Geology Fractional Melting Calculator

Perfect fractional extraction accumulated/instantaneous melts; constant bulkD, distinct from residual-liquid Rayleigh crystal fractionation. 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

Fractional melting removes successive melt increments from a reservoir under a specified partition coefficient.

Fractional melting removes successive melt increments from a reservoir under a specified partition coefficient.^[1]

Instantaneous and accumulated melt concentrations answer different questions and are not interchangeable with batch-melting concentrations. Use this tool to calculate fractional melting from the supplied measurements and assumptions.

When to use Geology Fractional Melting Calculator

Use this tool to calculate fractional melting 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 Fractional Melting Calculator and understand its results

Establish the measurement units, sampled interval, calibration or model edition and geological assumptions before entering data.
Enter initialTrace, bulkPartition, extractedFractions, using the field meanings and rules below, then run the tool.
Read accumulatedMelt, instantaneousMelt. 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
initialTrace	Initial trace	number	Required
bulkPartition	Bulk partition	number	Required
extractedFractions	Extracted fractions	list of number	Required

Require nonnegative initial trace concentration, positive bulk partition coefficient and melt fractions strictly between zero and one. Evaluate accumulated melt with expm1/log1p to reduce cancellation, and instantaneous melt with the residual fractional-melting relation. Return concentrations on the initial concentration basis; fractions 0 and 1 are rejected.

accumulated=−C0×expm1(log1p(−F)/D)/F; instantaneous=C0/D×exp((1/D−1)log1p(−F))

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

Output field	Meaning	Value type
accumulatedMelt	Accumulated Melt; follow the units, sign, ordering and evidence convention stated above	list of number
instantaneousMelt	Instantaneous Melt; follow the units, sign, ordering and evidence convention stated above	list of number

json

{
  "input": {
    "initialTrace": 10,
    "bulkPartition": 0.5,
    "extractedFractions": [
      0.5,
      0.75
    ]
  },
  "output": {
    "accumulatedMelt": [
      15,
      12.5
    ],
    "instantaneousMelt": [
      10,
      5
    ]
  }
}

Limitations and assumptions

Instantaneous and accumulated melt concentrations answer different questions and are not interchangeable with batch-melting concentrations. 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 Batch Melting Calculator for this related task: Batch melting keeps melt and residue in equilibrium under a specified bulk partition coefficient.

Use Geology Mixing Hyperbola Calculator when its separate inputs and assumptions fit the question: Two-endmember isotope mixing weights each isotope ratio by its contributing element concentration.

References

Geology Fractional Melting Calculator — tool.io

Similar or alternative tools

Geology Batch Melting Calculator
Batch melting keeps melt and residue in equilibrium under a specified bulk partition coefficient.
Geology Mixing Hyperbola Calculator
Two-endmember isotope mixing weights each isotope ratio by its contributing element concentration.