One column of rock, and the trace it produces. Type a thickness, a velocity and a
density into the table, and follow them left to right through five panels until a seismic wiggle comes
out the other end. Every step is on the screen. Change any number and watch which
panels move — and, just as usefully, which ones do not.
A seismic section is not a photograph
A seismic line resembles a photograph of a cliff face, only
blurrier, and it is often read that way. What a trace actually records is different.
A seismic trace is a sum. Every sample on it is the total of
everything arriving at that instant. It responds to the boundaries between rocks rather
than to the rocks themselves, and only where the rocks on either side differ in a particular
property.
This module builds a trace from a rock column in three
steps. Each step is a single line of arithmetic.
The whole chain, in three steps
1 · Velocity × density = impedance. The resistance the
rock offers to being set in motion by a passing wave. It is one number per layer, and it is the only
rock property seismic responds to.
2 · A change in impedance = a reflection. Where two layers meet, the
contrast between them sets how much energy bounces back. Same impedance either side, no echo, no
matter how different the rocks look in core.
3 · Each reflection ⊛ the wavelet, added up = the trace. Every
boundary sends back a copy of the same pulse, scaled and delayed. They overlap, they add, and what
you interpret is the total.
Panels 1 to 5 below are those three steps, in order. Every
later module builds on this chain.
Start from
The wavelet
Display
The earth model
Type in any box. The first layer starts at the surface; the last one continues below the section.
From rock to trace
Read left to right. Every panel shares the same two-way time axis. Panel 4 gives each interface its own lane so you can see the individual wavelets before they are added together.
1 Rock layers
2 Impedance
3 Reflectivity
4 ⊛ One wavelet per interface
5 = Their sum: the trace
Layers / interfaces5 / 4
Dominant frequency30 Hz
Wavelength in the thinnest bed— m
λ/4 there— m
Thinnest bed— m
Strongest reflection—
Verdict—
Try this — and what to watch for
Make a reflection vanish. Pick any interface and nudge the velocity and density of the
layer below until its impedance matches the layer above — watch the RC column hit zero.
The point: it is the fastest way to see that seismic responds to contrast, not to rock
type.
The reflection coefficient goes to zero and the event vanishes, even though the
rock type still changes. Seismic sees impedance contrast, not geology. A sand and a shale with the
same impedance are invisible to each other, and that is why some perfectly real formation tops
have no reflector to pick.
Separate velocity from density. Raise one layer's velocity by 20%, put it back, then
raise its density by 20% instead. The point: it shows why seismic alone cannot tell you
which rock property changed.
Both change impedance and both change the reflection. Seismic cannot tell you
which one did it — that ambiguity is the reason we need well logs, and the reason inversion is
harder than it looks.
Flip a reflection over. Make one layer slower and lighter than the one above it, so its
impedance drops. The point: soft-over-hard and hard-over-soft look opposite on a section,
and mixing them up is the classic well-tie error.
The reflection coefficient goes negative and the event changes color. A soft
layer over a hard one and a hard layer over a soft one produce opposite events. Getting this
backwards is the classic well-tie error.
Watch two reflections merge. Take the thinnest bed down from 40 m to 5 m, and keep an eye
on panels 3, 4 and 5 together.
The two spikes in panel 3 stay separate and keep their full size, because the
rock is still there. In panel 4 their wavelets slide toward each other until they overlap almost
completely, and panel 5 adds them into a single event. Nothing was lost in the rock or in the
reflectivity — it was lost in the addition. That gap between what exists and what you can see is
the whole subject of module 02.
Follow one interface through the chain. Change the density of a single layer and track
lane by lane which wavelet in panel 4 changes size.
Only the lanes for the interfaces at the top and base of that layer respond,
because a reflection coefficient belongs to a boundary and not to a layer. Each lane in panel 4
is the same wavelet every time, scaled by its coefficient and slid to its own time. That is all
convolution is, and panel 5 is just those lanes added across.
Make two wavelets cancel. Find a bed where the top and base coefficients have opposite
signs, then thin it until the two lanes in panel 4 sit almost on top of each other.
One is upside down relative to the other, so where they overlap they subtract.
Thin enough and they nearly erase each other, which is why a very thin bed with strong contrasts
can be almost invisible. Beds whose coefficients share a sign do the opposite and reinforce.
Change the wavelet, not the rock. Leave the table alone and sweep frequency from 15 Hz to
70 Hz. The point: it separates what the earth did from what your data did to it.
Panels 1 to 3 never move, because the earth has not changed. Only the wavelets in
panel 4 get narrower or broader, and the trace follows them. Every argument about what is or is
not resolvable is an argument about the shape in panel 4.
Switch polarity.The whole trace inverts and the color bar reverses with it. Nothing about the
rock changed. Polarity is a convention about how data is displayed, and if you do not know which
one your data uses, you cannot say whether a bright event is a hard streak or a soft one.
If you remember nothing else
Impedance is the only rock property seismic responds to, and only through the contrast at
a boundary. A thick uniform layer returns nothing from its middle.
Reflection coefficients are properties of interfaces, not of layers. They live at the
boundaries and nowhere else.
The wavelet is where resolution is decided. The reflectivity in panel 3 is as sharp as the
geology; the trace is only as sharp as the wavelet.
A trace is a sum, not a picture. Every sample in panel 5 is the total of every wavelet in
panel 4 that reaches it. No single event on a seismic section belongs to one interface alone.
Convolution is a smearing operation, and it is not reversible in practice. Everything you
interpret has been through it once already.
Method, assumptions, and where to read more
Acoustic impedance is velocity times density. At an interface the normal-incidence reflection
coefficient is R = (I₂ − I₁) / (I₂ + I₁), and the two-way time to each interface
accumulates as 2h/V through the layers above it. The trace is the reflectivity
convolved with a zero-phase wavelet, done here as a sum of shifted, scaled wavelets so interface timing
is exact rather than rounded to the sample grid. The first interface is placed at 50 ms so the top
reflection is clear of the start of the display.
This is normal incidence only, so there is no offset, no AVO, and no mode conversion; all three need
the full Zoeppritz equations rather than the single expression above. Also left out: transmission loss
through each interface, internal multiples, attenuation, and geometrical spreading. Each would reduce
deeper amplitudes, and real processing tries to correct for them. The wavelet is zero phase, which is
what processing aims for and rarely achieves exactly.
Sheriff, R.E., and Geldart, L.P., 1995, Exploration Seismology, 2nd ed.: Cambridge University Press.
Simm, R., and Bacon, M., 2014, Seismic Amplitude: An Interpreter's Handbook: Cambridge University Press.
Widess, M.B., 1973, How thin is a thin bed?: Geophysics, 38, 1176–1180.
For anything unfamiliar, the SEG Wiki hosts Sheriff's Encyclopedic Dictionary of Applied
Geophysics free at wiki.seg.org/wiki/Dictionary.
The two reflections from a single bed have stayed well separated here. The next module thins that bed
sideways until they overlap, which is the point where the thickness read from the trace stops
matching the thickness in the model.