Diagnostic Ratios

Diagnostic ratios are combinations of elements or isotopes that provide more information than individual concentrations alone. They are used to attribute contamination to a source, distinguish geological background from anthropogenic input, or characterize transformation processes. IsoFind automatically calculates the most common ratios using concentrations from the Geochemistry view and isotopic measurements from the Isotopes view. This page presents standard ratios organized by application.

Principles and Conditions of Use

An elemental ratio is the quotient of two concentrations measured on the same sample under identical analytical conditions. Its diagnostic value relies on two conditions. First, both elements must exhibit consistent environmental behavior: either mobile elements so that neither is selectively lost through differential leaching, or conversely, two conservative elements to treat the ratio as a source tracer. Second, the range of ratio variations across candidate sources must be sufficiently contrasted for the difference to be measurable above analytical noise.

Ratios are unitless values and therefore independent of absolute concentration. A Pb/Sr ratio of 0.3 remains the same whether a sample is highly diluted or highly concentrated, allowing for the comparison of different sample matrices without correction. This property makes ratios a particularly robust tool in environmental forensics.

Source Attribution Ratios

These ratios utilize conservative elements (which undergo little fractionation by environmental processes) to identify the origin of contamination. They are exceptionally robust because they preserve their signature from the source to the sample.

Ratio	Application	Typical Values
²⁰⁶Pb / ²⁰⁷Pb	Industrial vs. natural lead attribution	1.15 to 1.25 depending on ore origin
²⁰⁸Pb / ²⁰⁶Pb	Tetraethyl lead (fuel) vs. ammunition lead	2.05 to 2.15 depending on deposits
⁸⁷Sr / ⁸⁶Sr	Geological tracing (substrate age)	0.704 (recent volcanic) to 0.720 (ancient cratons)
Nd isotopes (εNd)	Crustal vs. mantellic origin	+5 to +10 (mantle); −10 to −20 (ancient crust)
Cu / Zn	Copper vs. zinc metallurgy	> 1 copper refineries; < 1 galvanization
Pb / Zn	Pb-Zn sulfide mines vs. diffuse sources	0.3 to 1 in mines; < 0.1 in non-impacted soils

The ²⁰⁶Pb/²⁰⁷Pb ratio is historically diagnostic of lead added to fuels (banned in France in 2000). Lead of Australian or Chinese origin has distinct signatures. On a contaminated site, measuring ²⁰⁶/²⁰⁷ helps determine if the contamination stems from legacy road traffic (values near 1.15), old paint, or recent industrial activity. This distinction cannot be made based on concentration alone.

Lithological Ratios and Geological Background

These ratios are used to characterize the natural geological context and distinguish background levels from contamination. A contrast with expected values for the reference lithology signals an external input.

Ratio	Diagnostic	Indicative Values
Ca / Mg	Pure limestone vs. dolomite	> 10 limestone; 1 to 3 dolomite
Na / K	Evaporitic origin vs. feldspar weathering	> 20 halite / evaporites; ~1 to 3 feldspars
Al / Si	Silicate weathering degree	Increases with weathering (clays)
Fe / Al	Fe oxyhydroxides vs. clay fraction	> 0.5 Fe oxides dominant
Mn / Fe	Typical redox pair	0.02 to 0.05 rock; rises in reducing waters
K / Rb	Feldspar fractionation assessment	200 to 500 differentiated granites
Eu / Eu*	Europium anomaly (REE)	< 1 feldspar fractionation; > 1 accumulation

Anthropogenic Enrichment Ratios

The Enrichment Factor (EF) compares a potentially contaminated sample to a natural geochemical reference, normalized to a conservative element. It allows for the separation of anthropogenic contribution from the natural background.

            EF = (X / R)_sample / (X / R)_reference
        

Where X is the element of interest (candidate contaminant) and R is the normalizing element, typically Al, Fe, Sc, or Ti. Interpretation follows a conventional grid.

EF Value	Interpretation
< 2	Natural geochemical background, no significant enrichment
2 to 5	Moderate enrichment, probable anthropogenic input
5 to 20	Significant enrichment, confirmed contamination
20 to 40	Severe enrichment
> 40	Extreme enrichment, intense local source

The geochemical reference can be a background sample from the same site (local background) or a mean composition of the Upper Continental Crust (UCC from Wedepohl or Rudnick-Gao). IsoFind supports both configurations via the reference parameter in the dedicated report block.

Redox Ratios and Process Indicators

Certain elemental ratios are sensitive to local physico-chemical conditions and serve as indirect indicators of the redox or biogeochemical regime.

