Integration of spatial dependencies in machine-learning algorithms for the assisted lithological interpretation of well-log data

IFP Energies nouvelles (IFPEN) est un acteur majeur de la recherche et de la formation dans les domaines de l’énergie, du transport et de l’environnement. Depuis les concepts scientifiques en recherche fondamentale jusqu’aux solutions technologiques en recherche appliquée, l’innovation est au cœur de son action, articulée autour de quatre orientations stratégiques : climat, environnement et économie circulaire ; énergies renouvelables ; mobilité durable ; hydrocarbures responsables.

Dans le cadre de la mission d’intérêt général confiée par les pouvoirs publics, IFPEN concentre ses efforts sur l’apport de solutions aux défis sociétaux et industriels de l’énergie et du climat, au service de la transition écologique. Partie intégrante d’IFPEN, IFP School, son école d’ingénieurs, prépare les générations futures à relever ces défis.

Integration of spatial dependencies in machine-learning algorithms for the assisted lithological interpretation of well-log data

Well logs are collections of data characterizing the geological formations traversed by a borehole. They take the form of correspondences between depth and sets of petrophysical measurements. The interpretation of these well logs in terms of rock types, or lithologies, is a cornerstone process in various domains related to the subsurface: energy resources production, carbon and gas storage, geothermal energy, water resources management, environmental studies, geotechnical engineering, etc.

Traditional methods rely heavily on expert judgment, which can be time-consuming and subjective. Machine-learning algorithms offer a promising tool to assist experts in their task, enabling the automation of data interpretation—at least partially. However, challenges remain in ensuring that these algorithms account for spatial dependencies inherent in geological data, provide explainable results, and incorporate geoscientific knowledge.

This internship focuses on the issue of spatial dependencies. Indeed, due to the history of sedimentary depositional environments, well-log data are autocorrelated in the sense that a given measurement is correlated, to a certain extent, to surrounding measurements belonging to either the same well or one nearby.

One method coming from Bayesian analysis which has been used with some success in this context, and has briefly compared to deep-learning algorithms, is the Hidden Markov Model (HMM). In this approach, the observed well-log data stem from the outcome of an inaccessible underlying Markov process whose states are the possible rock types considered; the goal is to select appropriate transition matrices and infer the Markov states from the knowledge of the well logs. Following a classical Bayesian approach, the best possible Markov states given the data can be expressed as an optimization problem hopefully solvable numerically. With this supervised method at hand, it is possible to predict rock formations along a given well where lithologies are unknown while taking spatial dependency into account, as well as provide confidence estimates of the predictions in terms of posterior probabilities.

Objectives

• Code the HMM for well-log interpretation in Python using existing libraries and literature results.
• Test the HMM on synthetic and real-case data by comparing it to other supervised approaches.
• Focus on single-well autocorrelation, and extend to multiple wells if time permits.

Requirements

Master 2-level internship

• Fluency in mathematics (analysis, probability and statistics)
• Solid grounding and interest in machine learning and its applications to environmental sciences
• Strong object-oriented programming skills (Python or C++, preferably Python)
• Ability to thrive in an R&D environment: curiosity, autonomy, initiative