is the one the borehole cannot answer on its own — what is the rock doing between the wells? For a mid-sized Middle East carbonate operator we worked with, closing that gap was the difference between an automated picking tool and a field-scale interpretation system. The bridge was geostatistics: take the per-well detections, compress them into continuous density logs, and krige those logs across the field to extend the interpretation outside any single borehole.
From a set of picks to a continuous log
The upstream model — a ResNet-10 Detection Transformer trained on dynamically normalised high-resolution borehole image logs from two different microresistivity imaging tools — emits a set of sinusoids per well, each carrying depth, dip, and azimuth. That set is exact but discrete: a list of features at irregular depths, one well at a time. Correlation needs the opposite representation. You cannot variogram a list of picks; you need a continuous curve sampled on a common grid so that any two wells can be compared at the same stratigraphic level.
So the first engineering step was to convert the model's output into two new well-log curves the operator had never had before: a bedding-density log and a fracture-density log. We counted detected sinusoids in a moving window and resampled to a fixed grid, evaluating bedding and fracture counts at 0.1 m intervals along the borehole. The grid spacing itself was a tuned parameter — we tested 5 cm, 10 cm, and 50 cm density grids and settled on a 10 cm grid, smoothed with a rolling-average kernel of 5 (a wider kernel of 10 for the more diffuse bedding signal). Too fine and the log was a noise comb; too coarse and it erased the very contrasts that distinguish a fractured zone from a tight one. The result is a pair of synthetic logs that read like any petrophysical curve — density versus depth — and that, crucially, are commensurable between wells.
Why a density log, not the raw picks
A geostatistical estimator interpolates a scalar field sampled at known locations. A list of sinusoids at irregular depths is not a field. Binning detections into a fixed-grid density log turns the model’s set prediction into exactly the input kriging needs — a continuous variable defined at every depth, identically on every well.
What is and is not correlatable — the finding that shaped the method
Before kriging anything, we had to learn which features carried lateral signal. This is the part of the work that textbook geostatistics skips and field data insists on. We ran every candidate curve — bedding density, fracture density, fracture strike, fracture area — through inter-well comparison in the target carbonate formation, where the model's picks were most systematic.
The verdict was specific and, for an interpreter, useful. Bedding density correlated cleanly between wells. Across three wells we examined in detail, two on the flanks showed matching bedding-density structure while the central well carried a distinct high-density band through its middle section — exactly the kind of stratigraphic signature a correlation panel is meant to reveal. Fracture density did not correlate: it was localised, a near-wellbore property rather than a layer-cake one, and kriging it would have manufactured a continuity that the geology does not have. Bedding-plane strike direction yielded no significant inter-well correlation either, and fracture area proved a poor correlation identifier — useful per-well, meaningless field-wide. A rose diagram on one well showed bedding planes trending E–W, N–S, and NE–SW; that azimuthal complexity is real, but it is local.
That asymmetry — bedding density correlatable, fracture density and strike not — is itself the deliverable. It tells the subsurface team which automated curve to trust for inter-well prediction and which to read only inside the borehole. Encoding that distinction into the pipeline prevented the single most dangerous failure mode of any correlation tool: confidently interpolating a quantity that has no lateral structure.
Kriging: the estimator and its variograms
With a correlatable variable in hand, the inter-well step is best linear unbiased prediction — kriging. The principle is the one that makes this whole class of method honest about uncertainty: it is the same domain-alignment idea that recurs across subsurface ML, where features observed at labelled locations must be projected onto the unlabelled space between them without distorting the underlying distribution.
For the field correlation we fit experimental variograms and tested three theoretical models — Gaussian, linear, and exponential — choosing per-pair by fit, since the spatial decay of bedding density is not the same in every direction or interval. The well geometry was favourable but not trivial: inter-well spacing ran roughly 40 to 80 m (a linear-kernel kriging at the ~40 m pairs, wider for the ~80 m pairs), close enough that the variogram range comfortably spanned neighbouring wells. We produced 2D kriged surfaces across the three closely-spaced wells, then lifted the same density logs into a 3D kriging over the field's topography so that bedding-density structure could be read as a volume rather than a fence.
