02 May 2024
 | 02 May 2024
Status: this preprint is currently under review for the journal GChron.

An optimization tool for identifying Multiple Diffusion Domain Model parameters

Andrew L. Gorin, Joshua M. Gorin, Marie Bergelin, and David L. Shuster

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 geological 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 gasses 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 (Lovera et al., 1997) assumes that no domains lose more than 60 % of their gas during early heating steps. This assumption is unverifiable, and we show that Lovera et al.’s (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.” 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 to interpret the 40Ar/39Ar results of Wong et al. (2023) from the Grayback Fault, AZ, USA. Although the resulting thermal histories are consistently ~ 60–75 °C higher than those found by Wong et al. 2023), they agree with independent observations from apatite fission track, zircon fission track, and (U-Th)/He (Howard and Foster, 1996).

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Andrew L. Gorin, Joshua M. Gorin, Marie Bergelin, and David L. Shuster

Status: open (until 26 Jun 2024)

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  • CC1: 'Comment on gchron-2024-11', Daniil Popov, 22 May 2024 reply
Andrew L. Gorin, Joshua M. Gorin, Marie Bergelin, and David L. Shuster

Model code and software

MDD Tool Kit Andrew L. Gorin and Joshua M. Gorin

Andrew L. Gorin, Joshua M. Gorin, Marie Bergelin, and David L. Shuster


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Short summary
The Multiple Diffusion Domain (MDD) model quantifies the temperature dependence of noble gas diffusivity in minerals. However, current methods for tuning MDD parameters can yield biased results, leading to underestimates of sample temperatures through geologic time. Our "MDD Tool Kit" software optimizes all MDD parameters simultaneously, overcoming these biases. We then apply this software to a previously published 40Ar/39Ar dataset (Wong, 2023) to showcase its efficacy.