Geomechanics to solve geological structure issues: forward, inverse and restoration modeling Frantz Maerten To cite this version: Frantz Maerten. Geomechanics to solve geological structure issues: forward, inverse and restoration modeling. Geophysics [physics.geo-ph]. UNIVERSITE MONTPELLIER II SCIENCES ET TECH- NIQUES DU LANGUEDOC, 2010. English. tel-00537899 HAL Id: tel-00537899 https://tel.archives-ouvertes.fr/tel-00537899 Submitted on 19 Nov 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITE MONTPELLIER II SCIENCES ET TECHNIQUES DU LANGUEDOC THESE pour obtenir le grade de DOCTEUR DE L’UNIVERSITE MONTPELLIER II Discipline : Structure et ´evolution de la lithosph`ere Ecole doctorale : SIBAGHE pr´esent´ee et soutenue publiquement par Frantz MAERTEN Le 17 juin 2010 Titre : Geomechanics to solve geological structure issues: forward, inverse and restoration modeling JURY: M. Jean Ch´ery U. Montpellier, France Directeur de th`ese M. David D. Pollard U. Stanford, USA Codirecteur de th`ese M. Bruno L´evy INRIA,France Rapporteur M. Yves Leroy ENS Paris, France Rapporteur M. Xavier Legrand Repsol,Madrid Examinateur M. Marc Daigni`eres U. Montpellier, France Examinateur RESUM´ E´ Utilisation de la g´eom´ecanique pour r´esoudre des probl`emes li´es aux structures g´eologiques: mod´elisation directe, inversion et restauration Diff´erentes applications de l’´elasticit´elin´eaire en g´eologie structurale sont pr´esent´ees dans cette th`ese `atravers le d´eveloppement de trois types de codes num´eriques. Le premier utilise la mod´elisation directe pour ´etudier les d´eplacements et champs de contraintes au- tour de zones faill´ees complexes. On montre que l’ajout de contraintes in´egalitaires, telles que la friction de Coulomb, permet d’expliquer l’angle d’initiation des dominos dans les re- lais extensifs. L’ajout de mat´eriaux h´et´erog`enes et d’optimisations, telles la parall´elisation sur processeurs multi-cœurs ainsi que la r´eduction de complexit´edes mod`eles, permettent l’´etude de mod`eles beaucoup plus complexes. Le second type de code num´erique utilise la mod´elisation inverse, aussi appel´ee estimation de param`etres. L’inversion lin´eaire de d´eplacements sur les failles ainsi que la d´etermination de pal´eo-contraintes utilisant une approche g´eom´ecanique sont d´evelopp´ees. Le dernier type de code num´erique concerne la restauration de structures complexes pliss´es et faill´ees. Il est notamment montr´equ’une telle m´ethode permet de v´erifier l’´equilibre de coupes g´eologiques, ainsi que de retrouver la chronologie des failles. Finalement, nous montrons que ce mˆeme code permet de lisser des horizons 3D faill´es, pliss´es et bruit´es en utilisant la g´eom´ecanique. MOTS-CLES:´ G´eologie structurale, ´elasticit´elin´eaire, mod´elisation directe, inversion, restauration 1 ABSTRACT Geomechanics to solve geological structure issues: forward, inverse and restoration modeling Different applications of linear elasticity in structural geology are presented in this the- sis through the development of three types of numerical computer codes. The first one uses forward modeling to study displacement and perturbed stress fields around com- plexly faulted regions. We show that incorporating inequality constraints, such as static Coulomb friction, enables one to explain the angle of initiation of jogs in extensional relays. Adding heterogeneous material properties and optimizations, such as paralleliza- tion on multicore architectures and complexity reduction, admits more complex models. The second type deals with inverse modeling, also called parameter estimation. Linear slip inversion on faults with complex geometry, as well as paleo-stress inversion using a geomechanical approach, are developed. The last type of numerical computer code is dedicated to restoration of complexly folded and faulted structures. It is shown that this technique enables one to check balanced cross-sections, and also to retrieve fault chronol- ogy. Finally, we show that this code allows one to smooth noisy 3D interpreted faulted and folded horizons using geomechanics. KEYWORDS: Structural geology, linear elasticity, forward modeling, inverse modeling, restoration modeling 2 “Imagination is more important than knowledge” Albert Einstein 3 Preface This thesis is comprised of work that started a while ago, when I was unemployed after a bachelor degree in geophysics and geology at the University of Montpellier II. It has been continued at Stanford University within the research group of Pr David