Sediment Grain Phi Bin Width Tool

Description

lowerPhi = -log2(coarse diameter); upperPhi = -log2(fine diameter); phiWidth = log2(coarse/fine); densityPerPhi = count/(total*phiWidth).

Spatial and grain-size summaries depend on area, bin width, scale and boundary conventions. Area-weighted coverage differs from pixel counts, while density per transformed grain-size unit differs from a raw bin fraction.

lowerPhi = -log2(coarse diameter); upperPhi = -log2(fine diameter); phiWidth = log2(coarse/fine); densityPerPhi = count/(total*phiWidth).

When to use this tool

Use Sediment Grain Phi Bin Width when checking a supplied spatial, grain-bin or ground-support quantity.

How to use the tool and how it works

Enter coarseDiameterMm, fineDiameterMm, count, total. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read lowerPhi, upperPhi, phiWidth, densityPerPhi. Use the output convention below.

Require positive fineDiameterMm and coarseDiameterMm > fineDiameterMm, positive whole total and count in [0,total]. lowerPhi = -log2(coarse diameter); upperPhi = -log2(fine diameter); phiWidth = log2(coarse/fine); densityPerPhi = count/(total*phiWidth).^[1]

Input field	Meaning and units	Accepted input
coarseDiameterMm	Coarse Diameter Mm	Required. Finite number.
fineDiameterMm	Fine Diameter Mm	Required. Finite number; strictly above 0.
count	Count	Required. Safe integer; minimum 0.
total	Total	Required. Safe integer; minimum 1.

Output field	Interpretation	Returned shape
lowerPhi	Lower Phi	Required. Finite number.
upperPhi	Upper Phi	Required. Finite number.
phiWidth	Phi Width	Required. Finite number.
densityPerPhi	Count fraction per phi-width unit, not raw bin probability.	Required. Finite number.

json

{
  "input": {
    "coarseDiameterMm": 2,
    "fineDiameterMm": 1,
    "count": 20,
    "total": 100
  },
  "output": {
    "lowerPhi": -1,
    "upperPhi": 0,
    "phiWidth": 1,
    "densityPerPhi": 0.2
  }
}

Limitations and assumptions

Diameters are in millimeters for the stated phi convention. Density per phi differs from a bin fraction; within-bin distribution and a full grain-size curve are not estimated.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use suitable mapping, grain-size and sampling methods for complete spatial distributions and geological interpretation.

References

Calculation and input contract: earth-science/sediment-grain-phi-bin-width — tool.io

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