Structural Interpretation of Sparse Fault Data Using Graph Theory and Geological Rules

Caumon, Guillaume; Laurent, Gautier; Bonneau, François

doi:10.1007/s11004-019-09800-0

Cited by 20 publications

(18 citation statements)

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“…Secondly, we introduce the utilisation of adjacency relationships between the different lithologies in post-regularisation to ensure that base topological rules are respected across the entirety of the three-dimensional volume. This is particularly important for structural geological interpretation (Freeman et al, 2010, Godefroy et al, 2019. In this paper, we extend 5 existing post-regularisation approaches (ie,, Tarabalka et al, 2009, Stavrakoudis et al, 2014, Cracknell and Reading, 2015) by integrating geological information in the classification analysis in the form of topological relationships (see Egenhofer and Herring 1990, Zlatanova, 2000, and Thiele et al, 2016, for the different topologies) defined by geological principles.…”

Section: Methodsmentioning

confidence: 89%

Towards geologically reasonable lithological classification from integrated geophysical inverse modelling: methodology and application case

Giraud

Lindsay

Jessell

et al. 2019

Preprint

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Abstract. We propose a methodology for the recovery of lithologies from geological and geophysical modelling results and apply it field data. Our technique relies on classification using self-organizing maps (SOM) paired with geoscientific consistency checks and uncertainty analysis. In the procedure we develop, the SOM is trained using prior geological information in the form of geological uncertainty, the expected spatial distribution of petrophysical properties, and constrained geophysical inversion results. We ensure local geological plausibility in the lithological model recovered from classification by enforcing basic topological rules through a process called post-regularisation. This prevents the three-dimensional lithological model from violating elementary geological principles while maintaining geophysical consistency. Interpretation of the resulting lithologies is complemented by the estimation of the uncertainty associated to the different nodes of the trained SOM. The application case we investigate uses data and models from the Yerrida Basin (Western Australia). Our results generally corroborate previous models of the region but they also suggest that the structural setting in some areas need to be updated. In particular, our results suggest the thinning of one of the greenstone belts in the area may be related to a deep structure not sampled by surface geological measurements and which was absent in previous geological models.

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Section: Methodsmentioning

confidence: 89%

Towards geologically reasonable lithological classification from integrated geophysical inverse modelling: methodology and application case

Giraud

Lindsay

Jessell

et al. 2019

Preprint

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“…Therefore, Cherpeau et al (2010bCherpeau et al ( , 2012 and Cherpeau and Caumon (2015) propose a parsimonious method which anchors the first simulated faults to the available evidence, before simulating unseen fault objects. All these iterative stochastic fault models are difficult to use in practice, because of the combinatorial complexity of the problem (Godefroy et al, 2019;Julio, 2015), of the difficulty to integrate geological, kinematical, and mechanical concepts into the stochastic model (Godefroy et al, 2017;Laurent et al, 2013; Journal of Geophysical Research: Solid Earth 10.1029/2020JB020022 Nicol et al, 2020;Røe et al, 2014;Rotevatn et al, 2019), and of the geometric challenges to robustly build such three-dimensional structural models (e.g., due to meshing issues, see Anquez et al, 2019;Zehner et al, 2015).…”

Section: Structural Uncertainty: State Of the Artmentioning

confidence: 99%

“…To include such a geological knowledge in the sampler, an association rule

R_{φ}^{boldassoc} false(𝕧_{i} \leftrightarrow 𝕧_{j} false)

quantifies the likelihood that two pieces of evidence ( 𝕧 i and 𝕧 j ) of the same family ( φ ) belong to the same fault (Godefroy et al, 2019). Association rules are defined from general structural concepts about faults and from some geometric characteristics associated with each fault family.…”

Section: Multi‐scenario Interpretations Using Graph Decompositionmentioning

confidence: 99%

“…(c and d) Generated interpreted synthetic parallel two‐dimensional seismic lines. An interactive three‐dimensional model is provided in Godefroy and Caumon (2020), in the form of an HTML page.…”

