One of the goal of our research group is to develop new software and technologies. Consortium sponsors can use and industrialize software, royalty-free. In addition to internal use of software by sponsors, several commercial software products or open-source projects have been based on RING technologies.

### Gocad

The Gocad software was initiated by Prof. Jean-Laurent Mallet and his research group in 1989 (Mallet, 1992b). The main goal of this academic project was to develop a geomodeling software using triangulated surfaces, which have the capability to manage overturned and highly faulted geological surfaces. From its inception, Gocad made the choice to use graphics workstation and work in three dimensions and not only with depth maps. One of the key technologies introduced in Gocad was Discrete Smooth Interpolation, DSI in short (Mallet, 1989; Mallet, 1992a; Mallet, 1997). This original method uses least-squares minimization to smooth triangulated surfaces under constraints representing geological information. The systematic approach to represent subsurface data and geological objects consistently with points, lines, surfaces and volumetric grids has been a distinctive feature of Gocad as compared to other software aimed at solving just one class of problems. This led to interesting uses of Gocad in geophysics, reservoir modeling, archeology, ore geology and even medicine!

During the 90's, the Gocad software, orgininally developped in C, was translated into C++ with the help of several sponsor companies. A spin-off company (T-Surf) was created in 1998 to take care of the software evolution, maintenance and support. The source code of the Gocad software was then fully transferred to T-Surf (acquired by Paradigm in 2006). Since then, RING has mostly been using the Gocad software development kit to do its research.

### Skua

At the beginning of the 2000's, Jean-Laurent Mallet started developing the Geochron concept and the first software prototypes with the help of his graduate students. The main idea is described in his 2004 Mathematical Geosciences paper (Mallet, 2004) and on several conference papers at the same period (Mallet et al., 2004; Macé et al., 2004; Moyen et al., 2004; Caumon et al. 2005; Royer et al., 2006; Caumon & Mallet, 2006; Tertois & Mallet, 2006; Frank et al., 2007; Tertois & Mallet, 2007). It is to numerically compute a chronostratigraphic transform mapping any subsurface point into its image in a flattened depositional space. The first implementation of this model used implicit surfaces (also known as level sets) on a tetrahedral mesh (Moyen et al., 2004). Implicit surfaces are able to deal with a very large number of data and make modeling more automatic than classical surface-based modeling and are available in the Consortium's StructuralLab's code.

In 2008, what had started as a research project to make the application of geostatistics easier became a commercial product: Paradigm introduced SKUA, the first commercial implementation of the Geochron concept, which also provided new reservoir gridding algorithms (Jayr et al., 2008; Gringarten et al. 2008a,b).

More recently, the SKUA Structure Uncertainty product (Tertois et al., 2010) has also benefited from prior research by the Consortium on the stochastic perturbation of implicit structural models (Caumon & Mallet, 2006; Caumon et al., 2007; Tertois & Mallet, 2007) implemented in the FaultMod code.

Since Prof. Mallet retired from the university in 2006, he has been deeply involved in further developing the theoretical framework of Geochron, as attested by his two recent books (Mallet, 2008; Mallet, 2014).

### Petrel** Volume Based Modeling**

In 2013, Schlumberger introduced a new structural modeling approach called volumetric based modeling (Souche et al., 2013). This method also builds on the concepts of implicit surfaces in tetrahedral meshes introduced by the Consortium during the 2000's and available in StructuralLab.

### LoopStructural

The LoopStructural open-source project (Grose et al., 2021a,b) is the most recent granchild of the implicit structural modeling codes originated by the RING-Gocad Consortium in the 2000's. It also reimplements and extends the following Consortium work on kinematic near-fault deformation available in the FaultMod code:

- A parametric method to model 3D displacements around faults with volumetric vector fields
- A parametric fault displacement model to introduce kinematic control into modeling faults from sparse data

### OpenGeode

The OpenGeode open-source project is the industrialization by Geode-solutions of the RINGMesh (Link to the paper) project initiated in the RING Consortium in 2014.

### PetroKarst

In 2019, Emerson industrialized a SKUA-GOCAD plugin named PetroKarst for Petrobras, dedicated to the spatial modeling of karsts, described in this paper. This plugin is based on several works peformed at RING on karst modeling with the ODSIM method in the KarstMod code:

- Sarah Vitel's PhD, which set the ground for representing the subsurface as a graph
- Vincent Henrion's PhD, which defined the ODSim Method and the two related papers:

- Vincent's paper karst modeling to generate random cave geometry around random fracture networks, published at the 2008 Geostatistics Congress
- The ODSIM paper on the generation of random envelopes around skeletons, published in Mathematical Geosciences

- Pauline Collon's paper on the simulation of branchwork karsts by combining fracture-based graphs paths and ODSIM.

### What is next?

If your company is a member of the Consortium, you can readily use the software prototypes developed by RING to test, evaluate and steer the technology before it becomes available on the market...

#### References

*Geostatistics Banff 2004*(pp. 703-712). Springer, Netherlands.

*Int. Assoc. for Mathematical Geology–XIth International Congres. 4p*.

*Petroleum Geostatistics, EAGE*.

*Computers & Geosciences*,

*33*(7), 932-943.

*SPE annual technical conference and exhibition (SPE 116649)*.

*Proc eighth geostatistical geostatistics congress*(Vol. 2, pp. 647-656).

*9th European Conference on the Mathematics of Oil Recovery*, EAGE.

*ACM Transactions on Graphics*,

*8*(2), 121-144.

*Computer-aided design*,

*24*(4), 178-191.

*Three-dimensional modeling with geoscientific information systems*(pp. 123-141). Springer Netherlands.

*Mathematical Geology*,

*29*(2), 199-219.

*Mathematical Geology*,

*36*(1), 1-32.

*66th EAGE Conference & Exhibition*.

*9th European Conference on the Mathematics of Oil Recovery, EAGE*.

*Proceedings of International Association of Mathematical Geology*, S14-22.

*75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013*.

*Proc. IAMG’2006*.

*Geological Society, London, Special Publications*,

*292*(1), 89-101.

*72nd EAGE Conference & Exhibition*.