Articles | Volume 16, issue 23
https://doi.org/10.5194/gmd-16-6987-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-6987-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
29 Nov 2023
Development and technical paper |
| 29 Nov 2023
| 29 Nov 2023
GeoINR 1.0: an implicit neural network approach to three-dimensional geological modelling
Michael Hillier
CORRESPONDING AUTHOR
Geological Survey of Canada, Natural Resources Canada, 601 Booth Street, Ottawa, ON K1A 0E8, Canada
Florian Wellmann
Computational Geoscience and Reservoir Engineering (CGRE), RWTH Aachen University, Mathieustr. 30, 52074 Aachen, Germany
Eric A. de Kemp
Geological Survey of Canada, Natural Resources Canada, 601 Booth Street, Ottawa, ON K1A 0E8, Canada
Boyan Brodaric
Geological Survey of Canada, Natural Resources Canada, 601 Booth Street, Ottawa, ON K1A 0E8, Canada
Ernst Schetselaar
Geological Survey of Canada, Natural Resources Canada, 601 Booth Street, Ottawa, ON K1A 0E8, Canada
Karine Bédard
Geological Survey of Canada, Natural Resources Canada, 490 rue de la Couronne, Quebec City, QC G1K 9A9, Canada
Related authors
Marion N. Parquer, Eric A. de Kemp, Boyan Brodaric, and Michael J. Hillier
Geosci. Model Dev., 18, 71–100, https://doi.org/10.5194/gmd-18-71-2025, https://doi.org/10.5194/gmd-18-71-2025, 2025
Short summary
Short summary
This is a proof-of-concept paper outlining a general approach to how 3D geological models would be checked to be geologically
reasonable. We do this with a consistency-checking tool that looks at geological feature pairs and their spatial, temporal, and internal polarity characteristics. The idea is to assess if geological relationships from a specific 3D geological model match what is allowed in the real world from the perspective of geological principles.
Marion N. Parquer, Eric A. de Kemp, Boyan Brodaric, and Michael J. Hillier
Geosci. Model Dev., 18, 71–100, https://doi.org/10.5194/gmd-18-71-2025, https://doi.org/10.5194/gmd-18-71-2025, 2025
Short summary
Short summary
This is a proof-of-concept paper outlining a general approach to how 3D geological models would be checked to be geologically
reasonable. We do this with a consistency-checking tool that looks at geological feature pairs and their spatial, temporal, and internal polarity characteristics. The idea is to assess if geological relationships from a specific 3D geological model match what is allowed in the real world from the perspective of geological principles.
Denise Degen, Moritz Ziegler, Oliver Heidbach, Andreas Henk, Karsten Reiter, and Florian Wellmann
EGUsphere, https://doi.org/10.5194/egusphere-2024-2932, https://doi.org/10.5194/egusphere-2024-2932, 2024
Short summary
Short summary
Obtaining reliable estimates of the subsurface state distributions is essential to determine the location of e.g. potential nuclear waste disposal sites. However, providing these is challenging since it requires solving the problem numerous times yielding high computational cost. To overcome this, we use a physics-based machine learning method to construct surrogate models. We demonstrate how it produces physics-preserving predictions, which differentiates it from purely data-driven approaches.
Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendricks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann
Geosci. Model Dev., 16, 7375–7409, https://doi.org/10.5194/gmd-16-7375-2023, https://doi.org/10.5194/gmd-16-7375-2023, 2023
Short summary
Short summary
In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.
Mohammad Moulaeifard, Simon Bernard, and Florian Wellmann
Geosci. Model Dev., 16, 3565–3579, https://doi.org/10.5194/gmd-16-3565-2023, https://doi.org/10.5194/gmd-16-3565-2023, 2023
Short summary
Short summary
In this work, we propose a flexible framework to generate and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the flexible control mesh, topologically similar to the main geological structure, watertight and controllable with few control points, to manage the geological structures. We exploited the subdivision surface method in our work, which is commonly used in the animation and gaming industry.
Michał P. Michalak, Lesław Teper, Florian Wellmann, Jerzy Żaba, Krzysztof Gaidzik, Marcin Kostur, Yuriy P. Maystrenko, and Paulina Leonowicz
Solid Earth, 13, 1697–1720, https://doi.org/10.5194/se-13-1697-2022, https://doi.org/10.5194/se-13-1697-2022, 2022
Short summary
Short summary
When characterizing geological/geophysical surfaces, various geometric attributes are calculated, such as dip angle (1D) or dip direction (2D). However, the boundaries between specific values may be subjective and without optimization significance, resulting from using default color palletes. This study proposes minimizing cosine distance among within-cluster observations to detect 3D anomalies. Our results suggest that the method holds promise for identification of megacylinders or megacones.
Eric A. de Kemp
Geosci. Model Dev., 14, 6661–6680, https://doi.org/10.5194/gmd-14-6661-2021, https://doi.org/10.5194/gmd-14-6661-2021, 2021
Short summary
Short summary
This is a proof of concept and review paper of spatial agents, with initial research focusing on geomodelling. The results may be of interest to others working on complex regional geological modelling with sparse data. Structural agent-based swarming behaviour is key to advancing this field. The study provides groundwork for research in structural geology 3D modelling with spatial agents. This work was done with NetLogo, a free agent modelling platform used mostly for teaching complex systems.
Alexander Schaaf, Miguel de la Varga, Florian Wellmann, and Clare E. Bond
Geosci. Model Dev., 14, 3899–3913, https://doi.org/10.5194/gmd-14-3899-2021, https://doi.org/10.5194/gmd-14-3899-2021, 2021
Short summary
Short summary
Uncertainty is an inherent property of any model of the subsurface. We show how geological topology information – how different regions of rocks in the subsurface are connected – can be used to train uncertain geological models to reduce uncertainty. More widely, the method demonstrates the use of probabilistic machine learning (Bayesian inference) to train structural geological models on auxiliary geological knowledge that can be encoded in graph structures.
Stephanie Thiesen, Diego M. Vieira, Mirko Mälicke, Ralf Loritz, J. Florian Wellmann, and Uwe Ehret
Hydrol. Earth Syst. Sci., 24, 4523–4540, https://doi.org/10.5194/hess-24-4523-2020, https://doi.org/10.5194/hess-24-4523-2020, 2020
Short summary
Short summary
A spatial interpolator has been proposed for exploring the information content of the data in the light of geostatistics and information theory. It showed comparable results to traditional interpolators, with the advantage of presenting generalization properties. We discussed three different ways of combining distributions and their implications for the probabilistic results. By its construction, the method provides a suitable and flexible framework for uncertainty analysis and decision-making.
Fabian Antonio Stamm, Miguel de la Varga, and Florian Wellmann
Solid Earth, 10, 2015–2043, https://doi.org/10.5194/se-10-2015-2019, https://doi.org/10.5194/se-10-2015-2019, 2019
Miguel de la Varga, Alexander Schaaf, and Florian Wellmann
Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, https://doi.org/10.5194/gmd-12-1-2019, 2019
Short summary
Short summary
GemPy is an open-source Python-based 3-D structural geological modeling software, which allows the implicit (i.e. automatic) creation of complex geological models from interface and orientation data. GemPy is implemented in the programming language Python, making use of a highly efficient underlying library, Theano, for efficient code generation that performs automatic differentiation. This enables the link to probabilistic machine-learning and Bayesian inference frameworks.
Raphael Schneeberger, Miguel de La Varga, Daniel Egli, Alfons Berger, Florian Kober, Florian Wellmann, and Marco Herwegh
Solid Earth, 8, 987–1002, https://doi.org/10.5194/se-8-987-2017, https://doi.org/10.5194/se-8-987-2017, 2017
Short summary
Short summary
Structural 3-D modelling has become a widely used technique within applied projects. We performed a typical modelling workflow for a study site with the occurrence of an underground facility. This exceptional setting enabled us to test the surface-based extrapolation of faults with the mapped faults underground. We estimated the extrapolation-related uncertainty with probabilistic 2-D interpolation. This research was conducted to improve structural 3-D modelling in less-constrained areas.
