Several rocks, one amplitude

The trace on the left is the measurement, and it is the only information available. There is no well, no log, and nothing to say what is down there. It shows a strong trough at the top of something, which is what an interpreter would call a bright spot.

The controls above build a candidate rock, and the trace on the right is what that rock would produce. Moving the sliders until the two traces agree gives one match. The bar underneath shows how close the two are, with the tolerance set by the noise on the measurement.

Then keep going. After one match there is another, and it is a genuinely different rock — different porosity, different fluid, different saturation. The Show me another match button finds them, and it keeps finding them, because there are thousands. That is the subject of this module.

Take the first two unknowns together. The picture on the left repays a moment before anything is read into it, because the same kind of picture is used in the next two steps as well.

How to read it. It is a parameter space rather than a map of the ground. Every single point in it is a different rock: its position across is how much gas that rock holds, its position up the side is its porosity, and its color is the seismic amplitude it would produce — blue for a peak, red for a trough, white for nothing at all. The rocks that produce the measured amplitude lie in that field, and the black line runs through all of them. The small circle is the rock currently on the sliders.

So the black line is the answer to "what could this be", drawn all at once. Every point on it fits the measurement exactly as well as every other point. The panel beside it takes three rocks off that line and writes them out in full, with the trace each one produces, which are indistinguishable.

Read the three cards. A rock at 30% porosity full of gas, and a rock at 34% porosity with a tenth as much gas in it, sit on the same line and give the same trace. One is a discovery. The other is a wet sand with a trace of residual gas, and drilling it would be a dry hole.

The line is nearly flat over most of its length, which is the fizz-gas result from module 02 seen from the other side. Because the first few percent of gas does most of the work, almost the entire saturation axis maps into a narrow band of amplitude, and the contour has to run almost horizontally to stay inside it.

A reflection coefficient is a contrast between two rocks, so half of every amplitude belongs to the unit above. In module 03, changing the shale alone moved the reflection through zero and out the other side, with the reservoir untouched. Here it works in reverse: because the shale is not known exactly, a whole range of reservoirs becomes admissible.

Same picture as before, with the shale velocity along the bottom this time instead of saturation. Every point is still one rock, the color is still the amplitude it would produce, and the black line still runs through the ones that match the measurement. Along that line, a slow shale requires a soft, porous reservoir to produce the contrast, and a fast shale reaches the same contrast with a much tighter one. The reported porosity therefore depends on a property of a rock nobody set out to measure. The two cards beside it are the rocks at each end of that line.

This is the argument for using an interval that brackets the seal in any inversion, and the reason a nearby well that penetrated only the overburden is still worth a great deal. It constrains the half of the reflection that has nothing to do with the reservoir.

The picture on the left works exactly as it did in the last two steps: every point is a rock, now at a different thickness as well as a different porosity, colored by the amplitude it would give, with the black line through the ones that match.

The wedge module in the resolution set showed that below about a quarter wavelength the top and base reflections interfere and the measured amplitude runs above the reflection coefficient — by up to 45% for this wavelet. Running that backwards, a thin reservoir needs a weaker reflection coefficient to reach the same measured amplitude, and a weaker reflection coefficient means a stiffer, tighter rock.

So thickness and reservoir quality trade off against each other, and the trade is asymmetric in a way that matters. Below tuning, a thinner reservoir needs a tighter rock, so the measurement does set a lower bound on thickness. Above tuning the factor is exactly one and stays there, so every greater thickness produces an identical amplitude. The measurement puts no upper bound on thickness whatsoever. The two traces on the right are the thinnest and the thickest reservoirs on this panel that fit, and the second of those is only the end of the slider.

This is where amplitude-derived volumetrics go wrong. A bright amplitude gets read as a good reservoir, when part of the brightness was thickness all along — and the part that was thickness pushes the estimate in the opposite direction from the part that was quality. Below tuning, brighter means thinner.

The three previous steps each held everything but two parameters fixed. Now let all of them vary at once. The page sweeps every combination of porosity, clay content, fluid, saturation, shale velocity and thickness on the grid described in the Method tab, and keeps the ones whose amplitude matches the measurement within the tolerance.

Outside information enters next. Each switch below fixes one parameter at the value on the sliders, as though a well or a nearby measurement had established it. The count collapses, and one unknown does not collapse with it.

Non-uniqueness is not an argument against using amplitudes. It is an argument for using them a particular way, and the difference shows up in how a prospect is described.

