Articles | Volume 6, issue 2
https://doi.org/10.5194/gchron-6-227-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gchron-6-227-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
12 Jun 2024
Research article |
| 12 Jun 2024
| 12 Jun 2024
Solving crustal heat transfer for thermochronology using physics-informed neural networks
School of Earth and Ocean Sciences, University of Victoria, Victoria, Canada
Shengze Cai
Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou, China
Jean Braun
Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Potsdam, Germany
Related authors
Sean D. Willett, Frédéric Herman, Matthew Fox, Nadja Stalder, Todd A. Ehlers, Ruohong Jiao, and Rong Yang
Earth Surf. Dynam., 9, 1153–1221, https://doi.org/10.5194/esurf-9-1153-2021, https://doi.org/10.5194/esurf-9-1153-2021, 2021
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The cooling climate of the last few million years leading into the ice ages has been linked to increasing erosion rates by glaciers. One of the ways to measure this is through mineral cooling ages. In this paper, we investigate potential bias in these data and the methods used to analyse them. We find that the data are not themselves biased but that appropriate methods must be used. Past studies have used appropriate methods and are sound in methodology.
Chuanqi He, Ci-Jian Yang, Jens M. Turowski, Richard F. Ott, Jean Braun, Hui Tang, Shadi Ghantous, Xiaoping Yuan, and Gaia Stucky de Quay
Earth Syst. Sci. Data, 16, 1151–1166, https://doi.org/10.5194/essd-16-1151-2024, https://doi.org/10.5194/essd-16-1151-2024, 2024
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The shape of drainage basins and rivers holds significant implications for landscape evolution processes and dynamics. We used a global 90 m resolution topography to obtain ~0.7 million drainage basins with sizes over 50 km2. Our dataset contains the spatial distribution of drainage systems and their morphological parameters, supporting fields such as geomorphology, climatology, biology, ecology, hydrology, and natural hazards.
Amanda Lily Wild, Jean Braun, Alexander C. Whittaker, and Sebastien Castelltort
EGUsphere, https://doi.org/10.5194/egusphere-2024-351, https://doi.org/10.5194/egusphere-2024-351, 2024
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Sediments deposited within river channels form the stratigraphic record, which has been used to interpret tectonic events, basin subsidence, and changes in precipitation long after ancient mountain chains have eroded away. Our work combines methods for estimating gravel fining with a landscape evolution model in order to analyze the grain size preserved within the stratigraphic record with greater complexity (e.g. considering topography and channel dynamics) than past approaches.
Caroline Fenske, Jean Braun, François Guillocheau, and Cécile Robin
EGUsphere, https://doi.org/10.5194/egusphere-2024-160, https://doi.org/10.5194/egusphere-2024-160, 2024
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We have developed a new numerical model to represent the formation of ferricretes which are iron-rich, hard layers found in soils and at the surface of the Earth. We assume that the formation mechanism implies variations in the height of the water table and that the hardening rate is proportional to precipitation. The model allows us to quantify the potential feedbacks they generate on the surface topography and the thickness of the regolith/soil layer.
Boris Gailleton, Luca C. Malatesta, Guillaume Cordonnier, and Jean Braun
Geosci. Model Dev., 17, 71–90, https://doi.org/10.5194/gmd-17-71-2024, https://doi.org/10.5194/gmd-17-71-2024, 2024
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This contribution presents a new method to numerically explore the evolution of mountain ranges and surrounding areas. The method helps in monitoring with details on the timing and travel path of material eroded from the mountain ranges. It is particularly well suited to studies juxtaposing different domains – lakes or multiple rock types, for example – and enables the combination of different processes.
Esteban Acevedo-Trejos, Jean Braun, Katherine Kravitz, N. Alexia Raharinirina, and Benoît Bovy
Geosci. Model Dev., 16, 6921–6941, https://doi.org/10.5194/gmd-16-6921-2023, https://doi.org/10.5194/gmd-16-6921-2023, 2023
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The interplay of tectonics and climate influences the evolution of life and the patterns of biodiversity we observe on earth's surface. Here we present an adaptive speciation component coupled with a landscape evolution model that captures the essential earth-surface, ecological, and evolutionary processes that lead to the diversification of taxa. We can illustrate with our tool how life and landforms co-evolve to produce distinct biodiversity patterns on geological timescales.
Ngai-Ham Chan, Moritz Langer, Bennet Juhls, Tabea Rettelbach, Paul Overduin, Kimberly Huppert, and Jean Braun
Earth Surf. Dynam., 11, 259–285, https://doi.org/10.5194/esurf-11-259-2023, https://doi.org/10.5194/esurf-11-259-2023, 2023
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Arctic river deltas influence how nutrients and soil organic carbon, carried by sediments from the Arctic landscape, are retained or released into the Arctic Ocean. Under climate change, the deltas themselves and their ecosystems are becoming more vulnerable. We build upon previous models to reproduce for the first time an important feature ubiquitous to Arctic deltas and simulate its future under climate warming. This can impact the future of Arctic deltas and the carbon release they moderate.
Jean Braun
Earth Surf. Dynam., 10, 301–327, https://doi.org/10.5194/esurf-10-301-2022, https://doi.org/10.5194/esurf-10-301-2022, 2022
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By comparing two models for the transport of sediment, we find that they share a similar steady-state solution that adequately predicts the shape of most depositional systems made of a fan and an alluvial plain. The length of the fan is controlled by the size of the mountain drainage area feeding the sedimentary system and its slope by the incoming sedimentary flux. We show that the models differ in their transient behavior to external forcing and are characterized by different response times.
Sean D. Willett, Frédéric Herman, Matthew Fox, Nadja Stalder, Todd A. Ehlers, Ruohong Jiao, and Rong Yang
Earth Surf. Dynam., 9, 1153–1221, https://doi.org/10.5194/esurf-9-1153-2021, https://doi.org/10.5194/esurf-9-1153-2021, 2021
Short summary
Short summary
The cooling climate of the last few million years leading into the ice ages has been linked to increasing erosion rates by glaciers. One of the ways to measure this is through mineral cooling ages. In this paper, we investigate potential bias in these data and the methods used to analyse them. We find that the data are not themselves biased but that appropriate methods must be used. Past studies have used appropriate methods and are sound in methodology.