Section: Application To Sparse Data From Santos Basin Offshore Brazilmentioning

confidence: 99%

“…Associating labeled pieces of fault evidence (red: east dipping and blue: west dipping) interpreted (a) in map view or (b) on two‐dimensional seismic lines is an under‐constrained problem. (c1–c3) Several structural interpretations are possible (modified from Freeman et al, 1990; Godefroy et al, 2019). (d) In

𝔾^{bolda boldl boldl}

, the labeled nodes (i.e., the pieces of fault evidence) are linked by an edge if they may be part of the same fault.…”

Section: Introductionmentioning

confidence: 99%

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Multi‐scenario Interpretations From Sparse Fault Evidence Using Graph Theory and Geological Rules

2021

Self Cite

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The characterization of geological faults from geological and geophysical data is often subject to uncertainties, owing to data ambiguity and incomplete spatial coverage. We propose a stochastic sampling algorithm which generates fault network scenarios compatible with sparse fault evidence while honoring some geological concepts. This process is useful for reducing interpretation bias, formalizing interpretation concepts, and assessing first-order structural uncertainties. Each scenario is represented by an undirected association graph, where a fault corresponds to an isolated clique, which associates pieces of fault evidence represented as graph nodes. The simulation algorithm samples this association graph from the set of edges linking the pieces of fault evidence that may be interpreted as part of the same fault. Each edge carries a likelihood that the endpoints belong to the same fault surface, expressing some general and regional geological interpretation concepts. The algorithm is illustrated on several incomplete data sets made of three to six two-dimensional seismic lines extracted from a three-dimensional seismic image located in the Santos Basin, offshore Brazil. In all cases, the simulation method generates a large number of plausible fault networks, even when using restrictive interpretation rules. The case study experimentally confirms that retrieving the reference association is difficult due to the problem combinatorics. Restrictive and consistent rules increase the likelihood to recover the reference interpretation and reduce the diversity of the obtained realizations. We discuss how the proposed method fits in the quest to rigorously (1) address epistemic uncertainty during structural studies and (2) quantify subsurface uncertainty while preserving structural consistency. Plain Language Summary This paper presents a way to generate interpretation scenarios for geological faults from incomplete spatial observations. The method essentially solves a "connect the dots" exercise that honors the observations and geological interpretation concepts formulated as mathematical rules. The goal is to help interpreters to characterize how the lack of data affects geological structural uncertainty. The proposed method is original in the sense that it does not anchor the scenarios on a particular base case but rather uses a global characterization formulated with graph theory to generate possible fault network interpretations. The application on a faulted formation offshore Brazil where observations have been decimated shows that the method is able to consistently generate a set of interpretations encompassing the interpretation made from the full data set. It also highlights the computational challenge of the problem and the difficulty to check the results in settings where only incomplete observations exist. The proposed method, however, opens novel perspectives to address these challenges.

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Finite Difference Implicit Structural Modeling of Geological Structures

et al. 2020

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We introduce a new method for implicit structural modeling. The main developments in this paper are the new regularization operators we propose by extending inherent properties of the classic one-dimensional discrete second derivative operator to higher dimensions. The proposed regularization operators discretize naturally on the Cartesian grid using finite differences, owing to the highly symmetric nature of the Cartesian grid. Furthermore, the proposed regularization operators do not require any special treatment on boundary nodes, and their generalization to higher dimensions is straightforward. As a result, the proposed method has the advantage of being simple to implement. Numerical examples show that the proposed method is robust and numerically efficient.

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Structural Interpretation of Sparse Fault Data Using Graph Theory and Geological Rules

Cited by 20 publications

References 58 publications

Towards geologically reasonable lithological classification from integrated geophysical inverse modelling: methodology and application case

Towards geologically reasonable lithological classification from integrated geophysical inverse modelling: methodology and application case

Multi‐scenario Interpretations From Sparse Fault Evidence Using Graph Theory and Geological Rules

Finite Difference Implicit Structural Modeling of Geological Structures

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