Mixing Model
Definition
A mathematical framework for reconstructing the proportions of two or more isotopically distinct source materials in a mixture. Required whenever a forensic sample (soil on footwear, river sediment, bullet lead alloy) is composed of contributions from multiple geographic or industrial sources.
- Purpose
- Reconstructs source proportions in an isotopic mixture
- Applications
- Soil on footwear, river sediment, bullet lead alloy
- Input
- Isotopically distinct source materials
- Field
- Geoforensics and isotope analysis
Common questions
Why is a mixing model necessary rather than just measuring the isotope ratio of the mixed sample directly?+
The measured ratio of a mixture is only a single blended value, it does not by itself reveal how much came from each contributing source. A mixing model uses known or assumed end-member source signatures together with mass balance equations to solve for the proportional contribution of each source.
What happens to a mixing model's accuracy if one of the true source end-members is unknown?+
The calculated proportions become unreliable or biased, since the model can only apportion the mixture among the end-members it is given. Missing or mischaracterised source signatures is one of the main sources of error in isotope mixing analysis, so identifying all plausible sources beforehand matters.
Can a mixing model be applied with more than two source materials?+
Yes, though the mathematics becomes more complex and typically requires more independent isotope systems or tracers than sources to yield a unique solution; a two-source mixture can often be solved with a single isotope ratio, while three or more sources generally require multiple isotopic systems analysed together.
Related terms
- 87Sr/86Sr Ratio
- The ratio of radiogenic strontium-87 (produced by decay of rubidium-87) to the stable reference isotope strontium-86. Values range from roughly 0.703 in...
- Isoscape
- A map of isotope ratio variation across a geographic area, derived from systematic sampling of soil, water, plant, or mineral material; used...
- Lead Isotope Triple Plot
- A graphical display of 207Pb/204Pb against 206Pb/204Pb and 208Pb/204Pb against 206Pb/204Pb. Different ore deposits fall in distinct clusters on these plots, and...
- Radiogenic Ingrowth
- The progressive increase in a daughter isotope such as 87Sr over geological time as the parent nuclide (87Rb) decays. Materials with higher...
- Strontium Isoscape
- A map of 87Sr/86Sr values across a defined geographic area, built from measurements of soil, plants, or water. Used to compare the...