Amplitude attributes: RMS, envelope, and their friends

What is a seismic attribute?

A seismic attribute is any quantity computed from the seismic data that highlights a property of interest. Common categories:

• Amplitude attributes — RMS, envelope, magnitude, variance. Measure how much energy is at each location. (This section.)
• Frequency attributes — spectral decomposition, dominant frequency, bandwidth. Measure the colour of the wavelet at each location. Useful for thin-bed detection and lithology discrimination. (§6.2.)
• Geometric attributes — dip, azimuth, curvature. Describe reflector orientation and shape. (§6.3.)
• Coherence / discontinuity — similarity-based measures that highlight where reflectors break continuity (faults, channels). (§6.4.)
• Combined / classified attributes — meta-attributes built from the others. (§6.5.)

Critically: attributes are DERIVED from the seismic. They add no physical information the data didn’t already contain. What they add is VISIBILITY — they make certain properties easier for the human eye to recognize, or easier for downstream algorithms to classify. A good attribute surfaces something the interpreter cares about; a bad attribute manufactures features that aren’t there.

The simplest attribute: |amplitude|

Take the absolute value of each sample. Positive peaks and negative troughs both become positive spikes. This single transformation makes the STRENGTH of reflectors visually obvious — where is the loudest energy? — without the polarity distinction that a zero-centred palette enforces.

Useful when you want a first map of where the data has “mass”, independent of polarity. Nearly every other amplitude attribute is a variation on this theme.

RMS amplitude

Root-mean-square amplitude computed over a sliding time window is the workhorse of amplitude attributes. At each sample:

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where the window is $W$ samples wide and the sum runs over all samples in that window. RMS is always non-negative and approximates the “typical” amplitude magnitude near time $t$.

Two parameters matter:

• Window length. Short windows (5–10 samples) localize strongly — you see the amplitude of individual reflectors. Long windows (20–40 samples) smooth over multiple reflectors — you see interval-averaged amplitude trends. The right choice depends on what you're studying. Reservoir characterization usually uses windows tuned to a specific zone (say, a 30 ms window centred on a target horizon). Regional amplitude mapping might use 60–100 ms windows to highlight systematic trends.
• Window position. Centred windows (as shown above) produce RMS at each time sample by looking symmetrically around it. “Horizon-based” RMS windows are positioned RELATIVE to an interpreted horizon (“10 ms above to 20 ms below the horizon”), which is what most reservoir workflows use.

Envelope (instantaneous amplitude)

The envelope is the magnitude of the analytic signal. Mathematically it is the square root of the sum of squares of the seismic trace and its Hilbert transform. Conceptually, it is the smooth curve that bounds the oscillations of a trace from above — the amplitude envelope of the wavelet at every instant.

Envelope is useful because it is NOT wavelet-phase-dependent. RMS and peak-amplitude attributes depend on whether the reflector shows as a peak or a trough at the sample you are measuring. Envelope gives the same value regardless, because it captures the amplitude of the wavelet as a whole, not one sample of it. For reservoir characterization that compares amplitude across different phases or different datasets, envelope is often preferred.

The widget below approximates envelope as a short-window low-pass filter applied to |amplitude|. That approximation matches the true analytic envelope closely enough for teaching (and for many production uses), without needing an FFT in the browser.

Exercise

• The default view shows RMS amplitude with a 12-sample window next to the raw seismic. Notice how the bright reflectors in the raw view appear as hot zones in the RMS display, but without the polarity alternation — same signal, monotonic representation.
• Change the attribute to Magnitude. Compare to RMS. Magnitude is RMS with window 1 (so no smoothing); you see individual sample-level detail that RMS averages out.
• Change to Envelope (smooth) with window 7. The result is similar to RMS but smoother — the envelope captures the wavelet's amplitude as a coherent unit without sample-level fluctuations.
• Go back to RMS and slide the window slider up to 30. Watch the attribute transition from reflector-level detail to zone-averaged trends. The loud zones stay visible; the fine detail blurs out.
• Change the palette from Hot to Grayscale and back. Both are valid for amplitude attributes (always non-negative), but Hot gives a clearer visual hierarchy — brighter zones stand out more against the dark background.

Common amplitude-attribute pitfalls

• Gain dependence. RMS values are absolute; they depend on the processing's gain choices. A different processing vintage of the same survey will have different RMS values at every location. Never compare RMS between datasets without normalization.
• Tuning effects. At the tuning thickness (λ/4), amplitude is enhanced by constructive interference. A bright spot on RMS could be a thin-bed tuning artifact rather than a real high-impedance reflector. §1.7's tuning widget demonstrates this effect directly.
• Attenuation variation. Deep zones have lower RMS than shallow zones simply because high frequencies attenuate with depth. If you're looking at a deep target, normalize against the surrounding interval or use Q-compensated processing.
• Edge effects. RMS at the top and bottom of the data window uses incomplete windows. Values near trace boundaries are typically lower and should not be interpreted as genuine amplitude weakness.

When to use which amplitude attribute

• Magnitude — scanning a volume for the loudest individual events. Fast, no parameters.
• RMS (short window, 8–15 samples) — highlighting reflector-scale brightness variations. Standard first-pass amplitude map.
• RMS (long window, 40–100 samples) — interval-averaged amplitude. Good for regional trends, overview maps, and separating bright zones from quiet zones at basin scale.
• Envelope — phase-independent amplitude. Preferred when comparing across datasets with different phase characteristics, or when you want to avoid the “fake brightness” caused by phase-rotation artifacts.
• Variance — amplitude statistical scatter. Less common than RMS but useful for chaotic-zone detection where “how much the amplitude varies” matters more than “how big the amplitude is.”