J. Florian Wellmann, Sam T. Thiele, Mark D. Lindsay, and Mark W. Jessell
Geosci. Model Dev., 9, 1019–1035, https://doi.org/10.5194/gmd-9-1019-2016, https://doi.org/10.5194/gmd-9-1019-2016, 2016
Short summary
Short summary
We often obtain knowledge about the subsurface in the form of structural geological models, as a basis for subsurface usage or resource extraction. Here, we provide a modelling code to construct such models on the basis of significant deformational events in geological history, encapsulated in kinematic equations. Our methods simplify complex dynamic processes, but enable us to evaluate how events interact, and finally how certain we are about predictions of structures in the subsurface.
Related subject area
Numerical methods
Hydro-geomorphological modelling of leaky wooden dam efficacy from reach to catchment scale with CAESAR-Lisflood 1.9j
Enhancing single precision with quasi-double precision: achieving double-precision accuracy in the Model for Prediction Across Scales – Atmosphere (MPAS-A) version 8.2.1
Advances in land surface forecasting: a comparison of LSTM, gradient boosting, and feed-forward neural networks as prognostic state emulators in a case study with ecLand
Subgrid corrections for the linear inertial equations of a compound flood model – a case study using SFINCS 2.1.1 Dollerup release
Introducing Iterative Model Calibration (IMC) v1.0: a generalizable framework for numerical model calibration with a CAESAR-Lisflood case study
Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0
A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)
Assimilation of snow water equivalent from AMSR2 and IMS satellite data utilizing the local ensemble transform Kalman filter
The Paleochrono-1.1 probabilistic model to derive a common age model for several paleoclimatic sites using absolute and relative dating constraints
asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond
Explicit stochastic advection algorithms for the regional-scale particle-resolved atmospheric aerosol model WRF-PartMC (v1.0)
Potential based Thermodynamics with Consistent Conservative Cascade Transport for Implicit Large Eddy Simulation: PTerodaC3TILES version 1.0
The Measurement Error Proxy System Model: MEPSM v0.2
Numerical stabilization methods for level-set-based ice front migration
Modelling chemical advection during magma ascent
Consistent point data assimilation in Firedrake and Icepack
A computationally efficient parameterization of aerosol, cloud and precipitation pH for application at global and regional scale (EQSAM4Clim-v12)
Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2)
Assessing effects of climate and technology uncertainties in large natural resource allocation problems
VISIR-2: ship weather routing in Python
Incremental analysis update (IAU) in the Model for Prediction Across Scales coupled with the Joint Effort for Data assimilation Integration (MPAS–JEDI 2.0.0)
Decision-making strategies implemented in SolFinder 1.0 to identify eco-efficient aircraft trajectories: application study in AirTraf 3.0
CLAQC v1.0 – Country Level Air Quality Calculator. An Empirical Modeling Approach
Developing meshing workflows in Gmsh v4.11 for the geologic uncertainty assessment of high-temperature aquifer thermal energy storage
Development and preliminary validation of a land surface image assimilation system based on the Common Land Model
NorSand4AI: a comprehensive triaxial test simulation database for NorSand constitutive model materials
ParticleDA.jl v.1.0: a distributed particle-filtering data assimilation package
HETerogeneous vectorized or Parallel (HETPv1.0): an updated inorganic heterogeneous chemistry solver for the metastable-state NH4+–Na+–Ca2+–K+–Mg2+–SO42−–NO3−–Cl−–H2O system based on ISORROPIA II
Three-dimensional geological modelling of igneous intrusions in LoopStructural v1.5.10
Estimating volcanic ash emissions using retrieved satellite ash columns and inverse ash transport modeling using VolcanicAshInversion v1.2.1, within the operational eEMEP (emergency European Monitoring and Evaluation Programme) volcanic plume forecasting system (version rv4_17)
Accounting for uncertainties in forecasting tropical-cyclone-induced compound flooding
An automatic mesh generator for coupled 1D–2D hydrodynamic models
Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 1: Dust budget analyses and the impacts of a revised coupling scheme
Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes
jsmetrics v0.2.0: a Python package for metrics and algorithms used to identify or characterise atmospheric jet streams
P3D-BRNS v1.0.0: a three-dimensional, multiphase, multicomponent, pore-scale reactive transport modelling package for simulating biogeochemical processes in subsurface environments
MinVoellmy v1: a lightweight model for simulating rapid mass movements based on a modified Voellmy rheology
Scalable Feature Extraction and Tracking (SCAFET): a general framework for feature extraction from large climate data sets
Sweep interpolation: a cost-effective semi-Lagrangian scheme in the Global Environmental Multiscale model
CHONK 1.0: landscape evolution framework: cellular automata meets graph theory
Perspectives of physics-based machine learning strategies for geoscientific applications governed by partial differential equations
Calibration of absorbing boundary layers for geoacoustic wave modeling in pseudo-spectral time-domain methods
Parameterization and tuning of the Bay of Biscay Atlantis model v1
A comparison of Eulerian and Lagrangian methods for vertical particle transport in the water column
AutoQS v1: automatic parametrization of QuickSampling based on training images analysis
Implementation and application of ensemble optimal interpolation on an operational chemistry weather model for improving PM2.5 and visibility predictions
A dynamical core based on a discontinuous Galerkin method for higher-order finite-element sea ice modeling
GStatSim V1.0: a Python package for geostatistical interpolation and conditional simulation
Leveraging Google's Tensor Processing Units for tsunami-risk mitigation planning in the Pacific Northwest and beyond
An improved subgrid channel model with upwind-form artificial diffusion for river hydrodynamics and floodplain inundation simulation
Joshua M. Wolstenholme, Christopher J. Skinner, David Milan, Robert E. Thomas, and Daniel R. Parsons
Geosci. Model Dev., 18, 1395–1411, https://doi.org/10.5194/gmd-18-1395-2025, https://doi.org/10.5194/gmd-18-1395-2025, 2025
Short summary
Short summary
Leaky wooden dams are a type of natural flood management intervention that aims to reduce flood risk downstream by temporarily holding back water during a storm event and releasing it afterwards. These structures alter the river hydrology, and therefore the geomorphology, yet often this is excluded from numerical models. Here we show that by not simulating geomorphology, we are currently underestimating the efficacy of these structures to reduce the flood peak and store water.
Jiayi Lai, Lanning Wang, Qizhong Wu, Yizhou Yang, and Fang Wang
Geosci. Model Dev., 18, 1089–1102, https://doi.org/10.5194/gmd-18-1089-2025, https://doi.org/10.5194/gmd-18-1089-2025, 2025
Short summary
Short summary
High-performance computing limitations often hinder numerical model development. Traditional models use double precision for accuracy, which is computationally expensive. Lower precision reduces costs but can introduce errors. The quasi-double-precision (QDP) algorithm helps mitigate these errors. This study applies the QDP algorithm to the Model for Prediction Across Scales – Atmosphere, showing reduced errors and computational time, making it an efficient solution for large-scale simulations.
Marieke Wesselkamp, Matthew Chantry, Ewan Pinnington, Margarita Choulga, Souhail Boussetta, Maria Kalweit, Joschka Bödecker, Carsten F. Dormann, Florian Pappenberger, and Gianpaolo Balsamo
Geosci. Model Dev., 18, 921–937, https://doi.org/10.5194/gmd-18-921-2025, https://doi.org/10.5194/gmd-18-921-2025, 2025
Short summary
Short summary
We compared spatiotemporal forecasts of three machine learning models that learned water and energy
states on the land surface from a physical model scheme. The forecasting models were developed with reanalysis data and simulations on a European scale and transferred to the globe. We found that all approaches deliver highly accurate approximations of the physical dynamic at long time horizons, implying their usefulness to advance land surface forecasting with synthetic data.
states on the land surface from a physical model scheme. The forecasting models were developed with reanalysis data and simulations on a European scale and transferred to the globe. We found that all approaches deliver highly accurate approximations of the physical dynamic at long time horizons, implying their usefulness to advance land surface forecasting with synthetic data.
Maarten van Ormondt, Tim Leijnse, Roel de Goede, Kees Nederhoff, and Ap van Dongeren
Geosci. Model Dev., 18, 843–861, https://doi.org/10.5194/gmd-18-843-2025, https://doi.org/10.5194/gmd-18-843-2025, 2025
Short summary
Short summary
Accurate flood risk assessments are crucial for storm protection. To achieve efficiency, computational costs must be minimized. This paper introduces a novel subgrid approach for linear inertial equations (LIEs) with bed level and friction variations, implemented in the Super-Fast INundation of CoastS (SFINCS) model. Pre-processed lookup tables enhance simulation precision with lower costs. Validations show significant accuracy improvement even at coarser resolutions.
