Hypergraph-based fault observation association – theoretical framework and first results

@inproceedings{fratani_hypergraph-based_RM2023,
 abstract = {During geological exploration, interpretation of faults can be ambiguous and uncertain because of disparate and often sparse observations such as fault traces on 2D seismic images or outcrops. The problem of associating partial fault observations was considered by Godefroy et al. (2019), who decided to define a graph where each possible association of two fault observations (the graph nodes) are represented by an hyperedge. The likelihood of this association was computed by using expert geological rules. However, fault observations are not pairwise independent, which limits the consideration of higher-order effects. For instance, the multiple-point association can be used to infer the evolution of the throw along the fault. In addition, the definition of rules in a multiple-point problem is also difficult because of the very large number of cases to consider. Here, we propose a hypergraph formalism to generalise this approach to the likelihood of multiple-point fault data association. The framework uses hypergraphs to represent higher-order interactions between data in the multiple-point association problem. Moreover, a machine learning approach is suggested to augment or replace the geological rules. First, a computation of fault features (i.e. the length of the fault trace) from sections extracted from known 3D geological models is realised to create a data set of fault observations. The supervised machine learning problem is formulated as a classification problem to determine the probability that k fault observations belong to the same fault objects based on the feature vector. To prevent overfitting, we propose to mimic a partly interpreted case: we split the 3D domain in two disjoint sectors A and B, and use only data from sector A as training and data from sector B to test the method. This theoretical framework allows for a probabilistic representation of each possible association of fault observations in a region. In order to pass from this representation to several fault network interpretations, we argue that a clustering of the hypergraph needs to be considered.},
 author = {Fratani, Amandine and Caumon, Guillaume and Stoica, Radu Stefan and Giraud, Jeremie},
 booktitle = {2023 {RING} meeting},
 language = {en},
 pages = {12},
 publisher = {ASGA},
 title = {Hypergraph-based fault observation association – theoretical framework and first results},
 year = {2023}
}