Benjamin Campforts, Charles M. Shobe, Philippe Steer, Matthias Vanmaercke, Dimitri Lague, and Jean Braun
Geosci. Model Dev., 13, 3863–3886, https://doi.org/10.5194/gmd-13-3863-2020, https://doi.org/10.5194/gmd-13-3863-2020, 2020
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Landslides shape the Earth’s surface and are a dominant source of terrestrial sediment. Rivers, then, act as conveyor belts evacuating landslide-produced sediment. Understanding the interaction among rivers and landslides is important to predict the Earth’s surface response to past and future environmental changes and for mitigating natural hazards. We develop HyLands, a new numerical model that provides a toolbox to explore how landslides and rivers interact over several timescales.
Guillaume Cordonnier, Benoît Bovy, and Jean Braun
Earth Surf. Dynam., 7, 549–562, https://doi.org/10.5194/esurf-7-549-2019, https://doi.org/10.5194/esurf-7-549-2019, 2019
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We propose a new algorithm to solve the problem of flow routing across local depressions in the topography, one of the main computational bottlenecks in landscape evolution models. Our solution is more efficient than the state-of-the-art algorithms, with an optimal linear asymptotic complexity. The algorithm has been designed specifically to be used within landscape evolution models, and also suits more generally the efficient treatment of large digital elevation models.
Jean Braun, Lorenzo Gemignani, and Peter van der Beek
Earth Surf. Dynam., 6, 257–270, https://doi.org/10.5194/esurf-6-257-2018, https://doi.org/10.5194/esurf-6-257-2018, 2018
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We present a new method to interpret a type of data that geologists obtained by dating minerals in river sand samples. We show that such data contain information about the spatial distribution of the erosion rate (wear of surface rocks by natural processes such as river incision, land sliding or weathering) in the regions neighboring the river. This is important to understand the nature and efficiency of the processes responsible for surface erosion in mountain belts.
J. Braun, C. Voisin, A. T. Gourlan, and C. Chauvel
Earth Surf. Dynam., 3, 1–14, https://doi.org/10.5194/esurf-3-1-2015, https://doi.org/10.5194/esurf-3-1-2015, 2015
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We have derived a simple solution to the stream power law equation governing the erosion of rapidly uplifting tectonic areas assuming that rainfall varies as a periodic function of time. We show that the erosional response of this forcing is characterized by an amplification of the resulting erosional flux variations as well as a time lag. We show how this time lag can be important in interpreting several geological observations.
T. Croissant and J. Braun
Earth Surf. Dynam., 2, 155–166, https://doi.org/10.5194/esurf-2-155-2014, https://doi.org/10.5194/esurf-2-155-2014, 2014
Related subject area
Geochronological data analysis/statistics/modelling
In situ rubidium–strontium geochronology of white mica in young metamafic and metasomatic rocks from Syros: testing the limits of laser-ablation triple-quadrupole inductively coupled plasma mass spectrometer mica dating using different anchoring approaches
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Technical note: RA138 calcite U–Pb LA-ICP-MS primary reference material
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The daughter–parent plot: a tool for analyzing thermochronological data
Errorchrons and anchored isochrons in IsoplotR
Short communication: Resolving the discrepancy between U–Pb age estimates for the “Likhall” bed, a key level in the Ordovician timescale
Navigating the complexity of detrital rutile provenance: methodological insights from the Neotethys Orogen in Anatolia
Interpreting cooling dates and histories from laser ablation in-situ (U-Th-Sm)/He thermochronometry
Minimizing the effects of Pb loss in detrital and igneous U–Pb zircon geochronology by CA-LA-ICP-MS
Short Communication: Nanoscale heterogeneity of U and Pb in baddeleyite – implications for nanogeochronology and 238U series alpha recoil effects
Modeling apparent Pb loss in zircon U–Pb geochronology
Calibration methods for laser ablation Rb–Sr geochronology: comparisons and recommendation based on NIST glass and natural reference materials
Short communication: The Wasserstein distance as a dissimilarity metric for comparing detrital age spectra and other geological distributions
ChronoLorica: introduction of a soil–landscape evolution model combined with geochronometers
Technical note: colab_zirc_dims: a Google Colab-compatible toolset for automated and semi-automated measurement of mineral grains in laser ablation–inductively coupled plasma–mass spectrometry images using deep learning models
Calculation of uncertainty in the (U–Th) ∕ He system
Bayesian age–depth modelling applied to varve and radiometric dating to optimize the transfer of an existing high-resolution chronology to a new composite sediment profile from Holzmaar (West Eifel Volcanic Field, Germany)
Short communication: age2exhume – a MATLAB/Python script to calculate steady-state vertical exhumation rates from thermochronometric ages and application to the Himalaya
U and Th content in magnetite and Al spinel obtained by wet chemistry and laser ablation methods: implication for (U–Th) ∕ He thermochronometer
In situ LA-ICPMS U–Pb dating of sulfates: applicability of carbonate reference materials as matrix-matched standards
An algorithm for U–Pb geochronology by secondary ion mass spectrometry
Technical note: Rapid phase identification of apatite and zircon grains for geochronology using X-ray micro-computed tomography
Simulating sedimentary burial cycles – Part 2: Elemental-based multikinetic apatite fission-track interpretation and modelling techniques illustrated using examples from northern Yukon
sandbox – creating and analysing synthetic sediment sections with R
Improving age–depth relationships by using the LANDO (“Linked age and depth modeling”) model ensemble
How many grains are needed for quantifying catchment erosion from tracer thermochronology?
Short communication: Inverse isochron regression for Re–Os, K–Ca and other chronometers
Technical note: Analytical protocols and performance for apatite and zircon (U–Th) ∕ He analysis on quadrupole and magnetic sector mass spectrometer systems between 2007 and 2020
Simulating sedimentary burial cycles – Part 1: Investigating the role of apatite fission track annealing kinetics using synthetic data
The closure temperature(s) of zircon Raman dating
On the treatment of discordant detrital zircon U–Pb data
An evaluation of Deccan Traps eruption rates using geochronologic data
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Development of a multi-method chronology spanning the Last Glacial Interval from Orakei maar lake, Auckland, New Zealand
Robust isochron calculation
Resolving the timescales of magmatic and hydrothermal processes associated with porphyry deposit formation using zircon U–Pb petrochronology
Seasonal deposition processes and chronology of a varved Holocene lake sediment record from Chatyr Kol lake (Kyrgyz Republic)
Unifying the U–Pb and Th–Pb methods: joint isochron regression and common Pb correction
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Jesús Muñoz-Montecinos, Andrea Giuliani, Senan Oesch, Silvia Volante, Bradley Peters, and Whitney Behr
Geochronology, 6, 585–605, https://doi.org/10.5194/gchron-6-585-2024, https://doi.org/10.5194/gchron-6-585-2024, 2024
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Dating the roots of plate boundaries is essential for understanding geologic processes, but geochemical limitations, particularly in young mafic rocks, make this challenging. Advancements in mass spectrometry now enable high-resolution analysis of micro-domains. We assess these limitations by dating rocks from Syros. Multi-phase mineral analysis improves age uncertainty 6-fold. We emphasize the importance of the local geologic context and propose strategies to mitigate uncertainties.
