An optimization tool for identifying multiple-diffusion domain model parameters

Abstract

The multiple-diffusion domain (MDD) model empirically describes the diffusive behavior of noble gases in some terrestrial materials and has been commonly used to interpret 40Ar/39Ar stepwise degassing observations in K-feldspar. When applied in this manner, the MDD model can be used to test crustal exhumation scenarios by identifying the permissible thermal paths a rock sample could have undergone over geologic time, assuming the diffusive properties of Ar within the mineral are accurately understood. More generally, the MDD model provides a framework for quantifying the temperature-dependent diffusivity of noble gases in minerals. However, constraining MDD parameters that successfully predict the results of step-heating diffusion experiments is a complex task, and the assumptions made by existing numerical methods used to quantify model parameters can bias the absolute temperatures permitted by thermal modeling. For example, the most commonly used method assumes that no domains lose more than 60 % of their gas during early heating steps (Lovera et al., 1997). This assumption is unverifiable, and we show that the Lovera et al. (1997) procedure may bias predicted temperatures towards lower values when it is violated. To address this potential bias and to provide greater accessibility to the MDD model, we present a new open-source method for constraining MDD parameters from stepwise degassing experimental results, called the “MDD Tool Kit” (https://github.com/dgorin1/mddtoolkit, last access: 11 October 2024). This software optimizes all MDD parameters simultaneously and removes any need for user-defined Ea or regression fitting choices used by other tools. In doing so, this new method eliminates assumptions about the domain size distribution. To test the validity of our thermal predictions, we then use the MDD Tool Kit (https://github.com/dgorin1/mddtoolkit) to interpret 40Ar/39Ar results from the Grayback Fault, AZ, USA. Although the resulting thermal histories are consistently ∼ 60–75 °C higher than those found in previous studies, they agree with independent observations from apatite fission track, zircon fission track, and (U-Th)/He.