Evaluating calibration models in isotope geochemistry: Lessons from carbonates and sulfides

Geology routinely employs isotopic geochemistry with the main objective of measuring radiogenic or stable isotopic compositions to reconstruct the history of the Earth. A critical aspect of this analytical process lies in verifying the accuracy and reliability of the measurements performed. To this end, standards or reference materials are repeatedly analyzed enabling calibration or adjustment of experimental instruments. In order to ensure a strong correlation between the reference values and the averaged measurements, a linear regression is the most widely adopted. Among the available methodologies, this work advocates for the use of models compliant with the ISO 28037:2010 standard, which is specifically designed to perform linear regression in a statistically robust manner. The guidelines established by this standard are, regrettably, not always implemented correctly, and the statistical nature of the measurements is frequently overlooked. This study provides a detailed examination of the methodologies advocated by the standard, with the objective of facilitating their application to geochemical problems specifically, issues related to isotopic measurement by revisiting the underlying theoretical principles, assumptions, and the respective advantages and limitations inherent to each approach. To facilitate implementation and respect recommendations, we propose a software application developed in Python 3.14. This computational tool has been tested and validated using experimental datasets obtained from isotopic analyses of carbon, oxygen, and sulfur elements of fundamental interest in geological studies. The objective of this study is therefore to clearly and practically illustrate the challenges involved in geochemical calibration and adjustment.