E is for Envelope

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 interferring wavelets, but it has implications for how we work as seismic interpreters. Tomorrow we'll take a look at the envelope attribute in the context of real data.