**Speaker:** Amandine Fratani

**Date:** Thursday 28th of November 2024, 1:15pm.

**Abstract:**

When creating a geological model from borehole data or 2D sections, the interpretation of 3D faults is often ambiguous and uncertain. This work focuses on the problem of associating partial fault observations, which has recently been formalized using a graph in which each fault observation is represented as a graph node, and graph edges carry the potential of pairwise associations. The likelihood of an association is computed using selected expert geological rules. However, fault observations are not pairwise independent, which prevents the consideration of higher-order effects such as the distribution of the throw or the length along several aligned nodes. To complement this approach, we propose a mathematical formalism for the use of high-order associations. The definition of expert rules in a multiple-point problem is challenging because of the very high dimensionality of the problem. To alleviate this, we propose to supplement expert rules by supervised machine learning using analog or incomplete interpretations. This work uses a Random Forest learner trained from a set of selected fault features computed from fault traces extracted from known 3D geological models (e.g., the length of the fault trace, the throw value, etc.). The association likelihood inference is formulated as a classification problem to determine the probability that fault observations belong to the same fault object based on the variables computed from the features of the k observations. To prevent overfitting, we propose to mimic a partly interpreted case: we split the 3D domain in two disjoint, spatially contiguous sectors A and B, and use sector A as training and sector B for testing. Preliminary results demonstrate the ability of Random Forest to retrieve probabilities of triplets that complete the pairwise representation.

**Speaker:** Marius Rapenne

**Date:** Thursday 14th of November 2024, 1:15pm.

**Abstract: To Be Determined**

**Speaker:** Mohammad Mahdi Rajabi

**Date:** Friday 8th of November 2024, 1:15pm.

**Abstract:**

To address common challenges in neural networks—such as large data requirements, poor generalization, overfitting, lack of transparency, and physically unrealistic outputs—incorporating physical intuition into different stages of neural network design has proven to be highly effective. This approach leverages the strengths of neural networks while ensuring their outputs adhere, fully or partially, to established physical laws. As a result, it improves the reliability, interpretability, and practicality of neural networks and can reduce the need for vast training datasets. This methodology is particularly useful for modeling physical systems, such as those in solid and fluid mechanics, as well as cyber-physical systems like smart grids and autonomous vehicles. With the increasing number of techniques and publications in this area, a clear and structured review of these methods has become essential. I will present an overview of current methods, terminology, and best practices for integrating physics into neural networks, providing a detailed classification of approaches including pre-training integration, in-training integration, and architecture-level embedding. I will also discuss the limitations of existing methods and highlight promising directions for future research.

**Speaker:** Paul Baville

**Date:** Thursday 17th of October 2024, 1:15pm.

**Abstract:**

Computer-assisted multi-well correlation aims at computing a large set of possible stratigraphic correlation scenarios from the same input data. WeCo (an automated multi-well correlation software developed by the RING Team) uses an adapted version of the Dynamic Time Warping to classify the simulated realizations from the most likely (lowest correlation cost) to the less likely (highest correlation cost). This correlation cost is given by a cost function corresponding to a principle of correlation (e.g., lithostratigraphy, chronostratigraphy, etc.).

The aim of this project is to define a consistent metric to compare well correlations generated by WeCo, and to classify them according to other criteria than the correlation cost. Since a correlation can be represented by an directed acyclic graph, whose nodes represent marker associations and edges represent transitions between marker associations, this work aims at applying the Hausdorff distance to compare two graphs. In this work, the use of the Hausdorff distance to compare multiple well correlations helps us to identify clusters of well correlations which have different costs, and to differentiate two well correlations having the same correlation cost.

**Speaker:** Géraldine Pichot

**Date:** Thursday 10th of October 2024, 1:15pm.

**Abstract:**

In underground environments, fractures are numerous and present at all scales (from cm to km), with very heterogeneous properties. The most commonly used model for fractured rocks is the Discrete Fracture Matrix (DFM) model, in which fractures are represented as structures of codimension 1 (Discrete Fracture Network - DFN). In this work, stochastic DFNs are generated with the software DFN.lab (https://github.com/FractoryLabcom/software). It enables the generation of cubic-meter fractured rocks. The objective is to simulate efficiently single-phase flow in large-scale fractured porous media.etc.).