To make the surfaces interpretable rather than just colourful, we ran contour analysis every 30 m down-section across 10 wells, with a location plot covering 11, and confirmed the estimator against the raw logs: two wells with similar bedding-density signatures produced similar contour patterns at the 90–120 m level, which is the kind of internal consistency check that distinguishes a calibrated surface from a smooth lie. The full inter-well correlation was computed from 13 vertical wells.
The engineering underneath
None of this is a notebook script. The density-log generation, the variogram fitting, and the 2D/3D kriging are stages of a reproducible pipeline that consumes the Detection Transformer's output for a new well and emits updated correlation surfaces — the same data-engineering discipline that lets the upstream model retrain as wells arrive. Depth is the spine of the whole system, and it is unforgiving: the high-resolution borehole image logs run as long as 250 m, and at the native digital-log-format resolution a single pixel is 3 cm, so an irreducible ±3 cm depth uncertainty rides under every pick. Carrying that error budget cleanly from raw image to kriged surface — rather than letting it compound silently through resampling and gridding — is what makes the output validator-ready instead of merely plausible.
What the field picture changes
The value of correlation is operational, not aesthetic. An isolated pick tells a driller where rock fractured in a well already drilled. A kriged bedding-density surface tells a planner where a productive interval is likely to sit at a location not yet drilled — the input that turns image-log interpretation into directional and infill-drilling guidance, and that flags candidate new productive zones between existing wells.
The operator's own assessment of the well-to-well capability, measured against their prior manual workflow, was a roughly 60% lift in interpretation productivity and a 75% gain in interpretation accuracy, with the broader automated stack delivering interpretation about 5× faster than hand-picking. Against the correlation targets the team set, the kriged surfaces hit 95% on target precision and 90% on stratigraphic success — numbers that hold only because the pipeline kriges the one curve that earned the right to be kriged.
Before
One well at a time
Detection model picks fractures and bedding planes inside each borehole — exact, but blind between wells
After
A field-scale surface
Bedding-density logs kriged (Gaussian/linear/exponential variograms, ~40–80 m spacing) into 2D/3D surfaces, contoured every 30 m
~60% productivity, ~75% accuracy lift; 95% target precision, 90% stratigraphic success vs the manual workflow
The honest limits
The correlation is only as good as the variable's true lateral continuity, and we measured that rather than assumed it — which is why fracture density and strike were deliberately left un-kriged. The surfaces are built from 13 vertical wells of a single confidential field; the variogram ranges and the choice between Gaussian, linear, and exponential models are calibrated to this carbonate stratigraphy and would need refitting elsewhere. And kriging interpolates, it does not extrapolate: confidence falls away beyond the well envelope, so the surface is a planning prior between known control points, not a prediction into virgin acreage. Stated plainly, those caveats are what keep the 3D field picture trustworthy — a correlation tool that knows the boundary of its own competence is worth far more than one that smooths confidently past it.
Turning per-well picks into a 3D field interpretation
- Correlation needs a continuous variable, not a list of picks: detected sinusoids were binned into bedding- and fracture-density logs at 0.1 m intervals on a tuned 10 cm grid (rolling-average kernel 5–10), making wells directly comparable at the same depth.
- Measure correlatability before you krige: bedding density correlated cleanly between wells, but fracture density, strike, and fracture area did not — so only the bedding-density log was kriged, preventing a smooth, confident, and wrong interpolation.
- Kriging (Gaussian/linear/exponential variograms, ~40–80 m well spacing) produced 2D and 3D surfaces across 13 vertical wells, contoured every 30 m — extending interpretation outside the borehole and lifting interpretation productivity ~60% and accuracy ~75% against the manual workflow.
References
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Well-to-well correlation results, variogram selection, kriging configuration, and productivity/accuracy figures derived from internal Phase-3 reporting on a 13-well Middle East carbonate dataset logged with two different microresistivity imaging tools; data and code withheld under operator confidentiality.
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Cressie, N. (1990). The Origins of Kriging. Mathematical Geology, 22(3), 239–252.
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Carion et al. (2020). End-to-End Object Detection with Transformers (DETR). ECCV 2020. https://arxiv.org/abs/2005.12872
