Description
Compute predictedDelta33 as 1000 times expm1(exponent times log1p(delta34/1000)), then capitalDelta33 as measured delta33 minus that prediction.
An isotope ratio depends on which isotope is in the numerator and denominator. Delta notation compares a ratio with a reference on a per-mil scale, while mixing and decay models require explicit amount and system assumptions.
Compute predictedDelta33 as 1000 times expm1(exponent times log1p(delta34/1000)), then capitalDelta33 as measured delta33 minus that prediction.
When to use this tool
Use Sulfur Isotope Mass Dependent Offset Term when you need a stated isotope-reference, mixing, or one-step decay calculation.
How to use the tool and how it works
- Enter delta33, delta34, exponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read predictedDelta33, capitalDelta33. Use the output convention below.
Require delta33 at least -1000, delta34 greater than -1000, and positive exponent. Compute predictedDelta33 as 1000 times expm1(exponent times log1p(delta34/1000)), then capitalDelta33 as measured delta33 minus that prediction.1
The nonlinear capital-delta definition subtracts 1000[(1+δ34/1000)^exponent−1] from δ33. Here the exponent is supplied explicitly; the output is not the alternative logarithmic capital-delta definition.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| delta33 | Sulfur-33 delta in per mil on the compatible standard basis. | Required. Finite number; minimum -1000. |
| delta34 | Sulfur-34 delta in per mil, strictly above -1000. | Required. Finite number; strictly above -1000. |
| exponent | Positive caller-supplied mass-dependent exponent; not a fixed selected value. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| predictedDelta33 | Predicted Delta33 | Required. Finite number. |
| capitalDelta33 | Capital Delta33 | Required. Finite number. |
{
"input": {
"delta33": 5,
"delta34": 10,
"exponent": 0.5
},
"output": {
"predictedDelta33": 4.987562112089027,
"capitalDelta33": 0.012437887910972556
}
}Limitations and assumptions
- Both delta inputs and offsets are per mil relative to compatible isotope standards. The exponent is caller supplied; this nonlinear mass-dependent model does not choose standards or prove a geological process.
- 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 the appropriate reference materials and full isotope model for interpretation. Preserve ratio orientation, reference scale, denominator-isotope weighting, uncertainty, and any open-system or fractionation effects.
References
-
Calculation and input contract: geochemistry/sulfur-isotope-mass-dependent-offset-term — tool.io
-
Mass-independent sulfur isotopic compositions in present-day sulfate aerosols — Romero and Thiemens, Journal of Geophysical Research: Atmospheres
Similar or alternative tools
- Isotope Standard Delta Residual
Compute delta as 1000 times (sample ratio divided by standard ratio minus one), then return reported minus derived delta as the residual.
- Isotope Delta To Ratio Standard Term
Return sampleRatio equal to standardRatio times (1+deltaPerMil/1000).