Andrew L. Gorin, Joshua M. Gorin, Marie Bergelin, and David L. Shuster
Geochronology, 6, 521–540, https://doi.org/10.5194/gchron-6-521-2024, https://doi.org/10.5194/gchron-6-521-2024, 2024
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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.
Marcel Guillong, Elias Samankassou, Inigo A. Müller, Dawid Szymanowski, Nathan Looser, Lorenzo Tavazzani, Óscar Merino-Tomé, Juan R. Bahamonde, Yannick Buret, and Maria Ovtcharova
Geochronology, 6, 465–474, https://doi.org/10.5194/gchron-6-465-2024, https://doi.org/10.5194/gchron-6-465-2024, 2024
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RA138 is a new reference material for U–Pb dating of carbonate samples via laser ablation inductively coupled plasma mass spectrometry. RA138 exhibits variable U–Pb ratios and consistent U content, resulting in a precise isochron with low uncertainty. Isotope dilution thermal ionization mass spectrometry analyses fix a reference age of 321.99 ± 0.65 Ma. This research advances our ability to date carbonate samples accurately, providing insights into geological processes and historical timelines.
Nil Irvalı, Ulysses S. Ninnemann, Are Olsen, Neil L. Rose, David J. R. Thornalley, Tor L. Mjell, and François Counillon
Geochronology, 6, 449–463, https://doi.org/10.5194/gchron-6-449-2024, https://doi.org/10.5194/gchron-6-449-2024, 2024
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Marine sediments are excellent archives for reconstructing past changes in climate and ocean circulation. Yet, dating uncertainties, particularly during the 20th century, pose major challenges. Here we propose a novel chronostratigraphic approach that uses anthropogenic signals, such as the oceanic 13C Suess effect and spheroidal carbonaceous fly-ash particles, to reduce age model uncertainties in high-resolution marine archives over the 20th century.
Birk Härtel and Eva Enkelmann
Geochronology, 6, 429–448, https://doi.org/10.5194/gchron-6-429-2024, https://doi.org/10.5194/gchron-6-429-2024, 2024
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We present a new data analysis workflow for thermochronological data based on plots of radiogenic daughter vs. radioactive parent concentration. The daughter–parent relationship helps to identify the sources of age variation. Our workflow classifies the daughter–parent relationship and provides further suggestions, e.g., if a dataset can be described by a sample age and which type of sample age to report. We also introduce Incaplot, which is software for creating daughter–parent plots.
Pieter Vermeesch
Geochronology, 6, 397–407, https://doi.org/10.5194/gchron-6-397-2024, https://doi.org/10.5194/gchron-6-397-2024, 2024
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The age of some geological materials can be estimated from the ratio of certain radiogenic "daughter" isotopes to their radioactive "parent". However, in many cases, the age estimation process is complicated by the presence of an inherited component of non-radiogenic daughter isotopes. This paper presents an improved algorithm to estimate the radiogenic and non-radiogenic components, either separately or jointly.
André Navin Paul, Anders Lindskog, and Urs Schaltegger
Geochronology, 6, 325–335, https://doi.org/10.5194/gchron-6-325-2024, https://doi.org/10.5194/gchron-6-325-2024, 2024
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The “Likhall” bed helps to constrain the timing of increased meteorite bombardment of the Earth during the Ordovician period. It is important to understand the timing of this meteorite bombardment when attempting to correlate it with biodiversity changes during the Ordovician period. Calibrating a good age for the “Likhall” bed is, however, challenging and benefited in this study from advances in sample preparation.
Megan A. Mueller, Alexis Licht, Andreas Möller, Cailey B. Condit, Julie C. Fosdick, Faruk Ocakoğlu, and Clay Campbell
Geochronology, 6, 265–290, https://doi.org/10.5194/gchron-6-265-2024, https://doi.org/10.5194/gchron-6-265-2024, 2024
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Sedimentary provenance refers to the study of the origin of sedimentary rocks, tracing where sediment particles originated. Common sedimentary provenance techniques struggle to track mafic igneous and metamorphic rock sources and rutile forms in these rock types. We use rutile form ancient sedimentary rocks in Türkiye to present new recommendations and workflows for integrating rutile U–Pb ages and chemical composition into an accurate sedimentary provenance reconstruction.
Christoph Glotzbach and Todd A. Ehlers
Geochronology Discuss., https://doi.org/10.5194/gchron-2024-12, https://doi.org/10.5194/gchron-2024-12, 2024
Revised manuscript accepted for GChron
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The (U-Th)/He dating method helps understand rock’s cooling history. Synthetic modeling experiments were conducted to explore factors affecting in-situ vs. whole-grain (U-Th)/He dates. In-situ dates are often 30 % older than whole-grain dates, whereas very rapid cooling makes helium loss negligible, resulting in similar whole-grain and in-situ dates. In addition, in-situ data can reveal cooling histories even from a single grain by measuring helium distributions.
Erin E. Donaghy, Michael P. Eddy, Federico Moreno, and Mauricio Ibañez-Mejia
Geochronology, 6, 89–106, https://doi.org/10.5194/gchron-6-89-2024, https://doi.org/10.5194/gchron-6-89-2024, 2024
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Chemical abrasion (CA) is a technique that reduces or eliminates the effects of Pb loss in zircon U–Pb geochronology. However, CA has yet to be applied to large-n detrital zircon (DZ) analyses. We show that CA does not negatively impact or systematically bias U–Pb dates, improves the resolution of age populations defined by 206Pb/238U dates, and increases the percentage of concordant analyses in age populations defined by 207Pb/206Pb dates.
