Geology Pb Pb Isochron Calculator
Fit actual Pb–Pb isotope array then invert independently verified radiogenic slope/age curve (same U isotope ratio/decay constants); no log1p applied to Pb–Pb slope. Caller independently establishes matching units, evidence, method edition and applicability; output is not compliance, diagnosis, work-safety approval, geological identity or validated hazard prediction.
Description
A lead–lead isochron supplies a fitted isotope-ratio slope for comparison with an independently established age relation.
A lead–lead isochron supplies a fitted isotope-ratio slope for comparison with an independently established age relation.1
Multiple slope–age intersections can remain possible when the supplied reference is nonmonotonic. Use this tool to calculate pb pb isochron from the supplied measurements and assumptions.
When to use Geology Pb Pb Isochron Calculator
Use this tool to calculate pb pb isochron from the supplied measurements and assumptions. Establish the measurement units, sampled interval, calibration or model edition and geological assumptions before entering data.
How to use Geology Pb Pb Isochron Calculator and understand its results
- Establish the measurement units, sampled interval, calibration or model edition and geological assumptions before entering data.
- Enter pb206Pb204, pb207Pb204, candidateAges, callerConcordantRadiogenicSlopes, using the field meanings and rules below, then run the tool.
- Read fittedPbSlope, matchedCandidateAges, fitRSquared. Interpret the fields using their units, signs and evidence conventions below.
- If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| pb206Pb204 | Pb206 pb204 | list of number | Required |
| pb207Pb204 | Pb207 pb204 | list of number | Required |
| candidateAges | Candidate ages | list of number | Required |
| callerConcordantRadiogenicSlopes | Caller concordant radiogenic slopes | list of number | Required |
Fit the two aligned isotope-ratio lists by ordinary least squares, requiring at least two points and varying predictor values. Enter strictly increasing candidate ages with aligned radiogenic reference slopes. Return the fitted slope, every piecewise-linear reference crossing of that slope and R²; no crossing is a successful empty candidate list.
candidateAges=crossings(referenceAges,referenceSlopes,fittedSlope) Use the exact units, boundary rules, ordering and missing-evidence conventions above.
| Output field | Meaning | Value type |
|---|---|---|
| fittedPbSlope | Fitted Pb Slope; follow the units, sign, ordering and evidence convention stated above | number |
| matchedCandidateAges | Matched Candidate Ages; follow the units, sign, ordering and evidence convention stated above | list of number |
| fitRSquared | Fit R Squared; follow the units, sign, ordering and evidence convention stated above | number |
{
"input": {
"pb206Pb204": [
1,
2,
3
],
"pb207Pb204": [
2,
4,
6
],
"candidateAges": [
0,
1,
2
],
"callerConcordantRadiogenicSlopes": [
1,
2,
4
]
},
"output": {
"fittedPbSlope": 2,
"matchedCandidateAges": [
1
],
"fitRSquared": 1
}
}Limitations and assumptions
Multiple slope–age intersections can remain possible when the supplied reference is nonmonotonic. Interpretation depends on the units, sampling scope and exact model described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.
Alternative or Complementary methods
Use Geology U Th Disequilibrium Age Calculator for this related task: An activity-ratio age interpretation depends on a specified uranium–thorium evolution curve.
Use Geology U Pb Discordia Upper Intercept Calculator when its separate inputs and assumptions fit the question: A discordia line summarizes paired uranium–lead ratio observations in a chosen coordinate system.
References
-
Geology Pb Pb Isochron Calculator — tool.io
Similar or alternative tools
- Geology U Th Disequilibrium Age Calculator
An activity-ratio age interpretation depends on a specified uranium–thorium evolution curve.
- Geology U Pb Discordia Upper Intercept Calculator
A discordia line summarizes paired uranium–lead ratio observations in a chosen coordinate system.