My presentation will be divided into two parts. In the first part, I will present results on flow in fractured rocks such as granite rocks where flow only occurs in the fractures (the surrounding rock is impervious). These rocks are made up of millions of fractures and the meshing of this geometry is a challenge that we have taken up in recent years with the development of the MODFRAC software (https://team.inria.fr/serena/fr/research/software/modfrac/). I will then present the method we used to discretise the flow problem, the Hybrid High Order method, capable of supporting general elements. The problem is solved using a direct solver. The code we developed is called NEF++ (https://team.inria.fr/serena/fr/research/software/nefpp/). In the second part of my talk, I will present the recent results we have obtained on flow in fractured porous rocks. Due to the porosity of the rock, a 3D flow also occurs in the rock and this flow is

coupled to the 2D flow in the fractures. To discretise this problem, a mixed hybrid finite element is used. As the linear system may contain millions of unknowns, direct solvers are no longer an option due to the excessive RAM consumption and only iterative methods can be used. I will present several examples demonstrating the excellent performances obtained with GMRES preconditioned by HPDDM (https://petsc.org/main/manualpages/PC/PCHPDDM/).

**Speaker:** Zvi Koren

**Date:** Thursday 3rd of October 2024, 1:15pm.

**Abstract:**

This presentation introduces EarthStudy 360, a novel, target-oriented, seismic-driven system designed to generate the full image-domain scattering wavefield, decomposed into the local angle domain (LAD) coordinate system. This comprehensive image dataset serves as input for several key subsurface applications:

• High-definition subsurface model parameters: Utilizing full-azimuth reflection angle image data.

• High-resolution imaging: Enhancing structural and stratigraphic interpretation and reservoir characterization through directional (dip/azimuth) angle image data.

• Target markets: Addressing all subsurface imaging and interpretationhis correlation cost is given by a cost function corresponding to a principle of correlation (e.g., lithostratigraphy, chronostratigraphy, etc.).

EarthStudy 360 provides depth imaging processing experts and interpretation specialists with a complete set of image data, including accurate subsurface velocity models, structural attributes, medium properties, and reservoir characteristics. The rich information from all angles and azimuths ensures more reliable analysis and significantly reduces uncertainty. For instance, fracture analysis components offer precise information about fracture stress and orientation, which is crucial for optimizing drilling and achieving superior production rates.

In this presentation, I will describe the EarthStudy 360 seismic migration process in the local angle domain (LAD), the output, full-azimuth directional and opening-angle, common image gathers/volumes, and the corresponding applications for kinematic/dynamic parameter analyses and directional-based imaging (diffraction imaging). The system’s advantages will be demonstrated through numerous worldwide field examples.

**Speaker:** Hao Wang

**Date:** Thursday 26th of September 2024, 1:15pm.

**Abstract:**

The Callovo-Oxfordian (COx) claystone has been selected as the host formation for the construction of an Underground Research Laboratory (URL) in France, aimed at assessing the properties of COx claystone potentially involved in the geological disposal of radioactive waste. The mechanical behaviour of this claystone is crucial to the excavation of the URL, particularly in understanding the excavation damage zone (EDZ) around the openings, which reveals complex damage states influenced by stress paths and the properties of the host rock, such as anisotropy. In this study, the damage and anisotropic behaviour of COx claystone were investigated through triaxial tests using different loading paths that may occur near the openings. To further explore anisotropic mechanical behaviour, triaxial samples were prepared along different directions, based on the angle between the axial loading direction and the direction perpendicular to the bedding plane. The stress-strain curves from the triaxial tests displayed an elasto-plastic pattern. The measured elastic moduli showed a slight decrease with increasing deviator stress, indicating damage behaviour. Additionally, the Young's modulus and shear strength varied with the loading angle, highlighting the anisotropic nature of the COx claystone.

**Speaker:** Paul Cupillard

**Date:** Thursday 27th of June 2024, 1:15pm.

**Abstract:**

Non-periodic homogenization has proved to be an accurate asymptotic method for computing long-wavelength equivalent media for the seismic wave equation, turning small-scale heterogeneities and geometric complexity into smooth elastic properties. Using homogenized media allows i) decreasing the computation cost of wave propagation simulation and ii) studying the apparent, small-scale-induced anisotropy. After illustrating these two aspects briefly, I propose to analyze in great detail the accuracy of body waves simulated in homogenized 3D models of the subsurface. First, the behaviour of head-, reflected and refracted waves with respect to source-receiver offset, maximum frequency and velocity contrast across a planar interface, is investigated. Then, I consider the SEG-EAGE overthrust model to exemplify how the accuracy of simulated body waves anti-correlates with the distance to seismic source and the amount of apparent anisotropy. In high apparent anisotropy regions, we show that the first-order correction provided by the homogenization theory significantly improves the computed wavefield. The overall results of this analysis better frame the use of homogenized media in seismic wave simulation.

