Envelope

A seismic attribute. A phase-independent representation of amplitude, sometimes called instantaneous amplitude or reflection strength.

Simple model
There are 8 layers in this simple blocky earth model. You might say that there are only 7 important pieces of information for this cartoon earth; the 7 reflectivity contrasts at the layer boundaries.

The seismic traces however, have more information than that. On the zero phase trace, there are 21 extrema (peaks / troughs). Worse yet, on the phase rotated trace there are 28. So somehow, the process of wave propagation has embedded more information than we need. Actually, in that case, maybe we shouldn't call it information: it's noise.

It can be hard to tell what is real and what is side lobe and soon, you are assigning geological significance to noise. A literal interpretation of the peaks and troughs would produce far more layers than there actually are. If you interpret every extreme as being matched with a boundary, you would be wrong.

Consider the envelope. The envelope has extrema positioned exactly at each boundary, and perhaps more importantly, it literally envelopes (I enunciate it differently here for drama) the part of the waveform associated with that reflection. 7 boundaries, 7 bumps on the envelope, correctly positioned in the time domain.

Notice how the envelope encompasses all phase rotations from 0 to 360 degrees; it's phase invariant. Does this make it more robust? But it's so broad! Are we losing precision or accuracy by accompanying our trace with it's envelope? What does vertical resolution really mean anyway?

Does this mean that every time there is an envelope maximum, I can expect a true layer boundary? I for one, don't know if this is fool proof in the face of interfering wavelets, but it has implications for how we work as seismic interpreters.

Real data example
This seismic profile offshore Netherlands (the Open Seismic Repository's F3 dataset) is shown three ways to illustrate the relationship between amplitude and envelope.

The first panel consists of seismic amplitude values, the second panel is the envelope, and the third panel is a combination of the two (co-rendered with transparency). We have given them different color scales because amplitude values oscillate about zero and envelope values are always positive.

The envelope might be helpful in this case for simplifying the geology at the base of the clinoforms, but doesn't seem to provide any detail along the high relief slopes.

It also enhances the bright spot in the toesets of the clinoforms, but, more subtly, it suggests that there are 3 key interfaces, out of a series of about 10 peaks and troughs. Used in this way, it may help the interpreter decide which reflections are important, and which reflections are noise (sidelobe).

Another utility of envelope is that it is independent of phase. If the maximum on the envelope does not correspond to a peak or trough on the seismic amplitudes, the seismic amplitudes may not be zero phase. In environments where phase is wandering, either pre-stack or post-stack domain, the envelope attribute is a handy accompaniment to constrain reflection picking or AVO analyses: envelope vs offset, or EVO. It also makes me wonder if adding envelopes to the modeling of synthetic seismiograms might yield better well ties?