Reading inversion products: elastic to rock properties

Why the transform is necessary (and non-trivial)

An inversion cube is numbers in units of Ip (e.g., 7500 m/s·g/cc). A drilling decision requires answers in a DIFFERENT language:

• Where is net sand? (Vsh ≤ 35% AND porosity ≥ 15%)
• Where are hydrocarbons? (Sw ≤ 50%)
• Where is NET PAY? (all three conditions stacked)
• How much hydrocarbon volume? (net pay area × thickness × φ × (1−Sw))

Those questions are answered by the ROCK-PROPERTY cubes, not by Ip. The transform from elastic space to rock-property space is what unlocks the business value of the inversion.

The transform is NON-TRIVIAL because each rock property depends on a DIFFERENT combination of elastic attributes:

• Porosity correlates well with Ip alone (high φ → low Ip in reservoir sands).
• Vsh needs Vp/Vs or Ip+Vp/Vs (shale has high Vp/Vs; sand has lower).
• Sw needs Vp/Vs predominantly (gas drops Vp/Vs, water does not).
• Facies needs the full 2D (Ip, Vp/Vs) position and a classifier.

So the transform is NOT a single formula but a FAMILY of formulas, one per target property. And they’re all calibrated on well data from §7.2.

Exercise — cycle the property modes

• Open the widget in Ip (acoustic impedance) mode. This is the elastic output you got from §7.3’s inversion. You see high-Ip bands (caprock shale at top, middle shale, carbonate floor) and low-Ip bands (the sand reservoirs). The GAS column shows as a slightly lower-Ip blob inside the gas sand unit — but it’s subtle.
• Switch to Vp/Vs. Now the gas column JUMPS OUT — a distinct low-Vp/Vs anomaly (green/warm color) clearly separating the gas-filled upper portion of the gas sand from the brine-filled lower portion. This is why pre-stack inversion is indispensable for fluid work: Vp/Vs isolates the fluid signal in a way Ip cannot.
• Switch to Porosity (φ). Now the reservoir sand units light up as high-φ regions (dark green) while shales drop to low φ. The gas-water contact is NOT visible here — porosity doesn’t care about pore fluid. This product tells you WHERE the reservoir rocks are, not whether they’re hydrocarbon-bearing.
• Switch to Shale volume (Vsh). Clean reservoir sand bodies show as cream-colored (low Vsh); shale caps/middle show as dark brown (high Vsh); carbonate floor is mid-tone (matrix minerals, no clay). Combined with the porosity product, this is the LITHOLOGIC + RESERVOIR-QUALITY picture.
• Switch to Water saturation (Sw). The gas column stands out as red/orange (low Sw = hydrocarbons); the oil sand shows a fainter warm tone; the water sand below GWC is blue (high Sw). The sharp horizontal color transition in the gas sand is the GAS-WATER CONTACT — potentially the most valuable single feature your QI cube can reveal.
• Switch to Facies classification. Now the section becomes discrete colored patches — each voxel is assigned to its single most-likely class. Beautiful map, but the HARD boundaries hide uncertainty. A voxel right on the boundary between classes gets classified one way or the other with equal confidence in the display — which is an interpretive lie. §7.5 fixes that with probabilities.
• Now enable the “Simulate inversion uncertainty” checkbox and set the noise slider to 2×. Cycle through the modes again. Notice: Ip and Vp/Vs get grainy but recognizable. Porosity becomes noisy but the reservoir structure still shows. Vsh blurs — the sand-shale boundary becomes fuzzier. Sw gets significantly worse because it depends sensitively on Vp/Vs and magnifies any noise. Facies becomes a speckled mess because categorical outputs amplify noise at class boundaries.
• This is the KEY insight: the DERIVED rock-property products inherit inversion error, and the AMOUNT of error varies by property. Porosity is most robust (depends on a single attribute, large range). Saturation is least robust (needs both Ip and Vp/Vs, small class separations). Facies is fragile at the class boundaries.

