Fragmentation Index Percent

Measure fine-fragment mass share at an explicit phi sieve boundary; higher phi means smaller clasts, and the result is a grain-size proxy rather than magma fragmentation efficiency.

Description

The phi grain-size scale increases as particles become finer.

The phi grain-size scale increases as particles become finer. A measured sieve edge separates fine and coarse mass without assigning fractions within a bin.

Measure fine-fragment mass share at an explicit phi sieve boundary; higher phi means smaller clasts, and the result is a grain-size proxy rather than magma fragmentation efficiency.

When to use Fragmentation Index Percent

Use this tool to measure fine-fragment mass share at an explicit phi sieve boundary; higher phi means smaller clasts, and the result is a grain-size proxy rather than magma fragmentation efficiency.

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.

How to use Fragmentation Index Percent and understand its results

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
Enter phiBinBoundaries, sizeBinMassesGrams, fineBoundaryPhi using the field table and calculation rules, then run the tool.
Read fineFragmentMassPercent, coarseFragmentMassPercent. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
phiBinBoundaries	Phi bin boundaries	list of number	Required
sizeBinMassesGrams	Size bin masses grams	list of number	Required
fineBoundaryPhi	Fine boundary phi	number	Required

Align increasing bin boundaries with nonnegative bin masses. Require the fine boundary to be an existing edge and total mass positive. Sum fine mass by the lower phi edge and return its complement.^[1]

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

fine percent = 100 × mass in bins beginning at or above boundary phi/total mass

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
fineFragmentMassPercent	Fine fragment mass percent	number
coarseFragmentMassPercent	Coarse fragment mass percent	number

json

{
  "input": {
    "phiBinBoundaries": [
      -2,
      0,
      2,
      4
    ],
    "sizeBinMassesGrams": [
      10,
      20,
      70
    ],
    "fineBoundaryPhi": 2
  },
  "output": {
    "fineFragmentMassPercent": 70,
    "coarseFragmentMassPercent": 30
  }
}

Limitations and assumptions

This is a size-distribution proxy, not magma-fragmentation efficiency.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Juvenile Lithic Proportion Percent: Pool observed juvenile/lithic clast counts using a classified denominator and retain unclassified coverage separately; count proportions are not mass or volume proportions. For a complementary task, use Tephra Volume Weibull Integration: Integrate axisymmetric Weibull-form radial tephra thickness to a supplied truncation radius by bounded Simpson quadrature; caller panels control approximation and no infinite-tail volume or mapped dispersal is inferred.

References

Fragmentation Index Percent — tool.io

Similar or alternative tools

Juvenile Lithic Proportion Percent
Pool observed juvenile/lithic clast counts using a classified denominator and retain unclassified coverage separately; count proportions are not mass or volume proportions.
Tephra Volume Weibull Integration
Integrate axisymmetric Weibull-form radial tephra thickness to a supplied truncation radius by bounded Simpson quadrature; caller panels control approximation and no infinite-tail volume or mapped dispersal is inferred.