**Speaker:** Giusi Ruggiero

**Date:** Thursday 20th of June 2024, 1:15pm.

**Abstract:**

Seismic images techniques such as full waveform inversion (FWI) are based on frequency band-limited seismic data, and therefore they can only recover the smooth version of a true earth model, which is not suited for a proper geological interpretation at the small-scale. A relation between this smooth model and the true model can be established through the homogenization technique. In this study, we use the inverse homogenization, or downscaling, to address the problem of quantifying structural uncertainty. In the proposed approach, we apply the homogenization operator in the context of the elastic FWI (HFWI) to obtain the corresponding effective medium. As a second step, we carry out the downscaling inversion: assuming the HFWI solution represents the effective elastic properties of a true earth model, we aim to recover small-scale information. We define the downscaling with a Bayesian formulation and we show, in the case of a 2D fault model, how the inversion strategy is able recover fault-related parameters such as the location, spatial extent of fault-related deformation, slope angle and maximum slip.

**Speaker:** Marius Rapenne

**Date:** Thursday 13th of June 2024, 1:15pm.

**Abstract:**

With the constant increase of computational power, the numerical modelling of lithological site effects can now handle 3D, geologically complex settings. However, a computational overburden is reached when, e.g., uncertainties have to be quantified. A possible pathway towards decreasing the cost of seismic wave simulations in complex media is the non-periodic homogenization. This method is known to provide accurate effective media for wave propagation. In this work, we apply it to 2D sedimentary basins and explore its efficiency and accuracy in terms of amplification simulation. Two homogenization strategies are investigated: the Backus’ one, which considers the geological medium as a juxtaposition of 1D profiles, and the more general 2D homogenization, which involves the resolution of a partial differential equation. Using various velocity contrasts and geometries, we emphasize cases which require the general homogenization for an accurate modelling of amplification effects.

**Speaker:** Julien Herrero

**Date:** Thursday 6th of June 2024, 1:15pm.

**Abstract:**

We introduce a new method for post-stack seismic inversion using Bayesian transdimensional methods in layered media. We employ a reversible jump Markov chain Monte Carlo algorithm, defined within a parsimonious Bayesian framework, to infer not only the values of the model parameters but also the optimal number of layers required to describe the data. The parameterization includes a layer inclination angle to locally infer the stratigraphy from a group of adjacent seismic traces. The forward method generates a set of synthetic seismic traces using a classical convolution model. These synthetic traces are then compared with actual seismic traces to infer the geological model parameters that are layer acoustic impedances, interface depths, and dipping angles. We run the inversion on synthetic data obtained from a two-dimensional reference geometry and show its ability to recover the reference model parameters. This suggests the potential of the method to discover stratigraphic gaps in seismic reservoir characterization tasks. More generally, this demonstrates the capability of transdimensional inversion in quantitative interpretation tasks. It opens opportunities for inversion of entire post-stack seismic sections, accommodating lateral variability with relatively low computational time.

**Speaker:** Paul Marchal

**Date:** Thursday 23th of May 2024, 1:15pm.

**Abstract:**

In mining, assessing uncertainties is an essential step throughout the resource development cycle, from exploration campaigns to remediation and development strategy planning. Indeed, geological data are only partially covering the subsurface and are subject to two main types of uncertainty: i) sampling and measurement uncertainties, and ii) epistemic or conceptual uncertainties related to data interpretation. This paper focuses on the second ones. It aims to evaluate the diversity of conceptual interpretations that specialists and non-specialists have on data, and the potential impact this can have on the estimation of uranium deposit geometries. For this purpose, a case study was carried out in the context of an unconformity-associated uranium deposit in the Athabasca basin. Based on a reference section from this area, a cross-section with synthetic drillcores was produced and given to 30 people to correlate and interpret. Our objectives are multiple: defining metrics for comparing data interpretations, assessing the differences in interpretations between expert and non-expert uranium geologists. We defined a set of mathematical criteria (50) based on 4 key characteristics: i) mineralized zones, ii) associated altered zones, iii) associated structural network, and iv) interpretation glyphs and annotations. Individual and group analysis of the defined criteria (t-SNE, MDS) were performed. Digital Leapfrog models are also compared with hand-drawn models. Primary results show that the group of uranium experts is less dispersed overall in terms of property variance. They tend to propose mineralization zones that are more impacted by the influence of faults and unconformities. They are finally prone to produce less parsimonious interpretations, incorporating more geological concepts.