Steven Denyszyn, Donald W. Davis, and Denis Fougerouse
Geochronology Discuss., https://doi.org/10.5194/gchron-2024-4, https://doi.org/10.5194/gchron-2024-4, 2024
Revised manuscript accepted for GChron
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Decay of U to Pb in the mineral baddeleyite is used for precisely dating mafic rocks, but some daughter Pb atoms can be ejected out of the crystal, resulting in an age that appears too young. Atom Probe Tomography was used to map the distribution of U and Pb atoms in 3 dimensions within a baddeleyite crystal and estimate the average distance that Pb atoms are displaced by decay of U. This allows us to correct the measured age on a baddeleyite crystal knowing its size and shape.
Glenn R. Sharman and Matthew A. Malkowski
Geochronology, 6, 37–51, https://doi.org/10.5194/gchron-6-37-2024, https://doi.org/10.5194/gchron-6-37-2024, 2024
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The mineral zircon is widely used to determine the age of rocks based on the radioactive decay of U to Pb, but the measured U–Pb date can be too young if the zircon loses Pb. We present a method for estimating the distribution of apparent Pb loss by mathematical convolution. Applying this approach to 10 samples illustrates contrasting patterns of apparent Pb loss. This study highlights the importance of quantifying Pb loss to better understand its potential effects on zircon U–Pb dates.
Stijn Glorie, Sarah E. Gilbert, Martin Hand, and Jarred C. Lloyd
Geochronology, 6, 21–36, https://doi.org/10.5194/gchron-6-21-2024, https://doi.org/10.5194/gchron-6-21-2024, 2024
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Radiometric dating methods, involving laser ablation as the sample introduction, require robust calibrations to reference materials with similar ablation properties to the analysed samples. In the case of the rubidium–strontium dating method, calibrations are often conducted to nano powder with different ablation characteristics than the crystalline minerals. We describe the limitations of this approach and recommend an alternative calibration method involving natural minerals.
Alex Lipp and Pieter Vermeesch
Geochronology, 5, 263–270, https://doi.org/10.5194/gchron-5-263-2023, https://doi.org/10.5194/gchron-5-263-2023, 2023
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We propose using the Wasserstein-2 distance (W2) as an alternative to the widely used Kolmogorov–Smirnov (KS) statistic for analysing distributional data in geochronology. W2 measures the horizontal distance between observations, while KS measures vertical differences in cumulative distributions. Using case studies, we find that W2 is preferable in scenarios where the absolute age differences in observations provide important geological information. W2 has been added to the R package IsoplotR.
W. Marijn van der Meij, Arnaud J. A. M. Temme, Steven A. Binnie, and Tony Reimann
Geochronology, 5, 241–261, https://doi.org/10.5194/gchron-5-241-2023, https://doi.org/10.5194/gchron-5-241-2023, 2023
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We present our model ChronoLorica. We coupled the original Lorica model, which simulates soil and landscape evolution, with a geochronological module that traces cosmogenic nuclide inventories and particle ages through simulations. These properties are often measured in the field to determine rates of landscape change. The coupling enables calibration of the model and the study of how soil, landscapes and geochronometers change under complex boundary conditions such as intensive land management.
Michael C. Sitar and Ryan J. Leary
Geochronology, 5, 109–126, https://doi.org/10.5194/gchron-5-109-2023, https://doi.org/10.5194/gchron-5-109-2023, 2023
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We developed code to automatically and semi-automatically measure dimensions of detrital mineral grains in reflected-light images saved at laser ablation–inductively coupled plasma–mass spectrometry facilities that use Chromium targeting software. Our code uses trained deep learning models to segment grain images with greater accuracy than is achievable using other segmentation techniques. We implement our code in Jupyter notebooks which can also be run online via Google Colab.
Peter E. Martin, James R. Metcalf, and Rebecca M. Flowers
Geochronology, 5, 91–107, https://doi.org/10.5194/gchron-5-91-2023, https://doi.org/10.5194/gchron-5-91-2023, 2023
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There is currently no standardized method of performing uncertainty propagation in the (U–Th) / He system, causing data interpretation difficulties. We present two methods of uncertainty propagation and describe free, open-source software (HeCalc) to apply them. Compilation of real data using only analytical uncertainty as well as 2 % and 5 % uncertainties in FT yields respective median relative date uncertainties of 2.9 %, 3.3 %, and 5.0 % for apatites and 1.7 %, 3.3 %, and 5.0 % for zircons.
Stella Birlo, Wojciech Tylmann, and Bernd Zolitschka
Geochronology, 5, 65–90, https://doi.org/10.5194/gchron-5-65-2023, https://doi.org/10.5194/gchron-5-65-2023, 2023
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Sediment cores from the volcanic lake Holzmaar provide a very precise chronology based on tree-ring-like annual laminations or varves. We statistically combine this varve chronology with radiometric dating and tested three different methods to upgrade the age–depth model. However, only one of the three methods tested improved the dating accuracy considerably. With this work, an overview of different age integration methods is discussed and made available for increased future demands.
Peter van der Beek and Taylor F. Schildgen
Geochronology, 5, 35–49, https://doi.org/10.5194/gchron-5-35-2023, https://doi.org/10.5194/gchron-5-35-2023, 2023
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Thermochronometric data can provide unique insights into the patterns of rock exhumation and the driving mechanisms of landscape evolution. Several well-established thermal models allow for a detailed exploration of how cooling rates evolved in a limited area or along a transect, but more regional analyses have been challenging. We present age2exhume, a thermal model that can be used to rapidly provide a synoptic overview of exhumation rates from large regional thermochronologic datasets.
Marianna Corre, Arnaud Agranier, Martine Lanson, Cécile Gautheron, Fabrice Brunet, and Stéphane Schwartz
Geochronology, 4, 665–681, https://doi.org/10.5194/gchron-4-665-2022, https://doi.org/10.5194/gchron-4-665-2022, 2022
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This study is focused on the accurate measurement of U and Th by wet chemistry and laser ablation methods to improve (U–Th)/He dating of magnetite and spinel. The low U–Th content and the lack of specific U–Th standards significantly limit the accuracy of (U–Th)/He dating. Obtained U–Th results on natural and synthetic magnetite and aluminous spinel samples analyzed by wet chemistry methods and LA-ICP-MS sampling have important implications for the (U–Th)/He method and dates interpretation.
