The Geodynamic World Builder is an open-source code library intended to set up initial conditions for computational geodynamic models in both Cartesian and spherical geometries. The inputs for the JavaScript Object Notation (JSON)-style parameter file are not mathematical but rather a structured nested list describing tectonic features, e.g., a continental, an oceanic or a subducting plate. Each of these tectonic features can be assigned a specific temperature profile (e.g., plate model) or composition label (e.g., uniform). For each point in space, the Geodynamic World Builder can return the composition and/or temperature. It is written in C++ but can be used in almost any language through its C and Fortran wrappers. Various examples of 2-D and 3-D subduction settings are presented. The Geodynamic World Builder comes with an extensive online user manual.
Geodynamic modeling has been used in the past four decades to help us better understand the
physical processes of Earth's interior, including large-scale mantle convection and plate tectonics, or detailed processes of crustal deformation.
Numerical modeling of geodynamic processes involves solving the pertinent partial differential equations (PDEs) of mass, momentum and energy conservation supplemented with rheological laws, material parameters and with an equation of thermodynamic state relating, e.g., density, temperature and pressure
In this section, we describe the philosophy of how tectonic features such as plates, ridges, faults and slabs can be parameterized by lines and areas that implicitly define volumes to which temperature and composition models can be assigned. A composition is a part of the model that is assigned a particular identifying label and in addition an indicator which is given a value between 0 and 1. This indicator can be used by codes using the GWB output to ascribe physical properties to different model regions.
To minimize user effort, the GWB utilizes a parametrization of 3-D structures by 2-D coordinate input, by defining their (projected) location on the surface. The GWB can be used to create initial models in Cartesian and spherical geometries.
User input files should be specified in JavaScript Object Notation (JSON) (
The GWB uses a hierarchical overlay of features. This means that features defined first are spatially overlain by features defined later in places where both overlap. The GWB recognizes two types of features: area features and line features, which will be explained in the following sections. A possible third type of features, point features, will be discussed in Sect.
A continental plate is an “area feature” in the GWB and is defined by its surface perimeter and its thickness. The perimeter is specified as a list of points which enclose the continental area. Within the defined volume of the continental plate, the GWB offers various options for defining temperature values and compositions. For example, a continental plate can be assigned multiple layers of different compositions and a linear geotherm that matches a predefined adiabatic mantle temperature at the base of the lithosphere. We note that continental lithosphere with a variable thickness is a development for future releases of the GWB but can be mimicked in the present version by specifying contiguous continental areas with different thickness. Also, continental topography is currently not explicitly implemented, but it can be achieved through a sticky air approach, where air is a composition of varying thickness atop the model
Like the continental plate, the oceanic plate is parameterized as an area feature with a flat surface. We have implemented the “plate model”
The upper and lower mantles can also be parameterized as an area feature that starts below the lithosphere or at the surface and is overlain by lithosphere in a later building stage. This allows for defining a upper and lower mantle and to insert specific volumetric structures such as large low shear wave velocity provinces (LLSVPs) at the core-mantle boundary in the same way as, for example, an oceanic plate but at depth. In the present version, these mantle features can be assigned a radially uniform, linear or adiabatic temperature profile. Future versions may include laterally varying temperature or compositions, e.g., scaled from seismic tomography models
A subducting plate is a “line feature” in the GWB and is defined by the location of the trench and one or more depth segments each describing a part of the geometry of the subducting slab. They are defined by a length and by thicknesses and dip angles at the beginning and end of the slab segment. In sequence, these segments can make up a smoothly varying slab geometry which can, for example, flatten in the upper mantle transition zone, or may prescribe a slab entering the lower mantle. Every point in the trench coordinate list defines a vertical section of the subducting plate that may consist of one or several slab segments. Both sections and segments can vary in length, dip angle or thickness. The length of a subducting slab is always computed as the length along the top of the slab so that this can straightforwardly represent the amount of relative plate convergence during a certain period.
The dip angle is defined as the angle between the surface and the local plunge of the slab. The dip angle is specified at the start and end points of each depth segment along the vertical section. Dip angles are linearly interpolated along a segment. The overall direction of slab dip can be to either side of the trench and is selected by specifying for each subducting plate an additional point at the surface, the “dip point”, at the slab dip side of the trench segment (see Fig.
For each point at the surface of the slab, the depth and the distance to the trench, as measured along the surface, are available and can be used to assign slab temperatures, e.g., by using the
To allow for complicated fault shapes (e.g., listric faults), faults are also parameterized as line features. An important difference between faults and subducting plates is that for subducting plates the trench defines the top of the plate at the plate boundary, while for faults the line feature defines the center of the fault with respect to which a fault thickness can be defined.
The following design principles define the Geodynamic World Builder:
To exemplify input files and to show the capabilities of the Geodynamic World Builder, we show here three 2-D examples and two 3-D examples of the GWB visualized through the stand-alone visualization application. This application creates so-called vtu files which can be visualized by programs like ParaView (
se-2019-24Panel
The GWB has an option to create a ParaView file of the GWB input file. This can be useful for model creation or visualization support of presenting geodynamic hypotheses, or for checking the user-designed model prior to using it in a next step, e.g., for creating an initial model for geodynamic modeling.
Here, we show two subduction models, one in Cartesian coordinates (Fig.
This example is created by placing the features in a particular order in the input file. The features overlay, and in this case overwrite, an adiabatic background temperature and all compositions set to zero. This example consists of five features: an oceanic plate, a continental plate, an upper mantle, a lower mantle and a subducting plate. The first four do not overlap in their input definition, so the order of definition in the Geodynamic World Builder input file does not make a difference in the result. The subducting plate overwrites parts of the oceanic plate, continental plate and the upper mantle, which is effectuated by defining the slab after these three features. For each feature, temperature and composition models are selected.
The same as setup as in Fig.
We show in Fig.
The temperature field of the 3-D two-rift system example. Material with a temperature below 950 K has been omitted in order to better show the rifts. Note the second rift system in the background.
The temperature field of the 3-D subduction example. Note the smooth transition between the upper and lower parts of the subduction system in the top figure and the curved geometry of the slab in panel
Figure
SEPRAN is a general purpose finite element toolkit applied in engineering problems as well as in development of 2-D and 3-D numerical models in geodynamics and planetary science
Dimensionless viscosity field in log scale superimposed with 10 (dimensionless) temperature (between 0 and 0.82) isocontours.
A 2-D rectangular domain of 1000 km depth and 2000 km width is used. The initial thermal and composition state is created using the Fortran wrapper of the GWB library. The GWB tool is called in a loop over all nodal points of the finite element method (FEM) mesh to define the initial temperature field for the subsequent convection calculations. In a similar way, the material distribution of the initial state is defined by calling the composition function of the GWB library in a program loop over particle tracers. The input file for this example can be found in Appendix
ELEFANT is a 2-D/3-D finite element code for geodynamic problems
Example ELEFANT query routine using the GWB-supplied Fortran wrappers composition_3d() and temperature_3d():
The domain is a Cartesian box with dimensions
Since this example shows many interesting GWB features in action, while remaining relatively simple to explain, we provided Fig.
Connection between the GWB input file
ASPECT is an open-source community FEM designed for geodynamic problems
The 3-D ASPECT Caribbean example after 2.5 million years of evolution. The top image is a top view of the model where the top 50 km section is removed and where the viscosity field is shown with the velocity field indicated by the arrows. The bottom two figures are cutouts of the temperature field between 600 and 1535 K, showing in color the temperature (
The details of the setup are presented in Appendix
The finite element mesh used in the example of Sect.
We presented the Geodynamic World Builder version 0.2.0 as a tool for constructing 2-D and 3-D initial models of geodynamic settings involving crust/lithosphere, plate boundaries and subduction. The interface of the GWB with a numerical modeling code is based on a query of the modeling code to supply temperature, density or other information at a particular position. The advantage of this is that it allows for fast and parallel use for filling, for example, the temperature field of a geodynamics model. A downside of this approach is that operations which require information of neighbors, like adding diffusion, would be more expensive to perform. We think that at least the case of adding diffusion is more suited to be performed in the geodynamic model “tha” in the GWB.
This paper discusses version 0.2.0 of the Geodynamic World Builder, which is considered to be a beta version of the code. Input format and/or functionality may change between minor versions and this will be documented on the website. From version 1.0.0, we will use Semantic Versioning 2.0.0 (
The code is freely available at
2-D Cartesian subduction example. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
2-D spherical subduction example. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
3-D ocean spreading example input file. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
3-D subduction spreading example input file. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
2-D SEPRAN subduction example input file. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
3-D double subduction example input file. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
Input for the ASPECT example. The lines of green text (preceded by the double forward slashes) are comments and have no effect on the result.
MF wrote the code, the documentation and most of the paper, and coordinated with the other authors. CT provided advice on algorithms and general coding, coupled the code ELEFANT to the GWB, documented that, wrote the section related to ELEFANT and provided feedback on the rest of the paper. AvdB coupled SEPRAN to the GWB, documented that and wrote the section related to SEPRAN. WS provided advice during the project and contributed to the overall setup and writing of the paper.
The authors declare that they have no conflict of interest.
Menno Fraters acknowledges constructive feedback from the ASPECT community and especially from Timo Heister, Wolfgang Bangerth and Rene Gassmöller. The authors also acknowledge constructive proofreading by Robert Myhill, Henry Brett and Lucas van de Wiel. Menno Fraters and Cedric Thieulot are indebted to the Computational Infrastructure for Geodynamics (CIG) for their recurring participation in the ASPECT hackathons, during which the foundation of this work was laid out.
This work is funded by the Netherlands Organisation for Scientific Research (NWO), as part of the Caribbean Research program (grant no. 858.14.070) and partly supported by the Research Council of Norway through its Centres of Excellence funding scheme, project no. 223272.
Data visualization is carried out with ParaView software
This research has been supported by the Netherlands Organisation for Scientific Research (NWO) (grant no. 858.14.070) and the Research Council of Norway (grant no. 223272).
This paper was edited by Taras Gerya and reviewed by Fabio A. Capitanio and one anonymous referee.