Ratio	Diagnostic	Behavior
Fe²⁺ / Total Fe	Degree of iron reduction	> 0.5 anoxic conditions; < 0.1 oxic
Mn²⁺ / Total Mn	Early indicator of anoxia	Rises before Fe²⁺ (Mn reduced at higher Eh)
U / Th	Selective mobilization of uranium	U is mobile in oxic environments, Th is conservative
V / Cr	Hydrocarbon marker vs. industrial chromium	High V with hydrocarbons; Cr with plating activities
Mo / U	Euxinia (sulfidic anoxia)	> 4 in active sulfidic sediments

Petrogenic vs. Pyrogenic Ratios (PAHs)

For PAHs, isomeric ratios distinguish between petroleum-derived (petrogenic) and combustion-derived (pyrogenic) origins. These ratios are widely used in hydrocarbon contamination cases and are linked to the molecular component via the Molecules view.

PAH Ratio	Petrogenic	Pyrogenic
Phenanthrene / Anthracene	> 10	< 10
Fluoranthene / Pyrene	< 1	> 1 (combustion)
Fluoranthene / (Fluoranthene + Pyrene)	< 0.4	> 0.5 coal/wood combustion
Indeno[1,2,3-cd]pyrene / (IP + BgP)	< 0.2	> 0.5 biomass combustion
Benzo[a]anthracene / (BaA + Chrysene)	< 0.2	> 0.35 combustion
BaP / (BaP + Chrysene)	< 0.3	> 0.5 combustion

PAH ratios should not be used in isolation: interpretation can be ambiguous for weathered samples (selective photo-degradation, partial biodegradation). Combining multiple ratios with the full molecular signature (16 EPA PAHs) and ideally CSIA on naphthalene or phenanthrene provides a much more robust diagnosis than a single ratio.

Compound Isotopic Ratios (Perchlorate)

For perchlorate, the combination of δ¹⁸O and δ³⁷Cl allows for the distinction between synthetic (industrial) origin and natural origin (atmospheric deposition, Atacama). This is one of the few applications where dual isotopes are applied to an inorganic anion rather than an organochloride.

Perchlorate Origin	δ¹⁸O (‰)	δ³⁷Cl (‰)
Synthetic (Industrial)	−25 to −15	+1 to +2
Natural Atacama	+10 to +14	+5 to +6
Natural Atmospheric Deposition	+3 to +10	+0 to +3

The separation between the three origins is clear in the δ¹⁸O × δ³⁷Cl plot, making perchlorate an exemplary case of unambiguous isotopic forensics. The molecule_isotope_fractionation table in IsoFind contains the reference values for ClO₄⁻.

Nitrate Ratios: δ¹⁵N and δ¹⁸O

The δ¹⁵N-δ¹⁸O pair for nitrate is the standard for tracing the origin of nitrogen contamination in groundwater. Sources are well-separated in the isotopic plot.

Nitrate Source	δ¹⁵N (‰)	δ¹⁸O (‰)
Synthetic Fertilizers (Ammonium Nitrates)	−4 to +4	+18 to +22
Soil Nitrification	+2 to +8	−5 to +5
Domestic Effluents / Livestock	+10 to +20	−5 to +10
Atmospheric Deposition	−5 to +5	+50 to +80

Agricultural contamination from ammonium nitrates can be distinguished from livestock effluent contamination based on δ¹⁵N, with a typical difference of 10 to 15 ‰. Atmospheric deposition carries a very high δ¹⁸O, making it identifiable even in complex mixtures.

Automatic Calculation in IsoFind

IsoFind automatically calculates standard elemental ratios as soon as the two required concentrations are present in the Geochemistry view. Isotopic ratios are calculated from measurements in the Isotopes view. Calculation is triggered either upon opening a dedicated report block or via the API endpoint.

Context	IsoFind Behavior
Diagnostic Ratios Report Block	Automatic table of available ratios with interpretation
Sample Dashboard	Displays Ca/Mg and Mn/Fe widgets if measurements are present
Nexus Quick Match Provenance Module	Automatic calculation of Pb/Sr and Cu/Zn for attribution
CSV Ratio Export	One column per ratio, one row per sample

For a given sample, a ratio is only displayed if both corresponding concentrations exist and are above the LOQ. Ratios calculated on LOD/LOQ values are explicitly marked as indicative in reports to prevent over-interpretation.

Limitations and Best Practices

A diagnostic ratio never replaces a complete analysis. It guides interpretation but must be cross-referenced with other indicators (absolute concentrations, full isotopic signatures, site context).
The reference values provided here are indicative. Each watershed and lithology has its specificities; a local background study remains the essential foundation for any diagnosis.
Ratios are sensitive to analytical procedures: XRF and ICP-MS measurements on the same sample may yield significantly different ratios, especially for elements with variable speciation (Cr, Fe, Mn).
Isotopic fractionation can modify a ratio during migration: Fe²⁺ is lighter than Fe³⁺, and the shift of the redox front differentially enriches the two species downstream.
For regulatory cases, prioritize ratios documented in domain literature over exotic ratios. Defending an interpretation before an expert panel is simpler with recognized ratios.