Chayan Banerjee, Kien Nguyen, Clinton Fookes, Gregory Hancock, and Thomas Coulthard
Geosci. Model Dev., 18, 803–818, https://doi.org/10.5194/gmd-18-803-2025, https://doi.org/10.5194/gmd-18-803-2025, 2025
Short summary
Short summary
In geosciences, the reliance on numerical models necessitates the precise calibration of their parameters to effectively translate information from observed to unobserved settings. We introduce a generalizable framework for calibrating numerical models, with a case study of the geomorphological model CAESAR-Lisflood. This approach efficiently identifies the optimal set of parameters for a given numerical model, enabling retrospective and prospective analyses at various temporal resolutions.
Yuta Kawai and Hirofumi Tomita
Geosci. Model Dev., 18, 725–762, https://doi.org/10.5194/gmd-18-725-2025, https://doi.org/10.5194/gmd-18-725-2025, 2025
Short summary
Short summary
When considering future high-resolution atmospheric simulations with O(10–100 m) grid spacing, such as global large-eddy simulations, numerical errors with the conventional low-order dynamical cores can contaminate the effects of turbulent parameterization. To achieve high-order discretization, we developed a global atmospheric dynamical core using the discontinuous Galerkin method (DGM). By conducting several validation tests, we discussed the impact of a high-order DGM on atmospheric flows.
Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot M. Miller, and Arvind K. Saibaba
Geosci. Model Dev., 17, 8853–8872, https://doi.org/10.5194/gmd-17-8853-2024, https://doi.org/10.5194/gmd-17-8853-2024, 2024
Short summary
Short summary
Making an informed decision about what prior information to incorporate or discard in an inverse model is important yet very challenging, as it is often not straightforward to distinguish between informative and non-informative variables. In this study, we develop a new approach for incorporating prior information in an inverse model using predictor variables, while simultaneously selecting the relevant predictor variables for the estimation of the unknown quantity of interest.
Joonlee Lee, Myong-In Lee, Sunlae Tak, Eunkyo Seo, and Yong-Keun Lee
Geosci. Model Dev., 17, 8799–8816, https://doi.org/10.5194/gmd-17-8799-2024, https://doi.org/10.5194/gmd-17-8799-2024, 2024
Short summary
Short summary
We developed an advanced snow water equivalent (SWE) data assimilation framework using satellite data based on a land surface model. The results of this study highlight the beneficial impact of data assimilation by effectively combining land surface model and satellite-derived data according to their relative uncertainty, thereby controlling not only transitional regions but also the regions with heavy snow accumulation that are difficult to detect by satellite.
Frédéric Parrenin, Marie Bouchet, Christo Buizert, Emilie Capron, Ellen Corrick, Russell Drysdale, Kenji Kawamura, Amaëlle Landais, Robert Mulvaney, Ikumi Oyabu, and Sune Olander Rasmussen
Geosci. Model Dev., 17, 8735–8750, https://doi.org/10.5194/gmd-17-8735-2024, https://doi.org/10.5194/gmd-17-8735-2024, 2024
Short summary
Short summary
The Paleochrono-1.1 probabilistic dating model allows users to derive a common and optimized chronology for several paleoclimatic sites from various archives (ice cores, speleothems, marine cores, lake cores, etc.). It combines prior sedimentation scenarios with chronological information such as dated horizons, dated intervals, stratigraphic links and (for ice cores) Δdepth observations. Paleochrono-1.1 is available under an open-source license.
Joshua Hope-Collins, Abdalaziz Hamdan, Werner Bauer, Lawrence Mitchell, and Colin Cotter
EGUsphere, https://doi.org/https://doi.org/10.48550/arXiv.2409.18792, https://doi.org/https://doi.org/10.48550/arXiv.2409.18792, 2024
Short summary
Short summary
Effectively using modern supercomputers requires massively parallel algorithms. Time-parallel algorithms calculate the system state (e.g. the atmosphere) at multiple times simultaneously and have exciting potential, but are tricky to implement and still require development. We have developed software to simplify implementing and testing the ParaDiag algorithm on supercomputers. We show that for some atmospheric problems it can enable faster or more accurate solutions than traditional techniques.
Jeffrey H. Curtis, Nicole Riemer, and Matthew West
Geosci. Model Dev., 17, 8399–8420, https://doi.org/10.5194/gmd-17-8399-2024, https://doi.org/10.5194/gmd-17-8399-2024, 2024
Short summary
Short summary
This paper introduces a numerical method for simulating particle-based aerosol transport in atmospheric models. We detail the various numerical properties of the advection order method and demonstrate its implementation in a 3D weather prediction model (WRF) for the first time. Particle-based techniques improve the accuracy of aerosol size and composition predictions, which are key for aerosol–cloud and aerosol–radiation interactions.
John Thuburn
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-153, https://doi.org/10.5194/gmd-2024-153, 2024
Revised manuscript accepted for GMD
Short summary
Short summary
A new computational fluid dynamics code for simulating the atmospheric boundary layer and convection is presented. Moist thermodynamics is formulated via thermodynamic potentials, avoiding inconsistencies that can be introduced with conventional approaches. Numerical methods typical of weather and climate models are used, with no explicit subgrid scheme. Results highlight some advantages (e.g., large time steps) and disadvantages (e.g., weak vertical fluxes near the surface) of this approach.
Matt J. Fischer
Geosci. Model Dev., 17, 6745–6760, https://doi.org/10.5194/gmd-17-6745-2024, https://doi.org/10.5194/gmd-17-6745-2024, 2024
Short summary
Short summary
In paleoclimate research, proxy system models (PSMs) model chemical or biological systems which receive environmental input and output (e.g., geochemical signals). The environmental inputs are rarely noiseless, which causes problems when calibrating multi-input PSMs. Here a PSM is developed which includes generalized noise in both model inputs and outputs and prior information. A quasi-Bayesian method enhances the stability of the solution of the Measurement Error Proxy System Model.
Gong Cheng, Mathieu Morlighem, and G. Hilmar Gudmundsson
Geosci. Model Dev., 17, 6227–6247, https://doi.org/10.5194/gmd-17-6227-2024, https://doi.org/10.5194/gmd-17-6227-2024, 2024
Short summary
Short summary
We conducted a comprehensive analysis of the stabilization and reinitialization techniques currently employed in ISSM and Úa for solving level-set equations, specifically those related to the dynamic representation of moving ice fronts within numerical ice sheet models. Our results demonstrate that the streamline upwind Petrov–Galerkin (SUPG) method outperforms the other approaches. We found that excessively frequent reinitialization can lead to exceptionally high errors in simulations.
Hugo Dominguez, Nicolas Riel, and Pierre Lanari
Geosci. Model Dev., 17, 6105–6122, https://doi.org/10.5194/gmd-17-6105-2024, https://doi.org/10.5194/gmd-17-6105-2024, 2024
Short summary
Short summary
Predicting the behaviour of magmatic systems is important for understanding Earth's matter and heat transport. Numerical modelling is a technique that can predict complex systems at different scales of space and time by solving equations using various techniques. This study tests four algorithms to find the best way to transport the melt composition. The "weighted essentially non-oscillatory" algorithm emerges as the best choice, minimising errors and preserving system mass well.
Reuben W. Nixon-Hill, Daniel Shapero, Colin J. Cotter, and David A. Ham
Geosci. Model Dev., 17, 5369–5386, https://doi.org/10.5194/gmd-17-5369-2024, https://doi.org/10.5194/gmd-17-5369-2024, 2024
Short summary
Short summary
Scientists often use models to study complex processes, like the movement of ice sheets, and compare them to measurements for estimating quantities that are hard to measure. We highlight an approach that ensures accurate results from point data sources (e.g. height measurements) by evaluating the numerical solution at true point locations. This method improves accuracy, aids communication between scientists, and is well-suited for integration with specialised software that automates processes.
Swen Metzger, Samuel Rémy, Jason E. Williams, Vincent Huijnen, and Johannes Flemming
Geosci. Model Dev., 17, 5009–5021, https://doi.org/10.5194/gmd-17-5009-2024, https://doi.org/10.5194/gmd-17-5009-2024, 2024
Short summary
Short summary
EQSAM4Clim has recently been revised to provide an accurate and efficient method for calculating the acidity of atmospheric particles. It is based on an analytical concept that is sufficiently fast and free of numerical noise, which makes it attractive for air quality forecasting. Version 12 allows the calculation of aerosol composition based on the gas–liquid–solid and the reduced gas–liquid partitioning with the associated water uptake for both cases, including the acidity of the aerosols.
Niko Schmidt, Angelika Humbert, and Thomas Slawig
Geosci. Model Dev., 17, 4943–4959, https://doi.org/10.5194/gmd-17-4943-2024, https://doi.org/10.5194/gmd-17-4943-2024, 2024
Short summary
Short summary
Future sea-level rise is of big significance for coastal regions. The melting and acceleration of glaciers plays a major role in sea-level change. Computer simulation of glaciers costs a lot of computational resources. In this publication, we test a new way of simulating glaciers. This approach produces the same results but has the advantage that it needs much less computation time. As simulations can be obtained with fewer computation resources, higher resolution and physics become affordable.
Jevgenijs Steinbuks, Yongyang Cai, Jonas Jaegermeyr, and Thomas W. Hertel
Geosci. Model Dev., 17, 4791–4819, https://doi.org/10.5194/gmd-17-4791-2024, https://doi.org/10.5194/gmd-17-4791-2024, 2024
Short summary
Short summary
This paper applies a cutting-edge numerical method, SCEQ, to show how uncertain climate change and technological progress affect the future utilization of the world's scarce land resources. The paper's key insight is to illustrate how much global cropland will expand when future crop yields are unknown. The study finds the range of outcomes for land use change to be smaller when using this novel method compared to existing deterministic models.
Gianandrea Mannarini, Mario Leonardo Salinas, Lorenzo Carelli, Nicola Petacco, and Josip Orović
Geosci. Model Dev., 17, 4355–4382, https://doi.org/10.5194/gmd-17-4355-2024, https://doi.org/10.5194/gmd-17-4355-2024, 2024
Short summary
Short summary
Ship weather routing has the potential to reduce CO2 emissions, but it currently lacks open and verifiable research. The Python-refactored VISIR-2 model considers currents, waves, and wind to optimise routes. The model was validated, and its computational performance is quasi-linear. For a ferry sailing in the Mediterranean Sea, VISIR-2 yields the largest percentage emission savings for upwind navigation. Given the vessel performance curve, the model is generalisable across various vessel types.
Soyoung Ha, Jonathan J. Guerrette, Ivette Hernández Baños, William C. Skamarock, and Michael G. Duda
Geosci. Model Dev., 17, 4199–4211, https://doi.org/10.5194/gmd-17-4199-2024, https://doi.org/10.5194/gmd-17-4199-2024, 2024
Short summary
Short summary
To mitigate the imbalances in the initial conditions, this study introduces our recent implementation of the incremental analysis update (IAU) in the Model for Prediction Across Scales – Atmospheric (MPAS-A) component coupled with the Joint Effort for Data assimilation Integration (JEDI) through the cycling system. A month-long cycling run demonstrates the successful implementation of the IAU capability in the MPAS–JEDI cycling system.
Federica Castino, Feijia Yin, Volker Grewe, Hiroshi Yamashita, Sigrun Matthes, Simone Dietmüller, Sabine Baumann, Manuel Soler, Abolfazl Simorgh, Maximilian Mendiguchia Meuser, Florian Linke, and Benjamin Lührs
Geosci. Model Dev., 17, 4031–4052, https://doi.org/10.5194/gmd-17-4031-2024, https://doi.org/10.5194/gmd-17-4031-2024, 2024
Short summary
Short summary
We introduce SolFinder 1.0, a decision-making tool to select trade-offs between different objective functions for optimal aircraft trajectories, including fuel use, flight time, NOx emissions, contrail distance, and climate impact. The module is included in the AirTraf 3.0 submodel and uses weather conditions simulated by the EMAC atmospheric model. This paper focuses on the ability of SolFinder to identify eco-efficient trajectories, reducing a flight's climate impact at limited cost penalties.
Stefania Renna, Francesco Granella, Lara Aleluia Reis, and Paulina Estela Schulz-Antipa
EGUsphere, https://doi.org/10.2139/ssrn.4591252, https://doi.org/10.2139/ssrn.4591252, 2024
Short summary
Short summary
The Country Level Air Quality Calculator (CLAQC) is a new fast modeling tool that predicts globally country-level monthly and annual concentrations of two major air pollutants, fine particulate matter (PM2.5) and tropospheric ozone (O3). It was designed to inform national and regional climate and pollution mitigation policies. It is easy to use and computationally efficient, allowing the simulation of a large number of policy scenarios for policy assessments and optimization frameworks.
Ali Dashti, Jens C. Grimmer, Christophe Geuzaine, Florian Bauer, and Thomas Kohl
Geosci. Model Dev., 17, 3467–3485, https://doi.org/10.5194/gmd-17-3467-2024, https://doi.org/10.5194/gmd-17-3467-2024, 2024
Short summary
Short summary
This study developed new meshing workflows to enable the automatic generation of meshes that follow geological models. The workflow allows for importing several geological models as input for Gmsh and later exporting the same number of high-quality meshes. This way, geological uncertainty is directly included in the numerical simulations. This study evaluates the impact of the geological uncertainty on thermohydraulic performance of two reservoirs for high-temperature heat storage applications.
Wangbin Shen, Zhaohui Lin, Zhengkun Qin, and Juan Li
Geosci. Model Dev., 17, 3447–3465, https://doi.org/10.5194/gmd-17-3447-2024, https://doi.org/10.5194/gmd-17-3447-2024, 2024
Short summary
Short summary
In this study, a land surface image assimilation system capable of optimizing the spatial structure of the background field is constructed by introducing the curvelet analysis method and taking the similarity of image structure as a weak constraint. The findings demonstrate that the assimilation of surface soil moisture observation images effectively and reasonably enhances the spatial structure of soil moisture analysis field.
Luan Carlos de Sena Monteiro Ozelim, Michéle Dal Toé Casagrande, and André Luís Brasil Cavalcante
Geosci. Model Dev., 17, 3175–3197, https://doi.org/10.5194/gmd-17-3175-2024, https://doi.org/10.5194/gmd-17-3175-2024, 2024
Short summary
Short summary
The paper addresses synthetic dataset challenges in nonlinear constitutive modeling of soils, providing two datasets: one with 2000 soil types, 40 test conditions each (160 000 triaxial tests), and a second with 2048 soil types, 42 test conditions each (172 032 triaxial tests). Each dataset is a 4000×10 matrix applicable for multivariate forecasting and geotechnical simulations. In addition, a new Python code is introduced, empowering researchers to leverage Python packages for NorSand analyses.
Daniel Giles, Matthew M. Graham, Mosè Giordano, Tuomas Koskela, Alexandros Beskos, and Serge Guillas
Geosci. Model Dev., 17, 2427–2445, https://doi.org/10.5194/gmd-17-2427-2024, https://doi.org/10.5194/gmd-17-2427-2024, 2024
Short summary
Short summary
Digital twins of physical and human systems informed by real-time data are becoming ubiquitous across a wide range of settings. Progress for researchers is currently limited by a lack of tools to run these models effectively and efficiently. A key challenge is the optimal use of high-performance computing environments. The work presented here focuses on a developed open-source software platform which aims to improve this usage, with an emphasis placed on flexibility, efficiency, and scalability.
Stefan J. Miller, Paul A. Makar, and Colin J. Lee
Geosci. Model Dev., 17, 2197–2219, https://doi.org/10.5194/gmd-17-2197-2024, https://doi.org/10.5194/gmd-17-2197-2024, 2024
Short summary
Short summary
This work outlines a new solver written in Fortran to calculate the partitioning of metastable aerosols at thermodynamic equilibrium based on the forward algorithms of ISORROPIA II. The new code includes numerical improvements that decrease the computational speed (compared to ISORROPIA II) while improving the accuracy of the partitioning solution.
Fernanda Alvarado-Neves, Laurent Ailleres, Lachlan Grose, Alexander R. Cruden, and Robin Armit
Geosci. Model Dev., 17, 1975–1993, https://doi.org/10.5194/gmd-17-1975-2024, https://doi.org/10.5194/gmd-17-1975-2024, 2024
Short summary
Short summary
Previous work has demonstrated that adding geological knowledge to modelling methods creates more accurate and reliable models. Following this reasoning, we added constraints from magma emplacement mechanisms into existing modelling frameworks to improve the 3D characterisation of igneous intrusions. We tested the method on synthetic and real-world case studies, and the results show that our method can reproduce intrusion morphologies with no manual processing and using realistic datasets.
