Why Geodynamic Modeling?

Why Geodynamic Modeling?#

Geodynamic modeling is an ideal tool to investigate Earth processes, which are not directly observable, due to the spatial and temporal scales in which they operate.

Geodynamic processes occur over a wide range of timescales and spatial scales, and we have to take into account which of them can be included in any given model.

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Important: We always need to keep in mind that numerical models are inherently based on a series of assumptions and simplifications.
Thus, we must be aware of these assumptions and limitations when designing, analyzing, and interpreting modeling results.

What is a model?#

A model is a simplified version of nature that can be used to study and investigate certain aspects of Earth. Therefore, a model is never a complete representation of Earth and is always less complex than the real world.

All models are inherently wrong, but some are useful.
George Box

Types of models#

  • Analytical. Analytical models are mathematical models that have a closed form solution, i.e. the solution to the equations used to describe changes in a system can be expressed as a mathematical analytic function. A classic example is the solution for Lamb’s waves, a type of guided seismic wave that travels along the surface. Turcotte and Schubert [2014] give many for geodynamics.

Turcotte, D., & Schubert, G. (2014). Geodynamics (3rd ed.). Cambridge: Cambridge University Press.

  • Analogue. A laboratory experimental method using uncomplicated physical models with certain simple scales of time and length to model geological scenarios and simulate geodynamic evolutions. Some beautiful examples can be seen here: Thinking inside the (sand)box

  • Numerical. The use of numerical methods to solve a set of physical equations describing a physical process.

Physical model vs. numerical model vs. numerical code#

  • Physical model is the set of equations that describe a physical (or chemical) process occurring in the Earth.

  • Numerical model refers to a specific set of physical equations which are discretized and solved numerically with assumptions regarding initial and boundary conditions.

  • Numerical code can contain and solve one or more numerical models - i.e., different sets of discretized equations.

The models we are concerned with here are all forward models, by which we solve equations that describe the physics of a system. The modeling results are a prediction of how the system behaves given its physical state which afterwards can be compared to observations. Inverse models, however, use an existing dataset of observations to determine the conditions responsible for producing the observed dataset.

In the ideal case, our models can reproduce our observational data or prove our hypotheses. However, success is relative to how you define it.

Experiment, Fail, Learn, and Repeat.
- Richard Feynman

 


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Extra#

Some fun examples of failed models by Cedric Thieulot, Utrecht Unviersity: