In GEOREKA, a lot of effort has been put towards volumetric modelling: each geological domain is a volume, not a boundary. This idea is the core of our Domain Based Modelling (DBM). It means that every domain is represented by an implicit function. A complete geological model is then described by the relationships between the domain functions. The model description is then used to build a watertight tetrahedral model. The latter can subsequently be used directly in geophysics, flow modelling or even geostats.

General concept

As stated in the intro, any geological domain is a volume, not a boundary separating domains. Although this seems trivial, most modelling packages will force users to create boundaries between domains. Because of this, the whole concept in modelling geology changes. For volumetric modelling you do not define the actual boundary, but rather points that are inside the domain to model, and points outside of it.

This has small, but important consequences for modelling. No longer do you digitize contact points, but convert intervals to inside and outside points. Editing the volume happens by adding inside points, or reducing areas by creating additional outside points.

Due to decades of modelling boundaries, this can be a bit of a hurdle at first, but once used to the idea you will ask yourself why you haven’t been doing that earlier. It allows the user to focus on modelling one domain at a time, i.e. one volume at a time.

Domain relationships

Once a geological domain has been defined, the next step is to use it to create a model. In most cases, it might be obvious what unit is younger compared to other units. In other cases, it’s not so obvious. In our concept of geological model descriptors, that hardly is an issue. A model descriptor is used to define the order of the formations. This allows users to think in geological ageing terms. As an example we highlight this relatively simple model. The based unit is obviously faulted. However, younger units near the top are not. In a model descriptor, those younger units are therefore created first from their domain functions. Subsequently, the faults themselves are applied, before modelling the remaining units.

Thinking in volumes becomes a logical way to build geological models. In addition, the model descriptor will act as a direct documentation of the interpreted geological age of the domains.

Tetrahedral models

Geological models in GEOREKA have always been created as tetrahedral meshes instead of blocks. With our newly added tetrahedral optimization step, these meshes now result in nicely distributed tetrahedra with fine resolution where required and coarse resolution elsewhere.

No more blocks?

One of the main reasons behind using tetrahedra is there improved accuracy. There is no need for sub-blocking, but also no need for partial estimates for blocks crossing a geological boundary. Tetrahedra adhere to boundaries exactly, meaning a tetrahedron is either inside a domain, or outside of it.

Moreover, due to the flexibility of their size and shape, tetrahedra can produce very sharp boundaries as shown in our examples. The base unit is a single volume with very sharp edges due to faulting, something nearly impossible to do with standard block models.

No more triangles?

An advantage of tetrahedra over triangulated surfaces is that they are much less error prone. Triangles are 2D elements that have no volume by themselves. When a single triangle is missing in a model there is a hole and this can produce incorrect volume estimates. Tetrahedra are 3D elements and do have a volume. To get a volume estimate the volume of all tetrahedra are easily summed together. A ‘missing’ tetrahedron, if that exists, would still result in a valid volume.

Also, to go from a triangulated solid to a block model, a costly blocking procedure is needed to do it correctly, or if the model is needed for flow simulation or geophysics a costly meshing step would be needed.

Since this is already included in all our models you get all the benefits: accurate volumes, efficient tetrahedral meshes suitable for further use in simulators.

Finally, whenever a solid is needed, the shell of a tetrahedral models can be exported since that will consist of only triangles.