3D mantle flow imaged using the stereoscopic PIV technique in analogue models of slab rollover subduction (a, b) and slab rollback subduction (c, d). Adapted from Strak, Xue & Schellart (2024).
Geodynamic modelling helps us understand Earth’s internal processes by providing a framework to test hypotheses. Analogue modelling uses physical models governed by the laws of nature, with resolution down to Planck’s length. In contrast, numerical modelling employs mathematical methods to approximate solutions to the physical laws governing Earth’s processes. Each modelling approach comes with its own strengths and limitations, and making a choice between them is not always clear. To better understand this, I had the pleasure of speaking to Wouter Schellart about geodynamic modelling techniques and the rationale behind the use of both analogue and numerical modelling.
Wouter Schellart (https://orcid.org/0000-0002-9802-0143) is a Full Professor of Geodynamics and Tectonics in the Department of Earth Sciences at Vrije Universiteit Amsterdam. Currently in charge of the Kuenen-Escher Geodynamics Laboratory (KEG Lab) and leading the Geodynamics and Tectonics research group, his work primarily focuses on geodynamics and tectonics, using both analogue and numerical modelling techniques.
What are the pros and cons of analogue and numerical modelling?
Generally speaking, geodynamics modelling, both analogue and numerical, has many advantages, including:
- Investigating the progressive evolution of a particular geological or geodynamic process, providing a complete evolutionary picture of the process being investigated. In nature, many geological and geodynamic process occur over millions of years, such that their evolution is not directly observable.
- The particular geological or geodynamic process can be investigated in a controlled environment of the experimental laboratory or the virtual computer space.
- Geodynamic simulations allow the modeller to systematically investigate and quantify the influence of a particular physical parameter on a particular geodynamic process.
- Model results can be directly applied to the natural system to provide insight into the system in case the model is properly scaled.
- Last, but not least, running models, either in the lab or on a computer, can be great fun and exciting, for example when complicated processes unfold themselves live in front of your own eyes or when spectacular structures present themselves to you during a model run.
There are also advantages that are exclusive to analogue modelling, such as:
- Analogue models are actual physical experiments, so the physics is inherent to the system. In numerical models, physical processes are approximated with equations and numerical schemes.
- Analogue models are always four-dimensional (4D = 3D space + time), as experiments are always performed in three-dimensional space.
- Analogue models generally include a true free surface, as in most experimental set-ups the top surface is exposed to air.
Some advantages exclusive to numerical modelling are:
- Parametric investigations are generally easy and straightforward to perform in numerical models. For example, investigating the influence of change in viscosity of a particular domain in your model on the geodynamic evolution only requires the modeller to change the viscosity value in the input file and run the model again.
- Extracting quantitative information from the numerical model, such as the velocity field, strain field or stress field, is straightforward and can generally be done at any location within the model domain.
- Numerical models are generally more flexible and allow more processes, set-ups or boundary conditions to be included or implemented than is possible in analogue models, although this is obviously code-dependent. For example, numerical models allow for the implementation of Cartesian, cylindrical and spherical geometry, while analogue models only allow for Cartesian geometry (and inverted cylindrical geometry for models performed in a centrifuge). Another obvious example is that numerical models allow for the implementation of metamorphic reactions and phase changes, while analogue models do not.
Some disadvantages exclusive to analogue modelling are:
- Parametric investigations can be difficult in a number of cases. For those modelling investigations that involve changes in kinematics, such as the obliquity angle during rifting and the rate of convergence in accretionary wedge experiments, or geometry, such as the thickness of a particular strong or weak layer in the model, the parametric testing is straightforward. If the parametric study involves changes in material properties of a particular layer in the model, then complications can arise. For example, changing the viscosity of a particular layer in a model also changes the density of that layer, although generally by a small amount. In the ideal parametric investigation, only one parameter is changed at a time, not two or more.
- It is difficult to extract stress values directly from analogue experiments. It has been done in a number of cases, but the spatial distribution of stress measurements was generally limited to one or a few locations.
And several disadvantages exclusive to numerical modelling are:
- As already stated above, in numerical models, physical processes are approximated with equations and numerical schemes.
- Large-scale numerical 4D modelling requires major computational resources.
In which cases is analogue modelling preferable to numerical modelling?
I think analogue modelling is preferred over numerical modelling in case the modeller wants to investigate the long-term 3D structural, tectonic and topographic evolution of a domain that involves both brittle and ductile rheologies, in particular when it concerns a large-scale domain. A good example is the India-Eurasia-Sunda-Western Pacific collision-subduction system that involves continental deformation and mantle flow patterns at an enormous scale, but also includes smaller scale deformation structures such as thrust faults, folds, normal faults and strike-slip faults, as well as an evolving topography of mountain ranges, plateaus and basins. Analogue experiments simulating this complex, large-scale geodynamic system have thus far produced more realistic results than numerical models.
That being said, I think major scientific progress can be made and deeper understanding can be achieved when analogue and numerical models are combined in a synergistic manner to investigate the same geological phenomenon or geodynamic system. The modelling approaches are highly complementary and each has its own pros and cons, as described above.
The modelling approaches are highly complementary and each has its own pros and cons
What are the major research themes and specific modelling cases currently being investigated by your research group?
We are investigating, using both analogue and numerical modelling techniques, the India-Eurasia-Sunda collision-subduction system. We particularly focus on the following questions: What drives long-term India-Eurasia convergence, what drives Indian indentation into Eurasia, and what drives Indian continental subduction since the onset of collision some 50-60 million years ago? We use fully dynamic (buoyancy-driven) models, which we think are essential to try and answer these fundamental questions.
We also investigate the evolution of overriding plate surface topography and strain at subduction zones, in combination with mantle flow below the overriding plate, and explore how these might be associated with the spatial distribution of giant subduction earthquakes. The topography of the overriding plate has an important isostatic component, but part of the topography also has a dynamic origin due to, for example, mantle flow below the overriding plate and/or plate boundary forces. With our modelling we are trying to extract the wavelength and amplitude of the dynamically-induced topographic signals.
Why are these approaches (analogue and numerical modelling) best suited for the specific cases you mentioned?
Analogue and numerical models are ideally suited to provide the evolutionary picture of the developing structures, strain field, velocity field, topography, etc. Also, geodynamic models are ideally suited to test the physical/dynamic viability of a particular conceptual model, idea or theory. Without support from geodynamic models, the physical/dynamic viability of a conceptual model remains untested.
(…) geodynamic models are ideally suited to test the physical/dynamic viability of a particular conceptual model, idea or theory.
In your opinion, what does the future hold for analogue and numerical modelling, and how will they be used?
I think the future looks bright. Advanced visualization techniques in analogue modelling, such as PIV (Particle Image Velocimetry), tomographic PIV and X-ray computed tomography allow the quantification of, for example, velocity fields, strain fields and surface topography, and how these fields evolve through time. At the same time, increasing computational power allows 4D numerical modelling to become more standard. Together, this allows for the possibility to directly, systematically and quantitatively compare analogue and numerical modelling results. This will allow for both techniques to improve and provide more accurate results, which will ultimately lead to a better understanding of geological and geodynamic processes.
References Strak, V., Xue, K. & Schellart, W.P. Mantle upwelling induced by slab rollover subduction could explain widespread intraplate volcanism in Tibet. Commun Earth Environ 5, 510 (2024). https://doi.org/10.1038/s43247-024-01581-7
