Selected Publications


3-D Structural geological models: Concepts, methods, and uncertainties

structural geological model Copyright: © G. Caumon

Florian Wellmann and Guillaume Caumon (2018)

Our new review paper on “3-D Structural geological models: Concepts, methods, and uncertainties” has been published in the 2018 volume of “Advances in Geophysics”!

In this review paper, Florian Wellmann and Guillaume Caumon (Universitée de Lorraine, France) provide a detailed overview of the current state of 3-D geological modelling approaches, conceptual aspects of uncertainties in these models, and techniques to quantify them. With more than 100 pages and almost 400 references, we hope to cover many important aspects and describe relevant contributions to this field (without any claim of completeness - for such an extensive topic).

For more information, please visit the sciencedirect website. An open preprint version of the paper is also available.


An Explanation to the Nusselt–Rayleigh Discrepancy in Naturally Convected Porous Media

Copyright: © CGRE

Po-Wei Huang and Florian Wellmann (2021)

We model hydrothermal convection using a partial differential equation formed by Darcy velocity and temperature—the velocity formulation. Using the Elder problem as a bench- mark, we found that the velocity formulation is a valid model of hydrothermal convection. By performing simulations with Rayleigh numbers in the non-oscillatory regime, we show that multiple quasi-steady-state solutions can be one of the reasons that caused the Nusselt–Rayleigh discrepancy found in previous experiments. The results reveal more understandings about the nature of uncertainty of convection modes in porous media.

Publication available as open-access on the Transport in Porous Media website.


From Google Earth to 3D Geology Problem 2: Seeing Below the Surface of the Digital Earth

Google Earth to Geology Copyright: © CGRE

Florian Wellmann, Alexander Schaaf, Miguel de la Varga, Christoph von Hagke (2019)

The visualization of structural features in a three-dimensional (3D) context is an essential aspect of geological understanding—both implicit in the context of imagination and explicit in the form of generated 3D geometric models. Still, this understanding and intuition does not come naturally to all students, and we aim a lot of effort in teaching structural geology at the development of this understanding. In this project and teaching module, we strive to support this aim with an exercise to generate a 3D geological model directly out of combined satellite images and digital ele- vation models (DEMs) as an aid to answering geological questions. This method is technically possible on the basis of all programs that provide access to, and interaction with, these types of data. We make use here of the excellent pos- sibilities provided by the desktop version of Google Earth to view remote sensing data on DEMs and to select and extract points with relevant geological information.

Paper available on sciencedirect.


Pattern Extraction of Topsoil and Subsoil Heterogeneity and Soil‐Crop Interaction Using Unsupervised Bayesian Machine Learning

Wang 2019 abstract fig Copyright: © CGRE

Hui Wang, Florian Wellmann, Tianqi Zhang, Alexander Schaaf, Robin Maximilian Kanig, Elizabeth Verweij, Christian von Hebel, and Jan van der Kruk (2019)

The link between remotely sensed surface vegetation performances with the heterogeneity of subsurface physical properties is investigated by means of a Bayesian unsupervised learning approach. This question has considerable relevance and practical implications for precision agriculture as visible spatial differences in crop development and yield are often directly related to horizontal and vertical variations in soil texture caused by, for example, complex deposition/erosion processes. In addition, active and relict geomorphological settings, such as floodplains and buried paleochannels, can cast significant complexity into surface hydrology and crop modeling. This also requires a better approach to detect, quantify, and analyze topsoil and subsoil heterogeneity and soil‐crop interaction. In this work, we introduce a novel unsupervised Bayesian pattern recognition framework to address the extraction of these complex patterns. The proposed approach is first validated using two synthetic data sets and then applied to real‐world data sets of three test fields, which consists of satellite‐derived normalized difference vegetation index (NDVI) time series and proximal soil measurement data acquired by a multireceiver electromagnetic induction geophysical system. We show, for the first time, how the similarity and joint spatial patterns between crop NDVI time series and soil electromagnetic induction information can be extracted in a statistically rigorous means, and the associated heterogeneity and correlation can be analyzed in a quantitative manner. Some preliminary results from this study improve our understanding the link of above surface crop performance with the heterogeneous subsurface. Additional investigations have been planned for further testing the validity and generalization of these findings.

Full text available on the JGR Biogeosciences page.


