Geology U Pb Discordia Upper Intercept Calculator

Actual discordia regression intersected with independently matched piecewise-linear concordia, all witnesses and upper observed intercept retained; not extrapolated older geological event. 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 discordia line summarizes paired uranium–lead ratio observations in a chosen coordinate system.

A discordia line summarizes paired uranium–lead ratio observations in a chosen coordinate system.^[1]

Its intersections with an independently supplied concordia curve are conditional age candidates, with the upper intercept being the largest returned age. Use this tool to calculate u pb discordia upper intercept from the supplied measurements and assumptions.

When to use Geology U Pb Discordia Upper Intercept Calculator

Use this tool to calculate u pb discordia upper intercept 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 U Pb Discordia Upper Intercept Calculator and understand its results

Establish the measurement units, sampled interval, calibration or model edition and geological assumptions before entering data.
Enter measuredPb206U238, measuredPb207U235, callerConcordiaAges, callerConcordiaX, callerConcordiaY, using the field meanings and rules below, then run the tool.
Read upperObservedInterceptAge, allObservedInterceptAges. 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
measuredPb206U238	Measured pb206 u238	list of number	Required
measuredPb207U235	Measured pb207 u235	list of number	Required
callerConcordiaAges	Caller concordia ages	list of number	Required
callerConcordiaX	Caller concordia x	list of number	Required
callerConcordiaY	Caller concordia y	list of number	Required

Fit ordinary least squares to at least two aligned measured x/y isotope ratios with nonzero predictor variance. Enter aligned strictly increasing candidate ages and corresponding concordia x/y coordinates. Subtract the fitted line from concordia y, find every zero of that piecewise-linear residual curve and require at least one match. Return all ages plus their maximum as the upper intercept; flat zero segments contribute sampled knots. No analytical covariance weighting or concordia construction is provided.

line_y=intercept+slope×x; residual_j=concordiaY_j−line_y(concordiaX_j); upperAge=max(zeroCrossings(age,residual))

Use the exact units, boundary rules, ordering and missing-evidence conventions above.

Output field	Meaning	Value type
upperObservedInterceptAge	Upper Observed Intercept Age; follow the units, sign, ordering and evidence convention stated above	number
allObservedInterceptAges	All Observed Intercept Ages; follow the units, sign, ordering and evidence convention stated above	list of number

json

{
  "input": {
    "measuredPb206U238": [
      1,
      2,
      3
    ],
    "measuredPb207U235": [
      2,
      4,
      6
    ],
    "callerConcordiaAges": [
      0,
      1,
      2,
      3
    ],
    "callerConcordiaX": [
      0,
      1,
      2,
      3
    ],
    "callerConcordiaY": [
      1,
      2,
      3,
      7
    ]
  },
  "output": {
    "upperObservedInterceptAge": 2.5,
    "allObservedInterceptAges": [
      1,
      2.5
    ]
  }
}

Limitations and assumptions

Its intersections with an independently supplied concordia curve are conditional age candidates, with the upper intercept being the largest returned age. 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 Pb Pb Isochron Calculator for this related task: A lead–lead isochron supplies a fitted isotope-ratio slope for comparison with an independently established age relation.

Use Geology Re Os Isochron Age Calculator when its separate inputs and assumptions fit the question: A rhenium–osmium isochron estimates an initial ratio and age from paired isotope ratios under a shared-system model.

References

Geology U Pb Discordia Upper Intercept Calculator — tool.io

Similar or alternative tools

Geology Pb Pb Isochron Calculator
A lead–lead isochron supplies a fitted isotope-ratio slope for comparison with an independently established age relation.
Geology Re Os Isochron Age Calculator
A rhenium–osmium isochron estimates an initial ratio and age from paired isotope ratios under a shared-system model.