Aratz Beranoaguirre, Iuliana Vasiliev, and Axel Gerdes
Geochronology, 4, 601–616, https://doi.org/10.5194/gchron-4-601-2022, https://doi.org/10.5194/gchron-4-601-2022, 2022
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U–Pb dating by the in situ laser ablation mass spectrometry (LA-ICPMS) technique requires reference materials of the same nature as the samples to be analysed. Here, we have explored the suitability of using carbonate materials as a reference for sulfates, since there is no sulfate reference material. The results we obtained are satisfactory, and thus, from now on, the sulfates can also be analysed.
Pieter Vermeesch
Geochronology, 4, 561–576, https://doi.org/10.5194/gchron-4-561-2022, https://doi.org/10.5194/gchron-4-561-2022, 2022
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Secondary ion mass spectrometry (SIMS) is the oldest and most sensitive analytical technique for in situ U–Pb geochronology. This paper introduces a new algorithm for SIMS data reduction that treats data as
compositional data, which means that the relative abundances of 204Pb, 206Pb, 207Pb, and 238Pb are processed within a tetrahedral data space or
simplex. The new method is implemented in an eponymous computer programme that is compatible with the two dominant types of SIMS instruments.
Emily H. G. Cooperdock, Florian Hofmann, Ryley M. C. Tibbetts, Anahi Carrera, Aya Takase, and Aaron J. Celestian
Geochronology, 4, 501–515, https://doi.org/10.5194/gchron-4-501-2022, https://doi.org/10.5194/gchron-4-501-2022, 2022
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Apatite and zircon are the most widely used minerals for dating rocks, but they can be difficult to identify in some crushed rock samples. Incorrect mineral identification results in wasted analytical resources and inaccurate data. We show how X-ray computed tomography can be used to efficiently and accurately distinguish apatite from zircon based on density variations, and provide non-destructive 3D grain-specific size, shape, and inclusion information for improved data quality.
Dale R. Issler, Kalin T. McDannell, Paul B. O'Sullivan, and Larry S. Lane
Geochronology, 4, 373–397, https://doi.org/10.5194/gchron-4-373-2022, https://doi.org/10.5194/gchron-4-373-2022, 2022
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Phanerozoic sedimentary rocks of northern Canada have compositionally heterogeneous detrital apatite with high age dispersion caused by differential thermal annealing. Discrete apatite fission track kinetic populations with variable annealing temperatures are defined using elemental data but are poorly resolved using conventional parameters. Inverse thermal modelling of samples from northern Yukon reveals a record of multiple heating–cooling cycles consistent with geological constraints.
Michael Dietze, Sebastian Kreutzer, Margret C. Fuchs, and Sascha Meszner
Geochronology, 4, 323–338, https://doi.org/10.5194/gchron-4-323-2022, https://doi.org/10.5194/gchron-4-323-2022, 2022
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The R package sandbox is a collection of functions that allow the creation, sampling and analysis of fully virtual sediment sections, like having a virtual twin of real-world deposits. This article introduces the concept, features, and workflows required to use sandbox. It shows how a real-world sediment section can be mapped into the model and subsequently addresses a series of theoretical and practical questions, exploiting the flexibility of the model framework.
Gregor Pfalz, Bernhard Diekmann, Johann-Christoph Freytag, Liudmila Syrykh, Dmitry A. Subetto, and Boris K. Biskaborn
Geochronology, 4, 269–295, https://doi.org/10.5194/gchron-4-269-2022, https://doi.org/10.5194/gchron-4-269-2022, 2022
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We use age–depth modeling systems to understand the relationship between age and depth in lake sediment cores. However, depending on which modeling system we use, the model results may vary. We provide a tool to link different modeling systems in an interactive computational environment and make their results comparable. We demonstrate the power of our tool by highlighting three case studies in which we test our application for single-sediment cores and a collection of multiple sediment cores.
Andrea Madella, Christoph Glotzbach, and Todd A. Ehlers
Geochronology, 4, 177–190, https://doi.org/10.5194/gchron-4-177-2022, https://doi.org/10.5194/gchron-4-177-2022, 2022
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Cooling ages date the time at which minerals cross a certain isotherm on the way up to Earth's surface. Such ages can be measured from bedrock material and river sand. If spatial variations in bedrock ages are known in a river catchment, the spatial distribution of erosion can be inferred from the distribution of the ages measured from the river sand grains. Here we develop a new tool to help such analyses, with particular emphasis on quantifying uncertainties due to sample size.
Yang Li and Pieter Vermeesch
Geochronology, 3, 415–420, https://doi.org/10.5194/gchron-3-415-2021, https://doi.org/10.5194/gchron-3-415-2021, 2021
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A conventional isochron is a straight-line fit to two sets of isotopic ratios, D/d and P/d, where P is the radioactive parent, D is the radiogenic daughter, and d is a second isotope of the daughter element. The slope of this line is proportional to the age of the system. An inverse isochron is a linear fit through d/D and P/D. The horizontal intercept of this line is inversely proportional to the age. The latter approach is preferred when d<D, which is the case in Re–Os and K–Ca geochronology.
Cécile Gautheron, Rosella Pinna-Jamme, Alexis Derycke, Floriane Ahadi, Caroline Sanchez, Frédéric Haurine, Gael Monvoisin, Damien Barbosa, Guillaume Delpech, Joseph Maltese, Philippe Sarda, and Laurent Tassan-Got
Geochronology, 3, 351–370, https://doi.org/10.5194/gchron-3-351-2021, https://doi.org/10.5194/gchron-3-351-2021, 2021
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Apatite and zircon (U–Th) / He thermochronology is now a mainstream tool to reconstruct Earth's evolution through the history of cooling and exhumation over the first dozen kilometers. The geological implications of these data rely on the precision of measurements of He, U, Th, and Sm contents in crystals. This technical note documents the methods for He thermochronology developed at the GEOPS laboratory, Paris-Saclay University, that allow (U–Th) / He data to be obtained with precision.
Kalin T. McDannell and Dale R. Issler
Geochronology, 3, 321–335, https://doi.org/10.5194/gchron-3-321-2021, https://doi.org/10.5194/gchron-3-321-2021, 2021
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We generated a synthetic dataset applying published kinetic models and distinct annealing kinetics for the apatite fission track and (U–Th)/He methods using a predetermined thermal history. We then tested how well the true thermal history could be recovered under different data interpretation schemes and geologic constraint assumptions using the Bayesian QTQt software. Our results demonstrate that multikinetic data increase time–temperature resolution and can constrain complex thermal histories.