**Speaker:** Amandine Fratani

**Date:** Thursday 25th of April 2024, 1:15pm.

**Abstract:**

Interpretation of faults is a requirement for a 3D geological modelling process. However, due to the incomplete observations caused by the gap between 2D seismic images or outcrops, the results of this stage can be ambiguous and uncertain. Recently, a proposition of solution based on a graph formalism has been expressed. In the graph, fault observations are represented as nodes, and edges carry the potential of pairwise associations computed from selected expert geological rules. Main limit of this work is that fault observations are not pairwise independent, therefore considering pair prevents the consideration of higher-order effects such as the distribution of the throw along several aligned nodes. We propose to consider a multiple-point likelihood computation to extend the graph where expert rules are replaced using machine learning on analog or partly observed data. The model is trained from a set of selected features such as the length of the fault trace or the throw value. Features are computed from fault traces extracted from 3D geological models. Association potential of k fault observations are then directly computed using the trained model. To prevent overfitting in our small geological models dataset, we propose to mimic a partly interpreted case: we split a 3D domain in two disjoint, contiguous sectors A and B, and use sector A as training and sector B for testing. This presentation will show first results on 2 and 3 points association using a Random Forest algorithm.

**Speaker:** Thomas Bodin

**Date:** Thursday 11th of April 2024, 1:15pm.

**Abstract:**

Earth sciences are by essence multidisciplinary as different fields study the same objects and processes at different scales. In seismology, the challenge is that tomographic models constructed from long period seismograms only “sees” the crust and the mantle as an effective medium, where the smallest scales are given by the resolution power of seismic waves. On the other hand, geodynamics and geochemistry “see” the Earth as a mixture of different chemical components, with the smallest scales given by chemical diffusion. In this presentation, I will show how modern tools from inverse theory, computational statistics, and data science can surpass qualitative interpretations of results obtained separately in different fields. Within a Bayesian framework, we will propose a fully probabilistic approach to explore the ensemble of small-scale earth models compatible with a set of observations and constraints.

**Speaker:** Matthieu Lusseyran

**Date:** Thursday 4th of April 2024, 1:15pm.

**Abstract:**

Understanding the damage processes in clay-bearing rocks is a decisive factor in geological engineering, and for instance considering nuclear waste deep geological repositories. But, more generally they may also contribute to localized deformation, and thus the rupture of fault gauges in seismic zones. However, owing to their complex mineralogy, multiscale microstructures and anisotropy, the mechanisms of clay-rich rock damage and their chronology are not yet well understood. Here we focus on the impact of micro-damage on ultrasonic wave propagation velocity, which is confronted with the corresponding full deformation fields calculated by digital image correlation (DIC). The aim is to associate the acoustic signature with the active deformation mechanisms identified by DIC. To this end, an integrated experimental approach is proposed to characterize localization and to identify the related deformation micro-mechanisms during uniaxial compression of natural clayey rock samples (Tournemire shales) with two simultaneous measurements: 1) the evolution of P-wave velocity within the sample by active acoustics, 2) the development of the 2D mechanical full field by digital image correlation. Both experimental techniques are well known, but the innovation of our approach is to combine simultaneously both measurements. Deformation localization is a multiscale problem, which obviously occurs at the sample scale, but also at the fines scales of the microstructure. Therefore, we developed two different experimental setups. On the one hand, during uniaxial compression with a standard MTS loading frame the macro-scale localization patterns are characterized by optical observations, which image resolution is well suited to the cm sample scale (sample diameter: 3.6 cm and double in length). On the other hand, in order to characterize the initiation of micro-damage at the microstructure scale of the composite type of rock, the same loading protocol is reproduced (while keeping the acoustic diagnosis) on smaller scale mm-sized specimens (sample diameter : 8 mm, double in length), using a home-designed miniature loading frame fit for an environmental scanning electron microscope (ESEM). The latter analysis is carried out under controlled relative humidity of RH = 80%, hence preventing the samples to dry out due to the high vacuum. A similar acoustic signature is identified at both scales of observation, in spite of the variations of experimental conditions imposed by the environmental SEM. We are therefore confident to be able to understand the fracturing process from micro-cracking initiation (microscale) to sample failure (macroscale), and to assess its impact on ultrasonic wave propagation.