D. Pollard for four years, mainly on correcting, rewriting, enhancing and optimizing an existing 3D boundary element code. Then, several publications have emerged while at Igeoss, a start-up that we created in 2004 in Montpellier with my brother Laurent (who did his PhD with Pr David Pollard), and David Pollard himself. After my return to France from Stanford to start Igeoss, the idea of doing a PhD came to my mind when I realized that a VAE (”valorisation des acquis et de l’experience” which can be translated to ”appreciation of achievements and experiences”) was now possible in France to obtain the equivalent of a master degree in order to start a PhD. Marc Daigni`eres, a professor at the University of Montpellier II, successfully supported my request against a faculty commitee and I was able to start in November 2006, under the direction of Jean Chery (France) and Dave Pollard (USA). Walking in the world of geomechanics, numerical methods, optimizations and program- ming without any knowledge and background is not so simple, but can lead to new insights with the help of the imagination (hence the quote of this thesis). Eleven papers are pre- sented and one is in the appendix, which show the usefulness of linear elasticity. Although during this period three other papers were published (see appendix C), I do not include them within this thesis as I was only a little bit involved. I particularly show in this thesis that using the simple conceptual model of linear elasticity can lead to many application codes which are used to better understand geological struc- tures using either forward, inverse or restoration modeling. The large number of publica- tions using such codes by researchers around the world (more than one hundred twenty), demonstrates their importance. A complete list of publications in different geological do- mains can be obtained on the Igeoss support website at https://support.igeoss.com. Doing this thesis was the opportunity to start the company Igeoss in 2004 in Montpellier, and to continue the research on iBem3D, Dynel2D and Dynel3D while giving 13 inter- national conferences and writing 11 papers as well as a patent for the estimation of the state of stress in complex reservoirs using measures from well bores and faults geometry. 4 Finally, Igeoss integrated Schlumberger, the world’s leading supplier of technology in the oil and gas industry worldwide, after the acquisition in April 2010. 5 Acknowledgments I wish to thanks, first, Dave Pollard who gently guided me in the comprehension of structural geology and geomechanics while at Stanford University. He accepted to take me in his Rock Fracture Project (RFP) group while I was programming graphical interfaces in a small company in Montpellier, and without any knowledge in numerical codes and geomechanics. I think that his choice was mainly motivated by the fact that (1) Laurent, my brother, was already working with him as a ’very good’ PhD student, and that (2) during my free time in France, I was coding a new numerical code in 2D and 3D, namely Dynel. My brother Laurent is also greatly acknowledged, and it is still a pleasure to work together: him, the structural geologist, and me the analytical geologist. While at Stanford University (USA) and in Montpellier (FRANCE), I met many stu- dents, researchers and people from the industry who provided me a diversity of view- points in the domains of structural geology, geophysics and computer sciences. They include (alphabetical ordered): Fabrizio Agosta, Marco Antonellini, Atilla Aydin, Taixu Bai, Loic Bazalgette, Nicolas Bellahsen, Stephan Bergbauer, Stephan Bourne, Jean Ch´ery, Michele Cooke, Juliet Crider, Marc Daigni`eres, Nick Davatzes, Russell Davies, Guil- laume Deconchy, Guilhen De Joussineau, Xavier Du-Bernard, Peter Eichhubl, Patricia Fiore, Eric Flodin, Juan Mauricio Florez, Paul Gillespie, Radu Girbacea, Brita Gra- ham, Paul Griffiths, Joel Ita, Herv´eJourde, Simon Kattenhorn, Ole Kaven, Sotiris Kokkalas, S´ebatien Lacase Serge Lallemand, Xavier Legrand, Bruno Levy, Lidia Lon- ergan, Michel Lopez, Peter Lovely, Stephen Martel, Maurice Mattauer, Matteo Molinaro, Jordan Muller, Ovunc Multu, Rodrick Myers, Ian Mynatt, Fabien Pauget, Jean-Pierre Pe- tit, Jean-Christophe Perez, Phil Resor, Paul Segall, Michel Seranne, Roger Soliva, Kurt 6 Sternlof, Lans Taylor, Haiquing Wu, Scott Young, Amgad Younes, Wenbing Zhang, Marc Zoback, and certainly many other people... I thanks people who accepted to review this work in a short time: Bruno Levy and Yves