André R. Brodtkorb, Anna Benedictow, Heiko Klein, Arve Kylling, Agnes Nyiri, Alvaro Valdebenito, Espen Sollum, and Nina Kristiansen
Geosci. Model Dev., 17, 1957–1974, https://doi.org/10.5194/gmd-17-1957-2024, https://doi.org/10.5194/gmd-17-1957-2024, 2024
Short summary
Short summary
It is vital to know the extent and concentration of volcanic ash in the atmosphere during a volcanic eruption. Whilst satellite imagery may give an estimate of the ash right now (assuming no cloud coverage), we also need to know where it will be in the coming hours. This paper presents a method for estimating parameters for a volcanic eruption based on satellite observations of ash in the atmosphere. The software package is open source and applicable to similar inversion scenarios.
Kees Nederhoff, Maarten van Ormondt, Jay Veeramony, Ap van Dongeren, José Antonio Álvarez Antolínez, Tim Leijnse, and Dano Roelvink
Geosci. Model Dev., 17, 1789–1811, https://doi.org/10.5194/gmd-17-1789-2024, https://doi.org/10.5194/gmd-17-1789-2024, 2024
Short summary
Short summary
Forecasting tropical cyclones and their flooding impact is challenging. Our research introduces the Tropical Cyclone Forecasting Framework (TC-FF), enhancing cyclone predictions despite uncertainties. TC-FF generates global wind and flood scenarios, valuable even in data-limited regions. Applied to cases like Cyclone Idai, it showcases potential in bettering disaster preparation, marking progress in handling cyclone threats.
Younghun Kang and Ethan J. Kubatko
Geosci. Model Dev., 17, 1603–1625, https://doi.org/10.5194/gmd-17-1603-2024, https://doi.org/10.5194/gmd-17-1603-2024, 2024
Short summary
Short summary
Models used to simulate the flow of coastal and riverine waters, including flooding, require a geometric representation (or mesh) of geographic features that exhibit a range of disparate spatial scales from large, open waters to small, narrow channels. Representing these features in an accurate way without excessive computational overhead presents a challenge. Here, we develop an automatic mesh generation tool to help address this challenge. Our results demonstrate the efficacy of our approach.
Hui Wan, Kai Zhang, Christopher J. Vogl, Carol S. Woodward, Richard C. Easter, Philip J. Rasch, Yan Feng, and Hailong Wang
Geosci. Model Dev., 17, 1387–1407, https://doi.org/10.5194/gmd-17-1387-2024, https://doi.org/10.5194/gmd-17-1387-2024, 2024
Short summary
Short summary
Sophisticated numerical models of the Earth's atmosphere include representations of many physical and chemical processes. In numerical simulations, these processes need to be calculated in a certain sequence. This study reveals the weaknesses of the sequence of calculations used for aerosol processes in a global atmosphere model. A revision of the sequence is proposed and its impacts on the simulated global aerosol climatology are evaluated.
Christopher J. Vogl, Hui Wan, Carol S. Woodward, and Quan M. Bui
Geosci. Model Dev., 17, 1409–1428, https://doi.org/10.5194/gmd-17-1409-2024, https://doi.org/10.5194/gmd-17-1409-2024, 2024
Short summary
Short summary
Generally speaking, accurate climate simulation requires an accurate evolution of the underlying mathematical equations on large computers. The equations are typically formulated and evolved in process groups. Process coupling refers to how the evolution of each group is combined with that of other groups to evolve the full set of equations for the whole atmosphere. This work presents a mathematical framework to evaluate methods without the need to first implement the methods.
Tom Keel, Chris Brierley, and Tamsin Edwards
Geosci. Model Dev., 17, 1229–1247, https://doi.org/10.5194/gmd-17-1229-2024, https://doi.org/10.5194/gmd-17-1229-2024, 2024
Short summary
Short summary
Jet streams are an important control on surface weather as their speed and shape can modify the properties of weather systems. Establishing trends in the operation of jet streams may provide some indication of the future of weather in a warming world. Despite this, it has not been easy to establish trends, as many methods have been used to characterise them in data. We introduce a tool containing various implementations of jet stream statistics and algorithms that works in a standardised manner.
Amir Golparvar, Matthias Kästner, and Martin Thullner
Geosci. Model Dev., 17, 881–898, https://doi.org/10.5194/gmd-17-881-2024, https://doi.org/10.5194/gmd-17-881-2024, 2024
Short summary
Short summary
Coupled reaction transport modelling is an established and beneficial method for studying natural and synthetic porous material, with applications ranging from industrial processes to natural decompositions in terrestrial environments. Up to now, a framework that explicitly considers the porous structure (e.g. from µ-CT images) for modelling the transport of reactive species is missing. We presented a model that overcomes this limitation and represents a novel numerical simulation toolbox.
Stefan Hergarten
Geosci. Model Dev., 17, 781–794, https://doi.org/10.5194/gmd-17-781-2024, https://doi.org/10.5194/gmd-17-781-2024, 2024
Short summary
Short summary
The Voellmy rheology has been widely used for simulating snow and rock avalanches. Recently, a modified version of this rheology was proposed, which turned out to be able to predict the observed long runout of large rock avalanches theoretically. The software MinVoellmy presented here is the first numerical implementation of the modified rheology. It consists of MATLAB and Python classes, where simplicity and parsimony were the design goals.
Arjun Babu Nellikkattil, Danielle Lemmon, Travis Allen O'Brien, June-Yi Lee, and Jung-Eun Chu
Geosci. Model Dev., 17, 301–320, https://doi.org/10.5194/gmd-17-301-2024, https://doi.org/10.5194/gmd-17-301-2024, 2024
Short summary
Short summary
This study introduces a new computational framework called Scalable Feature Extraction and Tracking (SCAFET), designed to extract and track features in climate data. SCAFET stands out by using innovative shape-based metrics to identify features without relying on preconceived assumptions about the climate model or mean state. This approach allows more accurate comparisons between different models and scenarios.
Mohammad Mortezazadeh, Jean-François Cossette, Ashu Dastoor, Jean de Grandpré, Irena Ivanova, and Abdessamad Qaddouri
Geosci. Model Dev., 17, 335–346, https://doi.org/10.5194/gmd-17-335-2024, https://doi.org/10.5194/gmd-17-335-2024, 2024
Short summary
Short summary
The interpolation process is the most computationally expensive step of the semi-Lagrangian (SL) approach. In this paper we implement a new interpolation scheme into the semi-Lagrangian approach which has the same computational cost as a third-order polynomial scheme but with the accuracy of a fourth-order interpolation scheme. This improvement is achieved by using two third-order backward and forward polynomial interpolation schemes in two consecutive time steps.
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
Short summary
Short summary
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.
Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendricks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann
Geosci. Model Dev., 16, 7375–7409, https://doi.org/10.5194/gmd-16-7375-2023, https://doi.org/10.5194/gmd-16-7375-2023, 2023
Short summary
Short summary
In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.
Carlos Spa, Otilio Rojas, and Josep de la Puente
Geosci. Model Dev., 16, 7237–7252, https://doi.org/10.5194/gmd-16-7237-2023, https://doi.org/10.5194/gmd-16-7237-2023, 2023
Short summary
Short summary
This paper develops a calibration methodology of all absorbing techniques typically used by Fourier pseudo-spectral time-domain (PSTD) methods for geoacoustic wave simulations. The main contributions of the paper are (a) an implementation and quantitative comparison of all absorbing techniques available for PSTD methods through a simple and robust numerical experiment, and (b) a validation of these absorbing techniques in several 3-D seismic scenarios with gradual heterogeneity complexities.
Ane Lopez de Gamiz-Zearra, Cecilie Hansen, Xavier Corrales, Iñaki Quincoces, Izaskun Preciado, and Eider Andonegi
EGUsphere, https://doi.org/10.5194/egusphere-2023-1368, https://doi.org/10.5194/egusphere-2023-1368, 2023
Short summary
Short summary
This paper describes the development of the first calibrated end-to-end Atlantis model for the Bay of Biscay that will help us improve the comprehension of the spatial functioning of the Bay of Biscay ecosystem and help establishing management measures of human activities. Our results highlighted the importance of lower trophic levels to the pelagic system and demonstrate the importance of having accurate and precise data for biological processes.
