Module 03 · The rock
Modules 01 and 02 built a rock: grains, pore space, a fluid, and the four properties that come out — Vp, Vs, density and the two moduli behind them. None of that is a seismic measurement yet. This module follows the rock the rest of the way to a trace and keeps track of what is lost at each step, because two of the four properties do not arrive and the two that do arrive together.
The reservoir, the shale around it, and the trace they make — every panel on the page is computed from these five controls
Five controls — three for the reservoir, one for the shale, one for the seismic
Five steps, each one a place where something about the rock stops traveling with the signal. Every number quoted in the text is read off the running page.
Everything in modules 01 and 02 was about a single rock. A reflection is not a property of a rock. It happens where one rock meets a different one, and it depends on both of them equally.
So a reservoir needs a neighbor before there is anything to measure. Here it is a shale, above and below, and the shale has its own velocity, its own density and its own shear velocity — none of which depends on the reservoir. Its P-wave velocity is the fourth control on this page, and it will turn out to matter as much as the porosity does.
The two rocks are built differently. The reservoir comes from the grain-pack model of module 01 with a fluid inserted by module 02. The shale comes from an empirical trend, because a contact model between spherical grains does not describe a shale at all. The two rocks on this page are therefore not equally well founded.
1 The section shale, reservoir, shale
2 The four properties of each rock shale against reservoir
A normal-incidence reflection responds to the acoustic impedance of each rock, which is its P-wave velocity multiplied by its density. Two numbers go in and one comes out, and that is a loss, because a product cannot be undone. If two numbers multiply to twelve they might have been three and four, or two and six, or one and a half and eight.
The right-hand panel makes that concrete. It is the plane of all possible velocities and densities, with a curve drawn through every combination that has the same impedance as the reservoir. Every rock on that curve is a different rock, and no normal-incidence measurement distinguishes any of them from any other. A fast light rock and a slow heavy one land on the same point as far as the seismic is concerned.
This is the first of three places where the chain from a rock to an amplitude throws something away. The number of those losses is what makes working backwards from an amplitude hard.
1 Impedance of the two rocks velocity times density
2 Every rock with the reservoir's impedance the velocity-density plane
The reflection coefficient at the top of the reservoir is the difference in impedance across the boundary divided by the sum: R = (I₂ − I₁) / (I₂ + I₁). Two impedances go in and one number comes out, and again something is gone. Double both impedances and R does not move at all. A reflection reports the step and says nothing about the level.
The consequence is easy to miss. The amplitude belongs to the pair of rocks, not to the reservoir. Leave the reservoir completely alone — same porosity, same fluid, same everything — and change only the shale velocity. The reflection changes anyway, and within the range of this one control it passes through zero and changes sign.
The right-hand panel plots that directly: the reflection coefficient at the top of the reservoir as the shale velocity runs across its range, with the reservoir held fixed. The crossing point is where the two rocks happen to have the same impedance and the reflection vanishes entirely, leaving a real reservoir in a real shale with nothing to record it.
A bright amplitude therefore means the two rocks are different. It does not mean the reservoir is unusual, and an interpretation that treats the anomaly as a property of the sand alone has already made a mistake that no later processing recovers from.
1 Impedance through the section and the two reflection coefficients
2 The same reservoir in different shales only the shale is changing
The earth supplies two reflection coefficients, one at each boundary, at two instants in time. A seismic experiment does not record instants. It records a band-limited pulse, once for each reflection, added together — which is the convolution the resolution modules build from scratch.
The step is included here to close the chain rather than to teach it. The frequency control moves the wavelet without touching the rock, and the trace changes anyway. A seismic trace is an observation of the earth rather than the earth itself.
The reservoir is held thick enough that its top and base stay separate at every frequency the control reaches, so nothing on this page tunes. What happens when a bed is too thin for that — and it is a great deal — belongs to the wedge module in the resolution set.