Transform flavors used in industry

Three main families of transform, each with pros and cons:

• Linear multi-attribute regression. Fit a plane (or polynomial) in elastic space: φ = a + b·Ip + c·VpVs + d·Ip·VpVs. Calibrate coefficients on well logs by least-squares. Simple, explainable, robust to moderate noise. Best for properties with a linear relationship to elastic attributes. Default choice unless clearly inadequate.
• Template lookup. Grid the (Ip, VpVs) plane; assign each cell a (φ, Vsh, Sw) value from well-log averages. Apply to each voxel as a 2D lookup. Captures non-linearity naturally but can be unstable in sparsely-sampled cells. Popular for facies classification (where the “template” is really a set of labeled training clusters).
• Neural network / machine learning. Train a multi-layer network on log data: input features (Ip, VpVs, density, depth, time); output (φ, Vsh, Sw, facies). Captures arbitrary non-linearity. Risk: over-fits when training data is sparse; predictions in elastic-space regions that weren’t well-sampled by wells are unreliable. Use with care; always validate on blind wells. Becoming more common; not yet the default.

A robust QI team runs MULTIPLE transforms (linear + NN, say) and compares. Agreement between methods increases trust; disagreement flags regions for extra interpretation.

The reservoir-characterization integration: NET PAY

Once you have φ, Vsh, and Sw cubes, the asset team’s favorite integrated product is NET PAY:

NET PAY VOXEL = (Vsh < V_cut) AND (φ > φ_cut) AND (Sw < Sw_cut)

where the cutoffs (typical values: V_cut = 0.35, φ_cut = 0.10–0.15, Sw_cut = 0.50–0.60) are chosen per basin/reservoir to match what’s economically producible. Summing net-pay voxels across the reservoir gives NET PAY THICKNESS maps, which are the direct input to volume calculations:

STOOIP = Area × Net Pay Thickness × φ̅ × (1 − S̅w) / Bo

(STOOIP = stock-tank original oil in place; φ̅, S̅w = volume-averages over net pay; Bo = formation-volume factor converting reservoir volume to surface volume.)

The net-pay map is what goes on the exploration-manager’s wall and what drives drill decisions. Pretty much every rock-property cube’s business value flows through this integration.

Uncertainty propagation

Inversion errors don’t stay put — they propagate into the rock-property cubes, and some properties are more sensitive than others:

• Porosity depends mostly on Ip, with a large natural range (0–35%) compared to the inversion’s noise level. Relatively robust — a 5% Ip error translates to ≈1 porosity unit.
• Vsh depends on Vp/Vs and Ip. Vp/Vs noise is typically ∼3–5% relative, which translates to ±0.1 Vsh at boundaries. Medium robust.
• Sw depends most sensitively on Vp/Vs and is calibrated over a narrow Vp/Vs range (∼1.6–1.9 for sands). Small Vp/Vs errors can swing Sw by 0.2–0.3. LEAST robust.
• Facies (hard classification) is most fragile at boundaries — voxels near a class boundary flip category with small noise, producing “speckled” areas. This is why §7.5’s probabilistic classification is preferred.

The practical rule: present rock-property maps with ASSOCIATED UNCERTAINTY MAPS, not bare deterministic values. Asset teams interpreting a porosity map without seeing the uncertainty will over-trust the parts that are actually poorly constrained.

Common pitfalls and how to avoid them

• Using global-mean transforms for a heterogeneous reservoir. One linear regression calibrated on the whole section doesn’t capture that the caprock shale has a DIFFERENT Ip–φ relationship from the reservoir sand. Mitigate: calibrate per-facies, or use a sufficiently non-linear transform (NN) that discovers the structure automatically.
• Extrapolating beyond the well coverage. Transforms are reliable only where the elastic attributes fall in the range seen at the calibration wells. A voxel with Ip = 3500 (lower than any well) or Ip = 14000 (higher) is an EXTRAPOLATION and should be flagged/masked. Mitigate: build and display an extrapolation mask with the products.
• Applying oil-calibrated transforms to a gas prospect. If your wells are oil wells and your new prospect is potentially gas, your Sw transform may miss the gas case. Mitigate: use Gassmann to fluid-substitute the well logs to gas before calibrating, and validate with any analog gas wells available.
• Ignoring the LITHOLOGY dependence. Some transforms work for sand but give nonsense for carbonate (or vice versa). Mitigate: classify by facies first, then apply facies-specific porosity/Sw transforms.
• Presenting Sw maps where Vp/Vs is unavailable. If you only have post-stack (acoustic) inversion, you can make a φ map but NOT a reliable Sw map. Some vendors produce Sw maps anyway from Ip alone — these are usually just porosity maps with noise. Reject them. Sw needs Vp/Vs.
• Over-trusting the facies map. Hard facies boundaries in display suggest confident classification; the reality is probabilistic. Always provide BOTH the hard map (for quick reads) AND a confidence map (for honest interpretation). §7.5.