Attribute combination: RGB blending and classification

The RGB blend recipe

1. Pick three attributes. The best-known choice is three spectral-decomposition magnitudes, a low, a middle and a high frequency (Partyka et al. 1999; Henderson et al. 2007), but any three attributes you want to compare will do.
2. Scale each to the display. A channel value $a$ becomes a display level by a linear stretch from zero to a clip $c$: $u = \min(1, a/c)$, drawn at level $255\,u$. The clip is usually a high percentile of the values (the 99th, say), so that a few extreme values do not set the scale. Either each channel gets its own clip, or all three share one.
3. Combine. At each pixel, red shows the first channel's level, green the second's, blue the third's. A pixel looks red where the first channel leads, white where all three are near their clips, black where all three are near zero.

The arithmetic is trivial. The choices are not: which attributes, which clip, and whether the channels share a range decide what stands out.

Reading colours: the spectral RGB blend

In a spectral blend each channel is the magnitude of one frequency in a short window around each sample. Over a thin layer the reflections from its top and base interfere, and the spectrum of the pair peaks near the tuning frequency $f \approx V/4h$ for a layer of thickness $h$ and velocity $V$ (Partyka et al. 1999). Thick units brighten the low frequencies, thin ones the high frequencies, so a change of thickness or of layering shows as a change of hue. With the lowest frequency on red and the highest on blue:

• Red says the low frequency leads: thicker layering, or a zone where the high frequencies have been lost (absorption, or a processing effect).
• Green says the middle frequency leads, often near the survey's peak frequency.
• Blue says the high frequency leads: thin layering or sharp interfaces.
• Yellow, cyan and magenta say two channels lead together and the third is weak; white that all three are near their clips; black that all three are weak, as in a quiet interval.

Two cautions come with every one of these readings. First, a hue compares the channels as scaled: with each channel stretched to its own clip, red means "strong for a low frequency", not "more low-frequency energy than high". Second, the hue is a hint about thickness or fluid, never a measurement of it; Henderson et al. (2007) use spectral blends to delineate geological elements, which a well or a geological argument must then identify.

Exercise, the F3 RGB story

1. The figure opens on the time slice at 1000 ms with 15 Hz on red, 30 Hz on green and 60 Hz on blue, each scaled to its own 99th percentile. Dipping bands cross the slice; red leads in 33% of the pixels, green in 50% and blue in 16%; in the remaining 1% the brightest channels tie. Slide the time slice down to 1300 ms: the bands give way to the net of the polygonal faults.
2. Switch the range to one shared. The 60 Hz magnitude averages 2.3 times the 15 Hz magnitude at 1000 ms, so blue now leads in 55% of the pixels and red in 1%. Neither picture is wrong: the shared range compares raw energy, the separate ranges balance the spectrum so each frequency shows where it is strong for itself.
3. Move the clip to 100, the maximum. The few largest values now set each scale and the mean lightness of the blend falls from 61 to 47; drag it to 90 and a tenth of each channel goes flat at full intensity. Plate (c) shows each channel against its clip as you drag.
4. Set the colour vision to deuteranopia. A reader with that red-green deficiency keeps about half of the blend's differences in hue and saturation (51% here); with tritanopia, 37%. The classes do not change, because k-means works on the numbers, not on the colours.
5. Put RMS amplitude on red, discontinuity (one minus coherence) on green and curvature magnitude on blue, at 1300 ms. The polygonal faults stand out as a net of green and yellow lines where coherence drops. Now switch to one shared range: RMS amplitudes in the thousands share a scale with a discontinuity below one, and the green and blue channels go black.

Useful blend recipes besides spectral

The red, green and blue assignment is a convention. Pick the three that answer your question:

• Amplitude, frequency and discontinuity, a general-purpose blend: bright, distinctive reflectors on continuous rock stand out, and faults break the pattern.
• Discontinuity, dip and curvature, the structural blend: faults where coherence drops, folds where curvature rises, tilted ground where dip is high.
• One attribute from three vintages of a time-lapse (4D) survey, where a colour marks what changed between surveys.
• Inversion products (acoustic impedance, $V_P/V_S$, density), the rock-physics blend; a colour means a lithology or fluid only after calibration against wells.

Attributes in different units must each have their own range. One shared range is meaningful only when the three channels are the same kind of number, such as three spectral magnitudes.

Classification: what a class is, and what it is not

A blend leaves the grouping to the eye. Unsupervised classification does it with numbers: each pixel is a point whose coordinates are its attribute values, and a clustering method groups the points (Coléou et al. 2003). The simplest is k-means (MacQueen 1967): choose $k$, place $k$ centroids, give every point to its nearest centroid, move each centroid to the mean of its points, and repeat until nothing changes. The figure seeds it with k-means++ (Arthur and Vassilvitskii 2007) and keeps the best of three seeded starts, so the same settings always give the same classes.

• A class is a region of attribute space around a centroid, plate (d), not a facies. Sand and shale can share a class, and one rock can split across several.
• The classes follow the scaling. k-means minimises distances between scaled values, so a change of clip, of shared or separate ranges, or of attributes moves the boundaries. In practice each attribute is standardised first.
• More classes explain more variance. For the best partition into $k$ classes the share can only rise with $k$, and the figure's k-means follows it: on the F3 slice at 1300 ms five classes hold 58% of it and eight hold 68%. That number cannot choose $k$; geology and wells must.
• The labels are arbitrary. Class 3 is only the third centroid; the figure numbers them from darkest to brightest so the numbering is stable, and colours them as labels, not data.

Crossplotting (Section 5.5) is the supervised cousin: the interpreter draws the region in attribute space, then maps where its points lie. Self-organizing maps and machine-learning classifiers extend the same idea to more attributes than colour can show.

Common pitfalls of multi-attribute display

• A colour hides absolute values. "Green" says the green channel leads, not whether it is at 30% or 95% of its clip. Read magnitudes on the single attributes.
• The scaling is part of the picture. Separate ranges, a shared range and the clip each produce a different image of the same data. Report them with the figure.
• Green carries most of the brightness. Relative luminance weights linear red, green and blue by 0.2126, 0.7152 and 0.0722, so the attribute on green sets most of what looks bright and the attribute on blue contributes little; on the default F3 blend green carries 75% of it. Put the attribute whose fine detail matters most on green.
• Colour-blind readers. About 8% of men and 0.5% of women of northern European descent have a red-green deficiency. It collapses red and green onto one axis, and a blend that separates its attributes mainly by red against green loses much of its information. Check the blend with a simulation (Machado et al. 2009), and give the single attributes alongside it. No assignment of three attributes to red, green and blue is safe for every reader.
• RGB is not perceptually uniform. Equal steps in a channel are not equal steps in what we see, so a blend exaggerates some differences and hides others (Light and Bartlein 2004).
• The blend is only as good as its inputs. A noisy or mis-windowed attribute makes a striking but meaningless blend. Check each input on its own first.