Every other module has assumed a zero-phase wavelet, where the peak sits exactly on the
boundary that produced it. Real data is rarely quite zero phase. Rotate the wavelet here and watch
the event move away from the boundary that produced it while its shape and amplitude stay the same.
Nothing on the section marks the shift.
The zero-phase assumption
Every module before this one used a zero-phase wavelet.
That means its biggest peak sits exactly on the boundary that produced it, so picking the peak is the
same thing as picking the top of the sand.
Zero phase is what processing aims for. It remains an assumption about the
data in hand.
Rotating the phase shifts the pulse in time while
leaving its frequency content unchanged. The event keeps the same sharpness and the same amplitude,
and moves off the boundary.
Why a phase error matters
A phase error becomes a depth error, in the same
direction, on every horizon picked across the whole survey, so it does not average out. At 30 Hz a
90° rotation puts the pick about 6 ms — eight or nine meters — off the boundary.
The section carries no sign of it. There is no loss of sharpness and no
artifact: the horizon looks clean and sits in the wrong place.
A well tie is the measurement of that rotation.
The matching exercise below is the same procedure.
The wavelet
The well
Tie the well
The grey trace is the field seismic, recorded at a phase you cannot see. Rotate your wavelet until
the red line sits centered along the middle of the grey band. Use Trace size if the wiggles
are too small to judge.
Display
The well, and the seismic beside it
Teal marks where the rock actually changes. Crimson marks where you would put the horizon.
1 The well
impedance, and the tops you would log
2 The seismic
synthetic at your phase
3 The wavelet
and where its peak sits
4 How far the pick moves
against phase
Phase rotation0°
Period at peak frequency— ms
Peak sits this far off the boundary— ms
That is this much depth— m
Amplitude at the true boundary—
Nearest trough sits at— ms
Verdict—
Try this — and what to watch for
Start at zero phase and look at panel 2.The point: it is the case everybody draws on the whiteboard, and the one you should confirm rather than assume. Where is the peak relative to the teal line?
Exactly on it. This is the case everyone draws on the whiteboard, and it is the
reason zero phase is what processing aims for: the event and the rock are in the same place, so
picking the peak means picking the top of the sand.
Rotate to 30°, then 60°, then 90°.The point: the error grows steadily and nothing on the display marks it. Watch the readout for how far the peak has moved.
The event moves steadily away from the boundary, reaching about 6 ms by 90°,
which is eight or nine meters of depth at normal velocities. Its shape and amplitude do not
change, and a horizon picked on it carries the whole error.
Stop at exactly 90° and look at the true boundary.The point: 90° data is common, and it is the worst possible case for tying a well.The amplitude there is zero. The boundary sits on a zero crossing with a peak on
one side and a trough on the other, and the two are mirror images, so there is nothing in the
data to tell you which one to pick. Ninety-degree data is the worst case for tying a well, and it
is common, because that is what you get from minimum-phase data that has not been fully
converted.
Go to 180° and compare with the reverse polarity button.The point: these two get confused constantly, and here you can see they are the same operation.They are the same thing. A 180° rotation is a polarity flip, which is why the two
get confused so often. Anything between 0 and 180 is a partial flip, and there is no name for
it — only a number.
Switch the well to the thin sand.The point: it stacks this module on top of module 02, which is what real reservoirs do to you.Now two problems compound. Tuning has already merged the top and base into one
event, and phase then moves that merged event off both boundaries. Working out where the sand
really is from the seismic alone becomes impossible, which is precisely why thin reservoirs need
well control.
Then tie a well properly.The point: this is the actual job, and the reveal tells you what your error would have cost in meters. Turn on the matching game and rotate until the two traces sit on
top of each other.
This is what a well tie is: finding the rotation that makes the synthetic and the
seismic agree. Get it right and every horizon you pick is in the right place. Get it wrong by 40°
and every depth you post is wrong by the same few meters, consistently, across the whole
survey.
If you remember nothing else
Zero phase means the peak is on the boundary. That is the whole point of it, and it is an
assumption you should check rather than inherit.
Phase error becomes depth error, systematically and in the same direction everywhere. It
does not average out across a survey.
At 90° the boundary is a zero crossing, with a peak and a trough on either side and no way
to choose between them from the amplitude.
180° of phase and reversed polarity are the same operation. Knowing which convention your
data uses is the first question, not a detail.
A well tie is a phase measurement. That is what it is for, and it is why an untied survey
cannot give you reliable depths no matter how good the imaging.
Method, assumptions, and where to read more
Phase rotation is done exactly, in the frequency domain: the wavelet is transformed, positive
frequencies are multiplied by e−iφ and negative ones by the conjugate, and it is transformed
back. That is equivalent to w·cos φ − H{w}·sin φ, where H is the Hilbert
transform. It is checked against the cases with known answers — a 0° rotation reproduces the wavelet,
180° negates it, and 90° comes out antisymmetric to within rounding.
The well is a stack of layers with impedances, exactly as in module 01, and the synthetic is the
reflection coefficients convolved with the rotated wavelet. The pick shift quoted is the time of the
largest positive lobe of the rotated wavelet, which is where an interpreter tracking a peak would put
the horizon. Depth error uses the velocity you set, as V·Δt/2.
Left out: phase that varies with frequency, which is what most real data actually has and which no
single rotation can fix; phase drift with depth as the earth absorbs high frequencies; the stretch and
squeeze part of a real tie; and the fact that the sonic log itself needs correcting before any of this
works. The single constant rotation used here is the easy case.
White, R., and Simm, R., 2003, Tutorial: Good practice in well ties: First Break, 21, 75–83.
Simm, R., and Bacon, M., 2014, Seismic Amplitude: An Interpreter's Handbook: Cambridge.
Brown, A.R., 2011, Interpretation of Three-Dimensional Seismic Data, 7th ed.:
AAPG Memoir 42 / SEG Investigations in Geophysics No. 9.
For anything unfamiliar, the SEG Wiki hosts Sheriff's Encyclopedic Dictionary of Applied
Geophysics free at wiki.seg.org/wiki/Dictionary.
That is the whole set
Nine modules, one idea
Seismic does not show you rock. It shows you rock convolved with a wavelet, and that wavelet decides
which beds you resolve, which faults you map, how big a feature has to be to survive, whether a bright
spot means fluid or thickness, and whether your horizon sits on the boundary at all. Every limit you
have met is some fraction of one wavelength — and the wavelength is V / f, which
you can work out for your own target in about ten seconds.
Before relying on anything mapped from a section, work out λ/4 at that depth, in that rock, with
that bandwidth, and compare it with the size of the feature in question.