30 October 2024

All About Isochrons

Last month we discussed model ages and when they mathematically result in the most accurate and robust method for determining a sample's age. But, model ages only work when there was little to no initial daughter ¹⁸⁷Os at the time of formation. Unfortunately, there are many geologic samples for which this occurrence does not hold true and not accounting for initial ¹⁸⁷Os would lead to inaccurate ages.

Enter the isochron -- an alternative analytical and mathematical method for determining a sample's or sample suite's age with the bonus of calculating the ¹⁸⁷Os/¹⁸⁸Os of the system at time = 0. The ¹⁸⁷Os/¹⁸⁸Os will reflect the chemistry of the system from which the sample formed whether that be the saline hydrothermal fluid of a forming ore deposit, the seawater chemistry captured by organic-rich matter which will become a shale, or the metamorphic fluids from which graphite precipitates.

Here is a schematic, generic isochron built from sampling and analyzing five different samples. These "samples" may be co-genetic sulfide minerals, spatially-linked horizons in an organic-rich shale, mono-mineralic blebs along strike of a quartz vein or similar.

Most importantly, the samples must meet the following criteria to produce an isochron:
  1.) All must form at the same time (t).
  2.) All must incorporate the same initial ¹⁸⁷Os/¹⁸⁸Os at t = 0.
  3.) The system must remain closed after t = 0; no addition or subtraction of parent or daughter.
  4.) There must be varying ratio of Re:Os leading to ¹⁸⁷Re/¹⁸⁸Os spread.

These criteria are evident in the schematic isochron. At time = 0, all five samples form a horizontal line parallel to the abscissa (x-axis) and traced to the ordinate (y-axis) at the initial ¹⁸⁷Os/¹⁸⁸Os. As time progresses, the sample points shift up and to the left as ¹⁸⁷Re decays to ¹⁸⁷Os with Re-rich samples moving further as proportionally more ¹⁸⁷Os is created in the same amount of time as Re-poor samples. These lines only remain parallel in a closed system. Finally, if there is no spread in Re:Os, the isochron line is subject to extreme errors as the line is difficult to accurately fit to the clumped points.

The age of the sample is calculated from the slope of the line. As time progresses, the slope increases as more ¹⁸⁷Re decays thereby continually shifting the points further up and to the left. The initial ¹⁸⁷Os/¹⁸⁸Os of the system is the ordinate intercept of the line.

And that is the basics of the isochron approach to Re-Os dating, and a brief one at that. Of course, the detailed mathematics of fitting a line to the points, determining the error and robustness of the fitment, and application of the results can (and do) fill a textbook. AIRIE would be more than happy to help answer any detailed or application-specific questions you may have, please submit your query here @ Contact AIRIE.