An absolute value almost put a mineral in our porosity catalogue. The vug detector we built for a mid-sized Middle East carbonate operator ends in a contrast test: a candidate that clears the earlier shape screens has to prove it is genuinely different from the rock around it, and the first draft of that test measured the difference as a magnitude. It worked on almost everything. Then a reviewer pointed at one line of the change map and asked what would happen to a compact, roughly round grain of a mineral that reads with the opposite electrical character to a pore. The magnitude does not care which way the contrast runs. A bright mineral and a dark pore both register as large differences, and both would have been kept. The candidate that shape could not reject, magnitude could not reject either.
The fix was one character. We stopped taking the absolute value and read the sign of the difference instead. That single change is the whole subject of this piece, because it turns out the sign carries the entire discrimination between a dissolution pore and its mineral look-alike, and the direction of that sign is fixed by the mud in the borehole. The two shape screens that come before it, a circularity band and an area window, are worked through in a companion case study; this piece is only about the minus sign they hand off to.
What magnitude cannot see
Start with what the earlier screens leave on the table. Circularity and area both describe an outline. They ask whether a candidate is round enough and the right size to be a pore, and they answer that cleanly: elongated fracture traces and outsized washouts are gone by the time a candidate reaches the contrast test. What survives is a set of contours that are all plausibly pore-shaped. The problem is that a mineral grain can be pore-shaped too. Some minerals in a carbonate face sit in the right roundness band and the right size band and pass every geometric check, because geometry describes the boundary of a patch and says nothing about what fills it.
So the contrast test has to read the fill, not the outline. It compares the intensity inside a candidate against the intensity of a ring of rock just outside it, on a bounding box grown ten percent on each side so the test sees the candidate with a rim of its neighbourhood. Call the interior mean intensity and the vicinity mean intensity, and the quantity that matters is their difference.
The original test used the size of that difference. A candidate that stood far enough from its neighbourhood, in either direction, was judged a real bounded feature rather than a low-contrast fluctuation. That is a reasonable edge detector and a poor mineralogist. It answers the question "does this patch differ from its surroundings" and never the question "which way." For a pore and a mineral that differ from the rock by the same amount in opposite directions, magnitude returns the same verdict for both.
Why the sign is a mineralogy, not a threshold
The magnitude threw away a physics the sign keeps. On these logs a candidate's intensity is a reading of how the patch conducts relative to the carbonate around it, and under water-based mud a true dissolution pore is the more conductive feature. Conductive reads dark on a raw static image scaled from zero to two hundred fifty-five, so a genuine pore sits at a lower intensity than its vicinity. Its interior mean is below its vicinity mean, and the difference is negative.
A mineral of the opposite electrical character does the reverse. It is more resistive than the rock, reads brighter, sits at a higher intensity than its vicinity, and its difference comes out non-negative. The two classes we actually confuse land on opposite sides of zero, not at different distances from it. That is why the sign works where the magnitude fails: the axis that separates a pore from its look-alike is the direction of the contrast, and the sign is the only part of the difference that records direction. Two candidates that are identical in roundness, identical in size, and equal in the magnitude of their contrast are told apart by which side of zero they fall on.
Note what the sign is not. It is not a tuned cutoff sitting somewhere along a range of values, chosen by a sweep and defensible only within the field it was swept on. Zero is not a parameter. The boundary is fixed by the sign convention of the difference and the conduction physics of the mud, which is why it holds without calibration while the contrast-sensitivity constants around it, the ones that decide how strong a difference has to be to count as an edge at all, still need setting per borehole. The sign says which mineral class; the magnitude constants say whether the reading is trustworthy. Keeping those two jobs separate is the point.
The mud sets the direction
The convention above is written for water-based mud, and it is only half the rule. Swap to oil-based mud and the electrical relationship inverts: the resistive contrast of the pore fluid changes the polarity of the reading, and the feature that was dark becomes the brighter one against its neighbourhood. The mineral look-alike inverts with it. The sign test does not break under this, but it cannot be applied unchanged, because the same physical pore now produces a difference of the opposite sign.