• Report a range, not a value. An inversion returns one number per sample because it was asked for one. The set of models consistent with the data is what step 5 draws, and a porosity quoted without its admissible range has thrown away the part a decision depends on.
• Spend money where it narrows the set. Step 5 puts a number on what each piece of outside information is worth. Knowing the shale removes nine tenths of the solutions here. Nothing learned about the other parameters narrows the saturation, because the amplitude never carried that information in the first place.
• Test the alternatives as well as the preferred model. The useful question is not whether a model fits. It is which other models also fit, and whether any of them would change the decision. A model that fits is evidence in proportion to how many alternatives it excludes.
• Be specific about which ambiguity is present. "The amplitude is ambiguous" is not actionable. "This amplitude is consistent with 30% porosity at full gas saturation and with 34% porosity at 10% saturation, and seismic alone cannot separate those two" tells a drilling engineer exactly what the risk is.

The error this module is built against is the confident single answer. A forward model that reproduces the observed amplitude looks like a result, and searching for the alternatives takes longer than finding the first fit. The first fit is the start of the analysis rather than the end of it.

A second, subtler problem is that the size of the solution set depends on the parameter ranges allowed. Widen the shale range and more reservoirs become admissible; forbid low saturations and the fizz-gas ambiguity disappears by assumption rather than by evidence. Those ranges encode real geological knowledge and belong in the analysis, but they have to be stated, because a solution set means nothing without the parameter space it was searched in.

The forward model is modules 01 to 03's, unchanged: Voigt-Reuss-Hill mineral mixing, a Dvorkin-Nur soft-sand dry frame at 40% critical porosity and 23 MPa, Batzle-Wang fluids mixed by the Reuss average, Gassmann for the saturated modulus, and Castagna-Gardner for the bounding shale. Module 01's Method tab lists the assumptions in those steps and they all apply here. This module adds only the search.

The measurement. The observed amplitude is generated from a clean gas sand at 30% porosity, 45 m thick, under a 2700 m/s shale, with a 30 Hz Ricker. It is drawn noise-free and the noise setting is used only as the match tolerance, so that the counts quoted in the exercises are reproducible. On real data the noise also displaces the measured amplitude itself, which widens the solution set further than anything shown here.

The search grid. Porosity 5–35% in 1% steps, clay 0–30% in 10% steps, fluid brine, oil or gas, hydrocarbon saturation 5–100% in 5% steps, shale velocity 2300–3100 m/s in 100 m/s steps, thickness 10–55 m in 5 m steps. A hydrocarbon at zero saturation is the same rock as brine, so it is counted once rather than three times. That is 457,560 combinations, evaluated on every update.

Tuning is tabulated, not convolved. For a layer whose top and base reflections are equal and opposite, the peak amplitude is the reflection coefficient times a factor that depends only on the product of peak frequency and two-way time across the layer — not on the two separately. That factor is computed once into a table and interpolated, which is what makes a search of that size fast enough to run while a slider moves. The table is checked against directly convolved traces and against the closed form for its maximum, √6/2π ≈ 0.3898, where the layer thickness matches the wavelet's own peak-to-trough separation.

Counts are not probabilities. This is the most important caveat on the page. The survivor count is the number of cells in a hand-chosen grid, under an implicitly uniform weight, that reproduce the measurement. It is not the probability that the reservoir contains gas. Turning it into one would require a prior reflecting what is actually known about the basin, the depositional setting and the trap, and different priors give materially different answers from the same seismic. Read the counts as "this many distinct explanations exist", which is a statement about the measurement, and not as "this is how likely each is", which is a statement about geology that seismic alone cannot make.

Further departures from production practice.

• The wavelet is known exactly, and fixed at 30 Hz. In practice the wavelet is estimated, and errors in its amplitude and phase map straight into amplitude errors that this page treats as zero.
• One amplitude, one interface. Real interpretation uses the character of the whole event, its lateral behavior, its conformance to structure, and the base reflection as well as the top. Each of those is additional information and each shrinks the solution set. The point here is what the single amplitude does and does not carry, not that interpreters have nothing else.
• The two bounding shales are identical, so the base reflection is exactly the negative of the top and the tuning factor is the symmetric one. An asymmetric pair tunes differently and would need the full convolution rather than the table.
• Normal incidence only. Every rock counted here is counted on one number. Module 05 adds the offset dimension, and the interesting question there is which of these ambiguities it removes — the porosity–saturation contour in step 2 suggests it will not remove that one.
• No lateral information, no map. A single trace has no idea whether the anomaly conforms to a structural closure, which in practice is often worth more than the amplitude itself.