Birk Härtel, Raymond Jonckheere, Bastian Wauschkuhn, and Lothar Ratschbacher
Geochronology, 3, 259–272, https://doi.org/10.5194/gchron-3-259-2021, https://doi.org/10.5194/gchron-3-259-2021, 2021
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We carried out thermal annealing experiments between 500 and 1000 °C to determine the closure temperature of radiation-damage annealing in zircon (ZrSiO4). Our results show that the different Raman bands of zircon respond differently to annealing. The repair is highest for the external rotation Raman band near 356.6 cm−1. The closure temperature estimates range from 250 to 370 °C for different bands. The differences in closure temperatures offer the prospect of multi-T zircon Raman dating.
Pieter Vermeesch
Geochronology, 3, 247–257, https://doi.org/10.5194/gchron-3-247-2021, https://doi.org/10.5194/gchron-3-247-2021, 2021
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This paper shows that the current practice of filtering discordant U–Pb data based on the relative difference between the 206Pb/238U and 207Pb/206Pb ages is just one of several possible approaches to the problem and demonstrably not the best one. An alternative approach is to define discordance in terms of isotopic composition, as a log ratio distance between the measurement and the concordia line. Application to real data indicates that this reduces the positive bias of filtered age spectra.
Blair Schoene, Michael P. Eddy, C. Brenhin Keller, and Kyle M. Samperton
Geochronology, 3, 181–198, https://doi.org/10.5194/gchron-3-181-2021, https://doi.org/10.5194/gchron-3-181-2021, 2021
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We compare two published U–Pb and 40Ar / 39Ar geochronologic datasets to produce eruption rate models for the Deccan Traps large igneous province. Applying the same approach to each dataset, the resulting models agree well, but the higher-precision U–Pb dataset results in a more detailed eruption model than the lower-precision 40Ar / 39Ar data. We explore sources of geologic uncertainty and reiterate the importance of systematic uncertainties in comparing U–Pb and 40Ar / 39Ar datasets.
Nicholas P. McKay, Julien Emile-Geay, and Deborah Khider
Geochronology, 3, 149–169, https://doi.org/10.5194/gchron-3-149-2021, https://doi.org/10.5194/gchron-3-149-2021, 2021
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This paper describes geoChronR, an R package that streamlines the process of quantifying age uncertainties, propagating uncertainties through several common analyses, and visualizing the results. In addition to describing the structure and underlying theory of the package, we present five real-world use cases that illustrate common workflows in geoChronR. geoChronR is built on the Linked PaleoData framework, is open and extensible, and we welcome feedback and contributions from the community.
Leonie Peti, Kathryn E. Fitzsimmons, Jenni L. Hopkins, Andreas Nilsson, Toshiyuki Fujioka, David Fink, Charles Mifsud, Marcus Christl, Raimund Muscheler, and Paul C. Augustinus
Geochronology, 2, 367–410, https://doi.org/10.5194/gchron-2-367-2020, https://doi.org/10.5194/gchron-2-367-2020, 2020
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Orakei Basin – a former maar lake in Auckland, New Zealand – provides an outstanding sediment record over the last ca. 130 000 years, but an age model is required to allow the reconstruction of climate change and volcanic eruptions contained in the sequence. To construct a relationship between depth in the sediment core and age of deposition, we combined tephrochronology, radiocarbon dating, luminescence dating, and the relative intensity of the paleomagnetic field in a Bayesian age–depth model.
Roger Powell, Eleanor C. R. Green, Estephany Marillo Sialer, and Jon Woodhead
Geochronology, 2, 325–342, https://doi.org/10.5194/gchron-2-325-2020, https://doi.org/10.5194/gchron-2-325-2020, 2020
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The standard approach to isochron calculation assumes that the distribution of uncertainties on the data arising from isotopic analysis is strictly Gaussian. This excludes datasets that have more scatter, even though many appear to have age significance. Our new approach requires only that the central part of the uncertainty distribution of the data defines a "spine" in the trend of the data. A robust statistics approach is used to locate the spine, and an implementation in Python is given.
Simon J. E. Large, Jörn-Frederik Wotzlaw, Marcel Guillong, Albrecht von Quadt, and Christoph A. Heinrich
Geochronology, 2, 209–230, https://doi.org/10.5194/gchron-2-209-2020, https://doi.org/10.5194/gchron-2-209-2020, 2020
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The integration of zircon geochemistry and U–Pb geochronology (petrochronology) allows us to improve our understanding of magmatic processes. Here we could reconstruct the ~300 kyr evolution of the magma reservoir that sourced the magmas, fluids and metals to form the Batu Hijau porphyry Cu–Au deposit. The application of in situ LA-ICP-MS and high-precision CA–ID–TIMS geochronology to the same zircons further allowed an assessment of the strengths and limitations of the different techniques.
Julia Kalanke, Jens Mingram, Stefan Lauterbach, Ryskul Usubaliev, Rik Tjallingii, and Achim Brauer
Geochronology, 2, 133–154, https://doi.org/10.5194/gchron-2-133-2020, https://doi.org/10.5194/gchron-2-133-2020, 2020
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Our study presents the first seasonally laminated (varved) sediment record covering almost the entire Holocene in high mountainous arid Central Asia. The established floating varve chronology is confirmed by two terrestrial radiocarbon dates, whereby aquatic radiocarbon dates reveal decreasing reservoir ages up core. Changes in seasonal deposition characteristics are attributed to changes in runoff and precipitation and/or to evaporative summer conditions.
Pieter Vermeesch
Geochronology, 2, 119–131, https://doi.org/10.5194/gchron-2-119-2020, https://doi.org/10.5194/gchron-2-119-2020, 2020
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The U–Pb method is one of the most powerful and versatile methods in the geochronological toolbox. With two isotopes of uranium decaying to two different isotopes of lead, the U–Pb method offers an internal quality control that is absent from most other geochronological techniques. U-bearing minerals often contain significant amounts of Th, which decays to a third Pb isotope. This paper presents an algorithm to jointly process all three chronometers at once.
Jon Woodhead and Joseph Petrus
Geochronology, 1, 69–84, https://doi.org/10.5194/gchron-1-69-2019, https://doi.org/10.5194/gchron-1-69-2019, 2019
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Recently developed methods for in situ U–Pb age determination in carbonates have found widespread application, but the benefits and limitations of the method over bulk analysis approaches have yet to be fully explored. Here we use speleothems – cave carbonates such as stalagmites and flowstones – to investigate the utility of these in situ dating methodologies for challenging matrices with low U and Pb contents and predominantly late Cenozoic ages.