Tor Nordam, Ruben Kristiansen, Raymond Nepstad, Erik van Sebille, and Andy M. Booth
Geosci. Model Dev., 16, 5339–5363, https://doi.org/10.5194/gmd-16-5339-2023, https://doi.org/10.5194/gmd-16-5339-2023, 2023
Short summary
Short summary
We describe and compare two common methods, Eulerian and Lagrangian models, used to simulate the vertical transport of material in the ocean. They both solve the same transport problems but use different approaches for representing the underlying equations on the computer. The main focus of our study is on the numerical accuracy of the two approaches. Our results should be useful for other researchers creating or using these types of transport models.
Mathieu Gravey and Grégoire Mariethoz
Geosci. Model Dev., 16, 5265–5279, https://doi.org/10.5194/gmd-16-5265-2023, https://doi.org/10.5194/gmd-16-5265-2023, 2023
Short summary
Short summary
Multiple‐point geostatistics are widely used to simulate complex spatial structures based on a training image. The use of these methods relies on the possibility of finding optimal training images and parametrization of the simulation algorithms. Here, we propose finding an optimal set of parameters using only the training image as input. The main advantage of our approach is to remove the risk of overfitting an objective function.
Siting Li, Ping Wang, Hong Wang, Yue Peng, Zhaodong Liu, Wenjie Zhang, Hongli Liu, Yaqiang Wang, Huizheng Che, and Xiaoye Zhang
Geosci. Model Dev., 16, 4171–4191, https://doi.org/10.5194/gmd-16-4171-2023, https://doi.org/10.5194/gmd-16-4171-2023, 2023
Short summary
Short summary
Optimizing the initial state of atmospheric chemistry model input is one of the most essential methods to improve forecast accuracy. Considering the large computational load of the model, we introduce an ensemble optimal interpolation scheme (EnOI) for operational use and efficient updating of the initial fields of chemical components. The results suggest that EnOI provides a practical and cost-effective technique for improving the accuracy of chemical weather numerical forecasts.
Thomas Richter, Véronique Dansereau, Christian Lessig, and Piotr Minakowski
Geosci. Model Dev., 16, 3907–3926, https://doi.org/10.5194/gmd-16-3907-2023, https://doi.org/10.5194/gmd-16-3907-2023, 2023
Short summary
Short summary
Sea ice covers not only the pole regions but affects the weather and climate globally. For example, its white surface reflects more sunlight than land. The oceans around the poles are therefore kept cool, which affects the circulation in the oceans worldwide. Simulating the behavior and changes in sea ice on a computer is, however, very difficult. We propose a new computer simulation that better models how cracks in the ice change over time and show this by comparing to other simulations.
Emma J. MacKie, Michael Field, Lijing Wang, Zhen Yin, Nathan Schoedl, Matthew Hibbs, and Allan Zhang
Geosci. Model Dev., 16, 3765–3783, https://doi.org/10.5194/gmd-16-3765-2023, https://doi.org/10.5194/gmd-16-3765-2023, 2023
Short summary
Short summary
Earth scientists often have to fill in spatial gaps in measurements. This gap-filling or interpolation can be accomplished with geostatistical methods, where the statistical relationships between measurements are used to inform how these gaps should be filled. Despite the broad utility of these methods, there are few freely available geostatistical software applications. We present GStatSim, a Python package for performing different geostatistical interpolation methods.
Ian Madden, Simone Marras, and Jenny Suckale
Geosci. Model Dev., 16, 3479–3500, https://doi.org/10.5194/gmd-16-3479-2023, https://doi.org/10.5194/gmd-16-3479-2023, 2023
Short summary
Short summary
To aid risk managers who may wish to rapidly assess tsunami risk but may lack high-performance computing infrastructure, we provide an accessible software package able to rapidly model tsunami inundation over real topography by leveraging Google's Tensor Processing Unit, a high-performance hardware. Minimally trained users can take advantage of the rapid modeling abilities provided by this package via a web browser thanks to the ease of use of Google Cloud Platform.
Youtong Rong, Paul Bates, and Jeffrey Neal
Geosci. Model Dev., 16, 3291–3311, https://doi.org/10.5194/gmd-16-3291-2023, https://doi.org/10.5194/gmd-16-3291-2023, 2023
Short summary
Short summary
A novel subgrid channel (SGC) model is developed for river–floodplain modelling, allowing utilization of subgrid-scale bathymetric information while performing computations on relatively coarse grids. By including adaptive artificial diffusion, potential numerical instability, which the original SGC solver had, in low-friction regions such as urban areas is addressed. Evaluation of the new SGC model through structured tests confirmed that the accuracy and stability have improved.
Cited articles
Atzmon, M. and Lipman, Y.: Sal: Sign agnostic learning of shapes from raw data, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 2565–2574, https://doi.org/10.1109/CVPR42600.2020.00264, 2020.
Bédard, K., Marsh, A., Hillier, M., Music, T.: 3D geological model of the Western Canadian Sedimentary Basin in Saskatchewan, Canada, Geological Survey of Canada, Open File 8969, https://doi.org/10.4095/331747, 2023.
Bi, Z., Wu, X., Geng, Z., and Li, H.: Deep relative geologic time: a deep learning method for simultaneously interpreting 3- D seismic horizons and faults, J. Geophys. Res.-Sol. Ea., 126, e2021JB021882, https://doi.org/10.1029/2021JB021882, 2021.
Bi, Z., Wu, X., Li, Z., Chang, D., and Yong, X.: DeepISMNet: three-dimensional implicit structural modeling with convolutional neural network, Geosci. Model Dev., 15, 6841–6861, https://doi.org/10.5194/gmd-15-6841-2022, 2022.
Boisvert, J. B., Manchuk, J. G., and Deutsch, C. V.: Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances, Math. Geosci., 41, 585–601, https://doi.org/10.1007/s11004-009-9229-1, 2009.
Calcagno, P., Chilès, J. P., Courrioux, G., and Guillen, A.: Geological modelling from field data and geological knowledge: part I. Modelling method coupling 3D potential-field interpolation and geological rules, Phys. Earth Planet. Int., 171, 147–157, https://doi.org/10.1016/j.pepi.2008.06.013, 2008.
Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., and Evans, T. R.: Reconstruction and representation of 3D objects with radial basis functions, in: ACM SIGGRAPH 2001, Computer graphics proceedings. ACM Press, New York, 67–76, https://doi.org/10.1145/383259.383266, 2001.
Caumon, G.: Towards stochastic time-varying geological modeling, Math. Geosci., 42, 555–569, https://doi.org/10.1007/s11004-010-9280-y, 2010.
Caumon, G., Collon-Drouaillet P., Carlier Le de Veslud, C., Viseur, S., and Sausse, J.: Surface-based 3D modelling of geological structures, Math. Geosci., 41, 927–945, https://doi.org/10.1007/s11004-009-9244-2, 2009.
Caumon, G., Gray, G., Antoine, C., and Titeux, M.-O.: Three-Dimensional Implicit Stratigraphic Model Building From Remote Sensing Data on Tetrahedral Meshes: Theory and Application to a Regional Model of La Popa Basin, NE Mexico, IEEE T. Geosci. Remote, 51, 1613–1621, https://doi.org/10.1109/TGRS.2012.2207727, 2012.
Cowan, E., Beatson, R., Ross, H., Fright, W., McLennan, T., Evans, T., Carr, J., Lane, R., Bright, D., Gillman, A., Oshust, P., and Titley, M.: Practical implicit geological modelling, 5th Int. Min. Geol. Conf., 8, 89–99, 2003.