GemPy 1.0: open-source stochastic geological modeling and inversion

de la Varga 2019 fig Copyright: © CGRE

Miguel de la Varga, Alexander Schaaf, Florian Wellmann (2019)

This paper introduce the new open-sourcelibrary GemPy. GemPy is a tool for generating 3D structural geological models in Python. With GemPy, you can create complex models that include stratigraphical and structural features such as folds, faults and unconformities. It was furthermore designed to enable stochastic modeling to adress parameter and model uncertainties.this paper delves into the mathematical methods behind the software explaining some of its most prominent features.

You can find the paper on Geosci. Model Dev and more details about the software here.


Certified Reduced Basis Method in Geosciences: Addressing the challenge of high dimensional problems

Paper RB Copyright: © CGRE

Denise Degen, Karen Veroy, Florian Wellmann

One of the biggest challenges in Computational Geosciences is finding ways of efficiently simulating high-dimensional problems. In this paper we present the reduced basis method that constructs low-dimensional approximations to (high-dimensional) solutions of partial differential equations. In contrast to other widely used geoscientific reduction techniques, the reduced basis method reduces the Galerkin approximation space and not the physical space and is consequently much less restrictive. Another advantage is that, fort the problems considered in this paper, the method provides a bound to the error in the reduced order approximation, thus permitting an objective evaluation of the approximation quality. Using a geothermal conduction problem we demonstrate that depending on the model we obtain a maximum speed-up of three orders of magnitude with an error in the order of 10\textsuperscript{-8}. This significant reduction of the cost of the forward simulation allows to perform uncertainty quantification, inversions, and parameter studies for larger and more complex models than currently possible.

Paper now accepted for publication in Computational Geosciences , preprint available on EarthArXiv.


Uncertainty estimation for a geological model of the Sandstone greenstone belt, Western Australia – insights from integrated geological and geophysical inversion in a Bayesian inference framework

Greenstone Paper Copyright: © CGRE

Florian Wellmann, Miguel de la Varga, Ruth E. Murdie, Klaus Gessner and Mark Jessell

The spatial relationship between different rock types and relevant structural features is an important aspect in the characterization of ore-forming systems. Our knowledge about this geological architecture is often captured in 3D structural geological models. Multiple methods exist to generate these models, but one important problem remains: structural models often contain significant uncertainties. In recent years, several approaches have been developed to consider uncertainties in geological prior parameters that are used to create these models through the use of stochastic simulation methods. However, a disadvantage of these methods is that there is no guarantee that each simulated model is geologically reasonable – and that it forms a valid representation in the light of additional data (e.g. geophysical measurements). We address these shortcomings here with an approach for the integration of structural geological and geophysical data into a framework that explicitly considers model uncertainties. We combine existing implicit structural modelling methods with novel developments in probabilistic programming in a Bayesian framework. In an application of these concepts to a gold-bearing greenstone belt in Western Australia, we show that we are able to significantly reduce uncertainties in the final model by additional data integration. Although the final question always remains whether a predicted model suite is a suitable representation of accuracy or not, we conclude that our application of a Bayesian framework provides a novel quantitative approach to addressing uncertainty and optimization of model parameters.

Full text on Lyell Collection, Geological Society of London.


Actors, actions and uncertainties: Optimizing decision making based on 3-D structural geological models

Paper Actors, Actions and Uncertainties Copyright: © CGRE

Fabian Antonio Stamm, Miguel de la Varga and Florian Wellmann (2019)

Uncertainties are common in geological models and have a considerable impact on model interpretations and subsequent decision making. This is of particular significance for high-risk, high-reward sectors, such as hydrocarbon exploration and production. Recent advances allows us to view geological modeling as a statistical problem that we can address with probabilistic methods. Using stochastic simulations and Bayesian inference, uncertainties can be quantified and reduced by incorporating additional geological information. In this work, we propose custom loss functions as a decision-making tool that builds upon such probabilistic approaches.

Our results show that the optimizing estimators shift according to the characteristics of the underlying value distribution. While overall spread leads to separation, risk-averse and risk-friendly decisions converge in the decision space and decrease in expected loss given narrower distributions. We thus consider the degree of decision convergence to be a measure for the state of knowledge and its inherent uncertainty at the moment of decision making. This decisive uncertainty does not change in alignment with model uncertainty but depends on alterations of critical parameters and respective interdependencies, in particular relating to seal reliability. Additionally, actors are affected differently by one set of information, depending on their risk affinity. It is therefore important to identify the model parameters which are most influential for the final decision in order to optimize the decision-making process.

Paper available as open-access, published in journal “Solid Earth”