Cited articles
Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X.: TensorFlow: large-scale machine learning on heterogeneous systems, arXiv [preprint], https://doi.org/10.48550/arXiv.1603.04467, 16 March 2016. a, b
Boster, K. A., Cai, S., Ladrón-de Guevara, A., Sun, J., Zheng, X., Du, T., Thomas, J. H., Nedergaard, M., Karniadakis, G. E., and Kelley, D. H.: Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows, P. Natl. Acad. Sci. USA, 120, e2217744120, https://doi.org/10.1073/pnas.2217744120, 2023. a
Brandon, M. T., Roden-Tice, M. K., and Carver, J. I.: Late Cenozoic exhumation of the Cascadia accretionary wedge in the Olympic Mountains, northwest Washington State, Bull. Geol. Soc. Am., 110, 985–1009, https://doi.org/10.1130/0016-7606(1998)110<0985:LCEOTC>2.3.CO;2, 1998. a, b, c
Braun, J. and Robert, X.: Constraints on the rate of post-orogenic erosional decay from low-temperature thermochronological data: Application to the Dabie Shan, China, Earth Surf. Proc. Land., 30, 1203–1225, https://doi.org/10.1002/esp.1271, 2005. a, b, c, d
Braun, J., Beek, P. V. D., and Batt, G.: Quantitative thermochronology: numerical methods for the interpretation of thermochronological data, Cambridge University Press, 1st Edn., ISBN 978-0-521-83057-7, 978-0-511-61643-3, 978-1-107-40715-2, https://doi.org/10.1017/CBO9780511616433, 2006. a
Braun, J., van der Beek, P., Valla, P., Robert, X., Herman, F., Glotzbach, C., Pedersen, V., Perry, C., Simon-Labric, T., and Prigent, C.: Quantifying rates of landscape evolution and tectonic processes by thermochronology and numerical modeling of crustal heat transport using PECUBE, Tectonophysics, 524-525, 1–28, https://doi.org/10.1016/j.tecto.2011.12.035, 2012. a, b
Cai, S., Mao, Z., Wang, Z., Yin, M., and Karniadakis, G. E.: Physics-informed neural networks (PINNs) for fluid mechanics: A review, Acta Mech. Sinica, 37, 1727–1738, 2021a. a
Cai, S., Wang, Z., Fuest, F., Jeon, Y. J., Gray, C., and Karniadakis, G. E.: Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks, J. Fluid Mech., 915, A102, https://doi.org/10.1017/jfm.2021.135, 2021b. a
Dodson, M. H.: Closure temperature in cooling geochronological and petrological systems, Contrib. Mineral. Petr., 40, 259–274, https://doi.org/10.1007/BF00373790, 1973. a, b, c
Ehlers, T. A., Willett, S. D., Armstrong, P. A., and Chapman, D. S.: Exhumation of the central Wasatch Mountains, Utah: 2. Thermokinematic model of exhumation, erosion, and thermochronometer interpretation, J. Geophys. Res.-Sol. Ea., 108, 2173, https://doi.org/10.1029/2001JB001723, 2003. a
Fitzgerald, P. G. and Malusà, M. G.: Concept of the exhumed partial annealing (retention) zone and age-elevation profiles in thermochronology, in: Fission-track thermochronology and its application to geology, edited by: Malusà, M. G. and Fitzgerald, P. G., Springer International Publishing, 165–189, https://doi.org/10.1007/978-3-319-89421-8_9, 2019. a
Fitzgerald, P. G., Sorkhabi, R. B., Redfield, T. F., and Stump, E.: Uplift and denudation of the central Alaska Range: A case study in the use of apatite fission track thermochronology to determine absolute uplift parameters, J. Geophys. Res.-Sol. Ea., 100, 20175–20191, https://doi.org/10.1029/95JB02150, 1995. a
Fox, M., Herman, F., Willett, S. D., and May, D. A.: A linear inversion method to infer exhumation rates in space and time from thermochronometric data, Earth Surf. Dynam., 2, 47–65, https://doi.org/10.5194/esurf-2-47-2014, 2014. a, b, c, d
Gallagher, K.: Transdimensional inverse thermal history modeling for quantitative thermochronology, J. Geophys. Res.-Sol. Ea., 117, B02408, https://doi.org/10.1029/2011JB008825, 2012. a
Goodman, J. and Weare, J.: Ensemble samplers with affine invariance, Comm. App. Math. Com. Sc., 5, 65–80, https://doi.org/10.2140/camcos.2010.5.65, 2010. a
Hacker, B. R., Ratschbacher, L., Webb, L., and Shuwen, D.: What brought them up? Exhumation of the Dabie Shan ultrahigh-pressure rocks, Geology, 23, 743, https://doi.org/10.1130/0091-7613(1995)023<0743:WBTUEO>2.3.CO;2, 1995. a
He, Q. and Tartakovsky, A. M.: Physics‐informed neural network method for forward and backward advection‐dispersion equations, Water Resour. Res., 57, e2020WR029479, https://doi.org/10.1029/2020WR029479, 2021. a, b
Jagtap, A. D., Kawaguchi, K., and Karniadakis, G. E.: Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, J. Comput. Phys., 404, 109136, https://doi.org/10.1016/j.jcp.2019.109136, 2020. a
Jepson, G., Carrapa, B., George, S. W. M., Reeher, L. J., Kapp, P. A., Davis, G. H., Thomson, S. N., Amadori, C., Clinkscales, C., Jones, S., Gleadow, A. J. W., and Kohn, B. P.: Where did the Arizona‐Plano go? Protracted thinning via upper‐ to lower‐crustal processes, J. Geophys. Res.-Sol. Ea., 127, e2021JB023850, https://doi.org/10.1029/2021JB023850, 2022. a
Jiao, R.: jiaor/PINNs_Chron: v0 (Version v0), Zenodo [code], https://doi.org/10.5281/zenodo.11454363, 2024. a
Jiao, R., Seward, D., Little, T. A., and Kohn, B. P.: Thermal history and exhumation of basement rocks from Mesozoic to Cenozoic subduction cycles, central North Island, New Zealand, Tectonics, 33, 1920–1935, https://doi.org/10.1002/2014TC003653, 2014. a
Jones, D. R. and Martins, J. R. R. A.: The DIRECT algorithm: 25 years Later, J. Global Optim., 79, 521–566, https://doi.org/10.1007/s10898-020-00952-6, 2021. a
Jones, D. R., Perttunen, C. D., and Stuckman, B. E.: Lipschitzian optimization without the Lipschitz constant, J. Optimiz. Theory App., 79, 157–181, https://doi.org/10.1007/BF00941892, 1993. a, b