Davies, T., Nowrouzezahrai, D., and Jacobson, A.: On the Effectiveness of Weight-Encoded Neural Implicit 3D Shapes, arXiv [preprint], https://doi.org/10.48550/arXiv.2009.09808,17 January 2021.
de Kemp, E. A., Corrigan, D., St-Onge, M. R.: Evaluating the potential for three-dimensional structural modelling of the Archean and Paleoproterozoic rocks of central Baffin Island, Nunavut, Geological Survey of Canada, Current Research, 2001-C24, 22, https://doi.org/10.4095/212255, 2001.
de Kemp, E. A. and Sprague, K. B.: Interpretive Tools for 3-D Structural Geological Modeling Part I: Bézier-Based Curves, Ribbons and Grip Frames, Geoinformatica 7, 55–71, https://doi.org/10.1023/A:1022822227691, 2003.
de Kemp, E. A., Jessell, M. W., Aillères, L., Schetselaar, E. M., Hillier, M., Lindsay, M. D., and Brodaric, B.: Earth model construction in challenging geologic terrain: Designing workflows and algorithms that makes sense, in: Proceedings of Exploration'17: Sixth DMEC – Decennial International Conference on Mineral Exploration, edited by: Tschirhart, V. and Thomas, M. D., Integrating the Geosciences: The Challenge of Discovery, Toronto, Canada, 21–25 October 2017, 419–439, 2017.
de la Varga, M. and Wellmann, F.: Structural geologic modeling as an inference problem: a Bayesian perspective, Interpretation, 4, 1–16, https://doi.org/10.1190/INT-2015-0188.1, 2016.
de la Varga, M., Schaaf, A., and Wellmann, F.: GemPy 1.0: open-source stochastic geological modeling and inversion, Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, 2019.
Dubrule, O. and Kostov, C.: An interpolation method taking into account inequality constraints: I. Methodology, Math. Geosci., 18, 33–51, https://doi.org/10.1007/BF00897654, 1986.
Emmert-Streib, F., Yang, Z., Feng, H., Tripathi, S., and Dehmer, M.: An introductory review of deep learning for prediction models with big data, Fr. Art. Int., 3, 4, https://doi.org/10.3389/frai.2020.00004, 2020.
Frank, T., Tertois, A.-L. L., and Mallet, J.-L. L.: 3D-reconstruction of complex geological interfaces from irregularly distributed and noisy point data, Comput. Geosci., 33, 932–943, https://doi.org/10.1016/j.cageo.2006.11.014, 2007.
Glorot, X. and Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks, in: Proceedings of the thirteenth international conference on artificial intelligence and statistics, 249–256, http://proceedings.mlr.press/v9/glorot10a.html (last access: 17 November 2023), 2010.
Gonçalves, Í. G., Kumaira, S., and Guadagnin, F.: A machine learning approach to the potential-field method for implicit modeling of geological structures, Comput. Geosci., 103, 173–182, https://doi.org/10.1016/j.cageo.2017.03.015, 2017.
Gropp, A., Yariv, L., Haim, N., Atzmon, M., and Lipman, Y.: Implicit geometric regularization for learning shapes, arXiv [preprint], https://doi.org/10.48550/arXiv.2002.10099, 9 July 2020.
Grose, L., Ailleres, L., Laurent, G., Armit, R., and Jessell, M.: Inversion of geological knowledge for fold geometry, J. Struct. Geol., 119, 1–14, https://doi.org/10.1016/j.jsg.2018.11.010, 2019.
Grose, L., Ailleres, L., Laurent, G., Caumon, G., Jessell, M., and Armit, R.: Modelling of faults in LoopStructural 1.0, Geosci. Model Dev., 14, 6197–6213, https://doi.org/10.5194/gmd-14-6197-2021, 2021a.
Grose, L., Ailleres, L., Laurent, G., and Jessell, M.: LoopStructural 1.0: time-aware geological modelling, Geosci. Model Dev., 14, 3915–3937, https://doi.org/10.5194/gmd-14-3915-2021, 2021b.
He, K., Zhang, X., Ren, S., and Sun, J.: Delving deep into rectifiers: Surpassing human-level performance on imagenet classification, in: Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile, 1026–1034, https://doi.org/10.1109/ICCV.2015.123, 2015.
Hillier, M. J., Schetselaar, E. M., de Kemp, E. A., and Perron, G.: Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions, Math. Geosci., 46, 931–951, https://doi.org/10.1007/s11004-014-9540-3, 2014.
Hillier, M., de Kemp, E. A., and Schetselaar, E. M.: Implicitly modelled stratigraphic surfaces using generalized interpolation, in: AIP conference proceedings, 1738, 050004, International Conference of Numerical Analysis and Applied Mathematics, 22–28 September 2015, Rhodes, Greece, https://doi.org/10.1063/1.4951819, 2016.
Hillier, M., Wellmann, F., Brodaric, B., de Kemp, E. A., and Schetselaar, E.: Three-Dimensional Structural Geological Modeling Using Graph Neural Networks, Math. Geosci., 53, 1725–1749, https://doi.org/10.1007/s11004-021-09945-x, 2021.
Hillier, M., Wellmann, F., de Kemp, E. A., Brodaric, B., Schetselaar, E., and Bédard, K.: MichaelHillier/GeoINR: GeoINR 1.0: an implicit neural network approach to three-dimensional geological modelling, Zenodo [code and data set], https://doi.org/10.5281/zenodo.8352541, 2023.
Hornik, K., Stinchcombe, M., and White, H.: Multilayer feedforward networks are universal approximators, Neural Networks, 2, 359–366, https://doi.org/10.1016/0893-6080(89)90020-8, 1989.
Irakarama, M., Laurent, G., Renaudeau, J., and Caumon G.: Finite Difference Implicit Structural Modeling of Geological Structures, Math. Geosci. 53, 785–808, https://doi.org/10.1007/s11004-020-09887-w, 2021.
Jacot, A., Gabriel, F., and Hongler, C.: Neural tangent kernel: Convergence and generalization in neural networks, arXiv [preprint], https://doi.org/10.48550/arXiv.1806.07572, 10 February 2020.
Jessell, M. W., Ailleres, L., and de Kemp, E. A.: Towards an integrated inversion of geoscientific data: What price of geology?, Tectonophysics, 490, 294–306, https://doi.org/10.1016/j.tecto.2010.05.020, 2010.
Kirkwood, C., Economou, T., Pugeault, N., and Odbert, H.: Bayesian Deep Learning for Spatial Interpolation in the Presence of Auxiliary Information, Math. Geosci., 54, 507–531, https://doi.org/10.1007/s11004-021-09988-0, 2022
Lajaunie, C., Courrioux, G., and Manuel, L.: Foliation fields and 3D cartography in geology; principles of a method based on potential interpolation, Math. Geol., 29, 571–584, https://doi.org/10.1007/BF02775087, 1997.
Laurent, G., Ailleres, L., Grose, L., Caumon, G., Jessell, M., and Armit, R.: Implicit modeling of folds and overprinting deformation, Earth Planet. Sc. Lett., 456, 26–38, https://doi.org/10.1016/j.epsl.2016.09.040, 2016.
Li, H., Xu, Z., Taylor, G., Studer, C., and Goldstein, T.: Visualizing the loss landscape of neural nets, arXiv [preprint], https://doi.org/10.48550/arXiv.1712.09913, 7 November 2018.
Liaw, R., Liang, E., Nishihara, R., Moritz, P., Gonzalez, J. E., and Stoica, I.: Tune: A research platform for distributed model selection and training, arXix [preprint], https://doi.org/10.48550/arXiv.1807.05118, 13 July 2018.
Lindsay, M. D., Aillères, L., Jessel, M. W., de Kemp, E. A., and Betts, P. G.: Locating and quantifying geological uncertainty in three-dimensional models: Analysis of the Gippsland Basin, southeastern Australia, Technophysics, 546, 10–27, https://doi.org/10.1016/j.tecto.2012.04.007, 2012.
Llanas, B., Lantarón, S., and Sáinz, F. J.: Constructive Approximation of Discontinuous Functions by Neural Networks, Neural Process. Lett., 27, 209–226, https://doi.org/10.1007/s11063-007-9070-9, 2008.
Loshchilov, I. and Hutter, F.: Decoupled weight decay regularization, arXix [preprint], https://doi.org/10.48550/arXiv.1711.05101, 4 January 2017.
Ma, L., Liu, Y., Zhang, X., Ye, Y., Yin, G., and Johnson, B. A.: Deep learning in remote sensing applications: A meta-analysis and review, ISPRS J. Photogramm., 152, 166–177, https://doi.org/10.1016/j.isprsjprs.2019.04.015, 2019.
Mallet, J.-L.: Discrete smooth interpolation in geometric modelling, Computer-Aided Design, 24, 178–191, https://doi.org/10.1016/0010-4485(92)90054-E, 1992.