This is the part that makes the sign test a piece of petrophysics rather than a coincidence of one dataset. The direction of the inequality is not a fact about our field; it is a consequence of the mud in the borehole, and it is knowable in advance from the mud type on the header rather than fitted from the data. An interpreter reading the catalogue can check it against first principles: water-based, conductive pore, dark, negative difference. That chain is auditable end to end, and every rejection the test makes points to a specific reason a reader can verify, which is precisely what a magnitude threshold could never offer.
The instrument
The reader above is a single candidate at the contrast test. Its interior sits at one intensity, its vicinity at another, and the mean-difference between them is a point on the number line. Slide that point across zero and the verdict flips, because the sign is the verdict. The orange element is the boundary at a mean-difference of zero, the one line in the whole gate that is a claim about mineralogy rather than a calibrated dial. Toggle the mud type and the two mineral populations trade sides of the boundary, exactly as the physics of the borehole fluid demands. The magnitude, shown as distance from zero, is the same for a pore and its look-alike; only the side they fall on differs.
Where the sign stops being safe
The sign test is narrow on purpose, and its assumptions are its limits. It reads a mean intensity inside against a mean intensity outside, which presumes the vicinity ring is representative rock. In a densely vugular or heavily fractured interval the ring is itself full of anomalies, the vicinity mean drifts toward the interior mean, and a difference that should be clearly negative sits near zero where a little noise can push it the wrong way. The test is most reliable exactly where pores are sparse and most fragile where they crowd.
It also assumes a clean two-class world: conductive pore against resistive mineral. A patch that is genuinely ambiguous in polarity, a partially cemented pore or a mineralised pore margin, produces a difference near zero that the sign cannot confidently place, and near the boundary the test degrades gracefully rather than failing loudly, which means an interpreter should treat small-magnitude negatives as candidates for a second look rather than confirmed pores. And the whole reading inherits the roughly three-centimetre depth uncertainty of the image-log raster, so the sign improves which patches are kept, not the precision with which any one is placed. None of this argues against the sign. It argues for stating, next to every kept contour, how far from zero its difference sat, so a reader can see which rejections and acceptances were decisive and which were close.
Limitations
The sign convention is specific to water-based mud; the oil-based inversion is documented but was not separately validated here, so a catalogue built under oil-based mud must flip the inequality before it is trusted. The mean-difference assumes a representative vicinity, so its reliability falls in intervals where the neighbourhood is itself anomalous. The test discriminates two polarity classes and cannot resolve a genuinely intermediate patch, whose near-zero difference should be flagged rather than forced to a side. The contrast-sensitivity constants that decide whether a difference is large enough to count as a real edge remain per-borehole settings and are not universal. And the result rests on a single confidential internal source, with no external corroboration cited here; the sign convention and the numbers behind it are reproduced from that source under confidentiality, and the piece should be read as one operator's validated practice rather than an independently replicated finding.
References
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Vug-quantification manuscript and reviewer-response letters (the absolute-difference change map flagged for admitting opposite-polarity minerals; the fix stated as a sign check on the mean-difference, interior mean minus vicinity mean, with the rule that under water-based mud a negative mean-difference marks a conductive dissolution pore and a non-negative one marks an opposite-polarity mineral to be discarded, and the symmetric oil-based-mud logic documented; bounding-box expansion of ten percent per side; the mean-based contrast constants established per borehole from one or two representative sections) derived from internal work on a Middle East carbonate dataset logged with two microresistivity imaging tools; data and code withheld under operator confidentiality. This is the single source for the sign convention and its numbers; no external corroboration is cited, which is a deliberate constraint of the confidentiality terms rather than an omission.
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Companion piece on the two shape screens that precede the sign test, the circularity band and the area window: Killing Vug False Positives: The Circularity-and-Area Gate. Parameter-level mechanics of the classical-CV detector: Adaptive Thresholding for Vugs: The Eight Parameters of a Classical-CV Detector.