1 What the earth has two spikes
2 What is recorded the same two spikes, convolved with a wavelet
Modules 01 and 02 spent most of their length on the shear response: where it comes from, why a pore fluid leaves it alone, and why that makes a fluid visible. None of it has been used on this page. A normal-incidence reflection coefficient is built from Vp and density and nothing else. Vs appears nowhere in it.
That is not an approximation. At normal incidence the rock is compressed and nothing slides, so there is no shear deformation for the shear modulus to resist, and the shear velocity cannot enter the answer. Two rocks with the same impedance and completely different Vp/Vs produce identical traces.
The left-hand panel finds those rocks. It searches porosity and gas saturation for every combination that gives the reservoir's impedance, and there are many: the same impedance is reached by a high-porosity rock with a little gas and a lower-porosity rock full of it. The right-hand panel shows what those rocks have that the trace does not — a range of Vp/Vs values, all producing the same amplitude.
At the settings this module opens with the search finds sixteen such rocks, running from 2% gas saturation to 100%. Their reflection coefficients span 0.004 and their Vp/Vs values span 1.47 to 1.68 — a difference of about 14% in a rock property, arriving at the measurement as nothing at all.
Two things follow. The saturation ambiguity from module 02 survives into the amplitude, so a normal-incidence bright spot indicates gas without indicating how much. And a property that would separate these rocks exists in them and is not being measured. Getting at it is what the rest of this set does, and it starts with letting the wave arrive at an angle.
1 Rocks with the reservoir's impedance porosity against gas saturation
2 What those rocks differ in Vp/Vs, which the trace never sees
Modelling a prospect before drilling. The forward chain on this page is what a synthetic seismogram is. Build the rock, pair it with its neighbor, take the contrast, apply the wavelet, and compare the result with the real data. Every amplitude study starts here.
Knowing what the shale is doing. Step 3 is the reason a mapped amplitude anomaly can follow a change in the overburden rather than a change in the reservoir. Where the sealing shale varies laterally, the amplitude varies with it, and the resulting map looks like a fluid effect.
Reading an impedance inversion. An inversion recovers impedance, which is further along the chain than velocity and density but still short of the rock. The velocity-density ambiguity in step 2 does not go away because the data were inverted.
Knowing when to ask for more. Step 5 is a statement about what a single stacked amplitude can and cannot contain. When a question depends on Vp/Vs — which fluid questions usually do — a normal-incidence amplitude is not capable of answering it, however good the data are.
Each answer is a number read off this page at the settings described.
The reservoir is the module 01 soft-sand frame with the module 02 fluid put in by Gassmann's relation, at a fixed 23 MPa and 64 °C. Pressure and temperature are not controls here because this module is about what happens after the rock exists; module 02 is where they belong.
The shale is Castagna's mudrock line for Vs and Gardner's relation for density, both driven from the single velocity control. These are empirical trends fitted to data rather than models of a shale, and they are used because a contact model between spherical grains does not describe a shale at all. The two rocks on this page therefore rest on quite different footings, and the shale's Vs in particular should be treated as a plausible value rather than a computed one.
The reflection coefficients are the normal-incidence formula, (I₂ − I₁)/(I₂ + I₁), with impedance as Vp times density. This is exact at zero incidence angle and is the only case this module covers. Everything from module 04 onward is about what happens when the angle is not zero.
The equal-impedance search in step 5 scans porosity from 15% to 38% and gas saturation from 0 to 100%, keeping any rock whose impedance is within 0.5% of the reservoir's. The tolerance is there because the search is on a grid; a finer grid would fill in the curve rather than change it. The family it finds is real, but it is narrow: module 07 runs the same idea across clay content, the shale and the wavelet as well, and finds far more.
Fixed rather than controlled:
Next up
Step 5 ended on a property that exists in the rock and does not reach the trace. Reaching it means recording the reflection at more than one angle. Module 04 covers where the angles come from, why offset is not the same thing as angle, and what a gather is.
Go to module 04 →