Ketcham, R. A.: Forward and inverse modeling of low-temperature thermochronometry data, Rev. Miner. Geochem., 58, 275–314, https://doi.org/10.2138/rmg.2005.58.11, 2005. a
Ketcham, R. A., Carter, A., Donelick, R. A., Barbarand, J., and Hurford, A. J.: Improved modeling of fission-track annealing in apatite, Am. Mineral., 92, 799–810, https://doi.org/10.2138/am.2007.2281, 2007. a
Kingma, D. P. and Ba, J. L.: Adam: A method for stochastic optimization, arXiv [preprint], https://doi.org/10.48550/arXiv.1412.6980, 2015. a
Lagaris, I., Likas, A., and Fotiadis, D.: Artificial neural networks for solving ordinary and partial differential equations, IEEE T. Neural Networ., 9, 987–1000, https://doi.org/10.1109/72.712178, 1998. a
Lu, L., Meng, X., Mao, Z., and Karniadakis, G. E.: DeepXDE: a deep learnin library for solving differential equations, SIAM Rev., 63, 208–228, https://doi.org/10.1137/19M1274067, 2021. a
Luijendijk, E.: Beo v1.0: numerical model of heat flow and low-temperature thermochronology in hydrothermal systems, Geosci. Model Dev., 12, 4061–4073, https://doi.org/10.5194/gmd-12-4061-2019, 2019. a
Mancktelow, N. S. and Grasemann, B.: Time-dependent effects of heat advection and topography on cooling histories during erosion, Tectonophysics, 270, 167–195, https://doi.org/10.1016/S0040-1951(96)00279-X, 1997. a, b
Nie, S., Yin, A., Rowley, D. B., and Jin, Y.: Exhumation of the Dabie Shan ultra-high-pressure rocks and accumulation of the Songpan-Ganzi flysch sequence, central China, Geology, 22, 999, https://doi.org/10.1130/0091-7613(1994)022<0999:EOTDSU>2.3.CO;2, 1994. a
Raissi, M., Perdikaris, P., and Karniadakis, G. E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., 378, 686–707, 2019. a
Raissi, M., Yazdani, A., and Karniadakis, G. E.: Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Science, 367, 1026–1030, 2020. a
Rasht‐Behesht, M., Huber, C., Shukla, K., and Karniadakis, G. E.: Physics‐informed neural networks (PINNs) for wave propagation and full waveform inversions, J. Geophys. Res.-Sol. Ea., 127, e2021JB023120, https://doi.org/10.1029/2021JB023120, 2022. a, b, c
Ratschbacher, L., Franz, L., Enkelmann, E., Jonckheere, R., Pörschke, A., Hacker, B. R., Dong, S., and Zhang, Y.: The Sino-Korean–Yangtze suture, the Huwan detachment, and the Paleozoic–Tertiary exhumation of (ultra)high-pressure rocks along the Tongbai-Xinxian-Dabie Mountains, in: Ultrahigh-pressure metamorphism: Deep continental subduction, Geol. Soc. Am., https://doi.org/10.1130/2006.2403(03), 2006. a
Reiners, P. W. and Brandon, M. T.: Using thermochronology to understand orogenic erosion, Annu. Rev. Earth Pl. Sc., 34, 419–466, https://doi.org/10.1146/annurev.earth.34.031405.125202, 2006. a
Sambridge, M.: Geophysical inversion with a neighbourhood algorithm-I. Searching a parameter space, Geophys. J. Int., 138, 479–494, https://doi.org/10.1046/j.1365-246X.1999.00876.x, 1999a. a, b, c
Sambridge, M.: Geophysical inversion with a neighbourhood algorithm-II. Appraising the ensemble, Geophys. J. Int., 138, 727–746, https://doi.org/10.1046/j.1365-246x.1999.00900.x, 1999b. a
Shukla, K., Jagtap, A. D., and Karniadakis, G. E.: Parallel physics-informed neural networks via domain decomposition, J. Comput. Phys., 447, 110683, https://doi.org/10.1016/j.jcp.2021.110683, 2021. a
Stüwe, K., White, L., and Brown, R.: The influence of eroding topography on steady-state isotherms. Application to fission track analysis, Earth Planet. Sc. Lett., 124, 63–74, https://doi.org/10.1016/0012-821X(94)00068-9, 1994. a, b, c, d
van der Beek, P. and Schildgen, T. F.: Short communication: age2exhume – a MATLAB/Python script to calculate steady-state vertical exhumation rates from thermochronometric ages and application to the Himalaya, Geochronology, 5, 35–49, https://doi.org/10.5194/gchron-5-35-2023, 2023. a, b
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: fundamental algorithms for scientific computing in Python, Nat. Meth., 17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020. a, b
Waheed, U. B., Haghighat, E., Alkhalifah, T., Song, C., and Hao, Q.: PINNeik: Eikonal solution using physics-informed neural networks, Comput. Geosci., 155, 104833, https://doi.org/10.1016/j.cageo.2021.104833, 2021. a
Whipp, D.: HUGG/TC1D: v0.1, Zenodo [code], https://doi.org/10.5281/ZENODO.7124272, 2022. a
Willett, S. D. and Brandon, M. T.: On steady states in mountain belts, Geology, 30, 175–178, https://doi.org/10.1130/0091-7613(2002)030<0175:OSSIMB>2.0.CO;2, 2002. a
Willett, S. D. and Brandon, M. T.: Some analytical methods for converting thermochronometric age to erosion rate: age to erosion rate, Geochem. Geophy. Geosy., 14, 209–222, https://doi.org/10.1029/2012GC004279, 2013. a, b, c
Yang, L., Meng, X., and Karniadakis, G. E.: B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, J. Comput. Phys., 425, 109913, https://doi.org/10.1016/j.jcp.2020.109913, 2021. a
Short summary
We demonstrate a machine learning method to estimate the temperature changes in the Earth's crust over time. The method respects physical laws and conditions imposed by users. By using observed rock cooling ages as constraints, the method can be used to estimate the tectonic and landscape evolution of the Earth. We show the applications of the method using a synthetic rock uplift model in 1D and an evolution model of a real mountain range in 3D.
We demonstrate a machine learning method to estimate the temperature changes in the Earth's...
