Original synthetic study
Two equally good permeability fits with different noisy data
Different noisy core datasets can produce similarly convincing fits but different predictions. Residual size alone does not capture sampling uncertainty or geological representativeness.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Construct two transparent datasets
The study uses a shared log-linear permeability trend and two deterministic perturbation patterns in log10(k). Each observation and perturbation is included in the downloadable table. No random seed or hidden filtering changes the result.
Both fits use the same porosity values and the same log-space least-squares objective, so their differences can be traced to the supplied synthetic noise.
Inspect prediction, not only fit score
Compare fitted slopes and predictions at the low and high ends of the sampled range. Small differences in slope become larger when extrapolated.
A narrow residual spread is not a confidence interval. A defensible uncertainty analysis would need a stated error model, sampling design and treatment of geological populations.
Keep held-out information separate
A sample used in fitting cannot also serve as independent validation. Reserve data or use a documented resampling method when the purpose is prediction assessment.
The site's workflow computes a fitted relationship and diagnostics; this teaching study does not claim it automatically supplies a geological uncertainty model.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Evaluation porosity (%) = 20. Dataset A fitted k (mD): 100; Dataset B fitted k (mD): 100.
- Dataset A fitted k (mD)
- Dataset B fitted k (mD)
Worked example
Two equally close fits with different slopes
Porosity grid 10,15,20,25,30%; generating log10(k/mD) = 0.2φ − 2. Two explicit deterministic perturbation arrays are supplied in JSON.
Relation and unit basis
log10(kA) = -2.08 + 0.204φ; log10(kB) = -1.92 + 0.196φ
Both use unweighted log-space least squares. The residual pattern is shared, while opposite linear perturbations shift the fitted slopes.
1. Define the baseline
Evaluation porosity (%) = 20
Porosity grid 10,15,20,25,30%; generating log10(k/mD) = 0.2φ − 2. Two explicit deterministic perturbation arrays are supplied in JSON.
2. Select the relation
log10(kA) = -2.08 + 0.204φ; log10(kB) = -1.92 + 0.196φ
Both use unweighted log-space least squares. The residual pattern is shared, while opposite linear perturbations shift the fitted slopes.
3. Substitute the values
Fitted slopes A = 0.204, B = 0.196; both predict 100 mD at 20% porosity, with identical log-space residual RMSE but different predictions elsewhere
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Dataset A fitted k (mD) = 100; Dataset B fitted k (mD) = 100
Equal residual RMSE does not imply identical fitted parameters or predictions. These deterministic perturbations are not a probability model.
Result and interpretation
Dataset A fitted k (mD) = 100; Dataset B fitted k (mD) = 100
Equal residual RMSE does not imply identical fitted parameters or predictions. These deterministic perturbations are not a probability model.
Compare the two fitted predictions across the same evaluation porosities. Their source pairs remain available with the dataset.
Study data and reproduction
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Evaluation porosity (%) | Dataset A fitted k (mD) | Dataset B fitted k (mD) |
|---|---|---|
| 10 | 0.9120108 | 1.096478 |
| 15 | 9.549926 | 10.47129 |
| 20 | 100 | 100 |
| 25 | 1,047.129 | 954.9926 |
| 30 | 10,964.78 | 9,120.108 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. Why can two high-scoring fits disagree outside the measured interval?
Show the worked answer
The slope and intercept are uncertain and extrapolation amplifies their differences. A fit score measures agreement on the supplied data.
2. Reproduce the baseline Dataset A fitted k (mD) without rounding intermediate values.
Show the worked answer
Fitted slopes A = 0.204, B = 0.196; both predict 100 mD at 20% porosity, with identical log-space residual RMSE but different predictions elsewhere. Dataset A fitted k (mD) = 100. Equal residual RMSE does not imply identical fitted parameters or predictions. These deterministic perturbations are not a probability model.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Evaluation porosity (%) changes from 10 to 30. Other controls remain as stated in the premise. Dataset A fitted k (mD) changes from 0.912010839 to 10964.782.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Both use unweighted log-space least squares. The residual pattern is shared, while opposite linear perturbations shift the fitted slopes. Equal residual RMSE does not imply identical fitted parameters or predictions. These deterministic perturbations are not a probability model.
Before using the result
- Use identical fitting objectives.
- Retain perturbations and original pairs.
- Separate residual diagnostics from uncertainty estimates.
Equal residual RMSE does not imply identical fitted parameters or predictions. These deterministic perturbations are not a probability model.
Continue learning
Start with the broader workflow guide · Related method guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.