Mallet, J.-L.: Discrete modeling for natural objects, Math. Geol., 29, 199–219, https://doi.org/10.1007/BF02769628, 1997.
March, A. and Love, M.: Regional Stratigraphic Framework of the Phanerozoic in Saskatchewan; Saskatchewan Phanerozoic Fluids and Petroleum Systems Project; Sask. Ministry of the Economy, Saskatchewan Geological Survey, Open File 2014-1, https://publications.saskatchewan.ca/#/products/79907 (last access: 17 November 2023), 2014.
Mildenhall, B., Srinivasan, P. P., Tancik, M., Barron, J. T., Ramamoorthi, R., and Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis, Commun. ACM, 65, 99–106, https://doi.org/10.1145/3503250, 2021.
Park, J. J., Florence, P., Straub, J., Newcombe, R., and Lovegrove, S.: DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 165–174, https://openaccess.thecvf.com/content_CVPR_2019/html/Park_DeepSDF_Learning_Continuous_Signed_Distance_Functions_for_Shape_Representation_CVPR_2019_paper.html (last access: 17 November 2023), 2019.
Perol, T., Gharbi, M., and Denolle, M.: Convolutional neural network for earthquake detection and location, Sci. Adv., 4, e1700578, https://doi.org/10.1126/sciadv.1700578, 2018.
Pizzella, L., Alais, R., Lopez, S., Freulon X., and Rivoirard, J.: Taking Better Advantage of Fold Axis Data to Characterize Anisotropy of Complex Folded Structures in the Implicit Modeling Framework, Math. Geosci., 54, 95–130, https://doi.org/10.1007/s11004-021-09950-0, 2022.
Renaudeau, J., Malvesin, E., Maerten, F., and Caumon, G.: Implicit Structural Modeling by Minimization of the Bending Energy with Moving Least Squares Functions, Math. Geosci., 51, 693–724, https://doi.org/10.1007/s11004-019-09789-6, 2019.
Rodríguez, J. D., Pérez, A., and Lozano, J. A.: Sensitivity Analysis of k-Fold Cross Validation in Prediction Error Estimation, IEEE T. Pattern Anal., 32, 569–575, https://doi.org/10.1109/TPAMI.2009.187, 2009.
Ross, Z. E., Meier, M. A., and Hauksson E.: P Wave Arrival Picking and First-Motion Polarity Determination With Deep Learning, J. Geophys. Res.-Sol., 123, 5120–2129, https://doi.org/10.1029/2017JB015251, 2018.
Santa, F. D. and Pieraccini, S.: Discontinuous neural networks and discontinuity learning, J. Comput. Appl. Math., 419, 114678, https://doi.org/10.1016/j.cam.2022.114678, 2023.
Scott, D. J., St-Onge, M. R., and Corrigan, D.: Geology, Dewar Lakes, Nunavut, Geological Survey of Canada, Open File 4201, 2 sheets; 1 CD-ROM, map: scale 1:100000, https://doi.org/10.4095/213226, 2002.
Shi, Y., Wu, X., and Fomel, S.: SaltSeg: Automatic 3D salt segmentation using a deep convolutional neural network, Interpretation, 7, SE113–SE122, https://doi.org/10.1190/INT-2018-0235.1, 2019.
Shi, C. and Wang, Y.: Non-parametric machine learning methods for interpolation of spatially varying non-stationary and non-Gaussian geotechnical properties, Geosci. Front., 12, 339–350, https://doi.org/10.1016/j.gsf.2020.01.011, 2021
Sides, E. J.: Geological modelling of mineral deposits for prediction in mining, Geol. Rundsch., 86, 342–353, https://doi.org/10.1007/s005310050145, 1997.
Sitzmann, V., Martel, J., Bergman, A., Lindell, D., and Wetzstein, G.: Implicit Neural Representations with Periodic Activation Functions, Adv. Neur. In., 33, 7462–7473, 2020.
Sprague, K. B. and de Kemp, E. A.: Interpretive Tools for 3-D Structural Geological Modelling part II: Surface Design from Sparse Spatial Data, GeoInformatica 9, 5–32, https://doi.org/10.1007/s10707-004-5620-8, 2005.
St-Charles, P. -L., Rousseau, B., Ghosn, J., Nantel J.-P, Bellefleur, G., and Schetselaar, E.: A Multi-Survey Dataset and Benchmark for First Break Picking in Hard Rock Seismic Exploration, in: Proc. Neurips 2021 Workshop on Machine Learning for the Physical Sciences (ML4PS), https://ml4physicalsciences.github.io/2021/files/NeurIPS_ML4PS_2021_3.pdf (last access: 17 November 2023), 2021.
St-Onge, M. R., Scott, D. J., and Corrigan, D.: Geology, Straits Bay, Nunavut, Geological Survey of Canada, Open File 4200, map: scale 1:100000, https://doi.org/10.4095/213225, 2002.
Sullivan, C. B. and Kaszynski, A. A.: PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK), J. Open Source Softwa., 4, 1450, https://doi.org/10.21105/joss.01450, 2019.
Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., and Ng, R.: Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains, arXiv [preprint], https://doi.org/10.48550/arXiv.2006.10739, 18 June 2020.
Taubin, G.: Distance approximations for rasterizing implicit curves, ACM T. Graphic., 13, 3-42, https://doi.org/10.1145/174462.174531, 1994.
von Harten, J., de la Varga, M., Hillier, M., and Wellmann, F.: Informed Local Smoothing in 3D Implicit Geological Modeling, Minerals, 11, 1281, https://doi.org/10.3390/min11111281, 2021.
Wang, D. and Chen, G.: Seismic Stratum Segmentation Using an Encoder-Decoder Convolutional Neural Network, Math. Geo., 53, 1355–1374, https://doi.org/10.1007/s11004-020-09916-8, 2021.
Wang, P. S., Liu, Y., Yang, Y. Q., and Tong, X.: Spline positional encoding for learning 3d implicit signed distance fields, arXiv [preprint], https://doi.org/10.48550/arXiv.2106.01553, 28 October 2021.
Wang, S., Cai, Z., Si, X., and Cui, Y.: A Three-Dimensional Geological Structure Modeling Framework and Its Application in Machine Learning, Math. Geosci., 55, 163–200, https://doi.org/10.1007/s11004-022-10027-9, 2022.
Wellmann, F. and Caumon, G.: 3-D Structural geological models: Concepts, methods, and uncertainties, Adv. Geophys., 59, 1–121, https://doi.org/10.1016/bs.agph.2018.09.001, 2018.
Wellmann, J. F. and Regenauer-Lieb, K.: Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models, Technophysics, 526, 207–216, https://doi.org/10.1016/j.tecto.2011.05.001 , 2012.
Wu, X., Liang, L., Shi, Y., and Fomel, S.: FaultSeg3D: using synthetic datasets to train an end-to-end convolutional neural network for 3D seismic fault segmentation, Geophysics, 84, IM35– IM45, https://doi.org/10.1190/geo2018-0646.1, 2019.
Wu, Y., Lin, Y., Zhou, Z., Bolton, D. C., Liu, J., and Johnson, P.: DeepDetect: A cascaded region-based densely connected network for seismic event detection, IEEE T. Geosci. Remote, 57, 62–75, https://doi.org/10.1109/TGRS.2018.2852302, 2018.
Yang, L., Hyde, D., Grujic, O., Scheidt, C., and Caers, J.: Assessing and visualizing uncertainty of 3D geological surfaces using level sets with stochastic motion, Comput. Geosci., 122, 54–67, https://doi.org/10.1016/j.cageo.2018.10.006, 2019.
Zhuang, F., Qi, Z., Duan, K., Xi, D., Zhu, Y., Zhu, H., Xiong, H., and He, Q.: A Comprehensive Survey on Transfer Learning, Proc. IEEE, 109, 43–76, https://doi.org/10.1109/JPROC.2020.3004555, 2021.
Short summary
Neural networks can be used effectively to model three-dimensional geological structures from point data, sampling geological interfaces, units, and structural orientations. Existing neural network approaches for this type of modelling are advanced by the efficient incorporation of unconformities, new knowledge inputs, and improved data fitting techniques. These advances permit the modelling of more complex geology in diverse geological settings, different-sized areas, and various data regimes.
Neural networks can be used effectively to model three-dimensional geological structures from...
