What the lab simplifies

The teaching field

• Six fictional wells through the same layer-cake stratigraphy: shale, Sand A, a shale with coals, a limestone, a shale with anhydrite, Sand B and shale. Each well is 200 m, sampled every 15.24 cm, and vertical, so measured depth is true vertical depth.
• Six facies, all classes in the FORCE 2020 labels: sandstone, sandstone/shale, shale, limestone, coal and anhydrite. Coal and anhydrite are kept rare on purpose.
• Logs are Probe Lab's point responses for each rock, smoothed to each tool's vertical resolution, with noise matched to a FORCE 2020 interval. The deep and medium resistivity are induction curves.
• One mud for every well (fresh water based, 1.2 g/cm³, no barite), an 8.5 in bit and 25 cm of invasion in permeable beds. Sand A has an oil–water contact at 2045 m.
• Permeability comes from Pore Lab's Kozeny-Carman model, with grain size and sorting set bed by bed and about a quarter of a decade of variation from sample to sample. The 420 core plugs, every 30 cm through Sand A in Wells A, B and C, add a little laboratory measurement noise.
• Built-in problems, each placed for a chapter: a washout in Well D that corrupts density, neutron and Pe; no sonic in the top 40 m of Wells B and F; Well E logged with older tools (gamma ray 15 API high, neutron 0.04 low, density 0.035 g/cm³ high, Pe 0.4 high); a tight dolomitised limestone in Well F, harder than any rock in the other wells; beds thinner than the tools can resolve; and step-out wells: Well D with more compacted shales and density reading 0.02 g/cm³ high, and Well F with slightly compacted shales, a feldspathic Sand B and density reading 0.015 g/cm³ low.

Physics values still to check

The rock physics is copied from Probe Lab, whose research report marks some values as textbook figures still to be checked against a source. These are all the values so marked in the material table Fit Lab copies; not every one of these minerals appears in the teaching field. Two tool constants are also unverified: the density tool's mass attenuation coefficient at 662 keV, and the neutron tool's spacings and slowing-down lengths.

Where the lab differs from scikit-learn

k-means

From the same starting centroids, the same labels, centroids and inertia as KMeans. The figures start from your centroids or from seeded random starts; KMeans starts with k-means++ by default.

Linear regression

The same coefficients as LinearRegression and PolynomialFeatures, to within 10⁻⁹. Gradient descent is the lab's own, for showing the steps.

k-nearest neighbours

Brute-force search, the same predictions and vote shares as KNeighborsClassifier, including ties, which go to the class listed first.

Decision trees

CART with Gini impurity and 32-bit cutoffs, as DecisionTreeClassifier. When two logs tie exactly for the best cut, the lab tries the logs in order (or a seeded shuffle); scikit-learn's order is its own random one, so deep trees can part ways after the first exact tie.

Random forests

Bootstrap samples, the square root of the logs at each split and a soft vote, as RandomForestClassifier, but with the lab's own random numbers: blind-well accuracy is within two points of scikit-learn's average over ten seeds, and the sonic regression's error within its range.

Neural networks

The design of MLPRegressor (Glorot starts, ReLU, Adam, half the squared error plus an L2 penalty) with the lab's own random numbers; the training loss and the blind-well error fall within scikit-learn's spread over ten seeds. The figures use a learning rate of 0.01 and batches of 64 (scikit-learn's defaults are 0.001 and up to 200) so they train in about a second, and early stopping uses a validation well where scikit-learn holds back a random tenth.

Isolation forest

The design and defaults of IsolationForest (100 trees of 256 samples, a height limit of 8), with the lab's own random numbers; the washout's ROC AUC is within two points of scikit-learn's average over ten seeds.

Metrics

The same values as sklearn.metrics, to twelve decimal places. Where a facies is never called, its precision has nothing to divide by: scikit-learn reports 0 with a warning, and so does the lab, with a note or a dash in the figures.

Validation

Random splits are seeded. Block cross-validation assigns depth blocks to folds by a fixed rule, and per-well normalisation matches each well's 5th and 95th percentiles to a reference; both are the lab's own helpers, as scikit-learn has no direct equivalent.

Credits

• Rock physics and tool responses: Probe Lab. Permeability: Pore Lab. Vertical resolution smoothing: Bore Lab. All three are in the Labs series.
• Real wells: the FORCE 2020 Machine Learning Competition dataset. See the Data page for the citation and licences.