Copyright © 2020 Harsha S. Bhat SELFPUBLISHED TUFTE-LATEX.GITHUB.IO/TUFTE-LATEX Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0. Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. FOREWORD This manuscript encloses all documents required to obtain a Habilitation à Diriger des Recherches from École Normale Supérieure. I have synthesised my research work on supershear earthquakes, listed below, that were con- ducted over the last 13 years in collaboration with students, postdocs and colleagues at various institutions around the world. 1. Jara, J., L. Bruhat, S. Antoine, K. Okubo, M. Y. Thomas, Y. Klinger, R. Jolivet, and H. S. Bhat (2020). “Signature of supershear transition seen in damage and aftershock pattern”. submitted to Nat. Comm. 2. Amlani, F., H. S. Bhat, W. J. F. Simons, A. Schubnel, C. Vigny, A. J. Rosakis, J. Efendi, A. Elbanna, and H. Z. Abidin (2020). “Supershear Tsunamis and insights from the Mw 7.5 Palu Earthquake”. to appear in Nat. Geosci. 3. Mello, M., H. S. Bhat, and A. J. Rosakis (2016). “Spatiotemporal properties of sub-Rayleigh and supershear rupture velocity fields : Theory and Experiments”. J. Mech. Phys. Solids. DOI: 10.1016/j. jmps.2016.02.031. 4. Mello, M., H. S. Bhat, A. J. Rosakis, and H. Kanamori (2014). “Reproducing The Supershear Portion Of The 2002 Denali Earthquake Rupture In Laboratory”. Earth Planet. Sc. Lett. DOI: 10.1016/j.epsl. 2013.11.030. 5. Passelègue, F. X., A. Schubnel, S. Nielsen, H. S. Bhat, and R. Madariaga (2013). “From Sub-Rayleigh to Supershear Ruptures During Stick-Slip Experiments on Crustal Rocks”. Science. DOI: 10.1126/ science.1235637. 6. Dunham, E. M. and H. S. Bhat (2008). “Attenuation of radiated ground motion and stresses from three-dimensional supershear ruptures”. J. Geophys. Res. DOI: 10.1029/2007JB005182. 7. Bhat, H. S., R. Dmowska, G. C. P. King, Y. Klinger, and J. R. Rice (2007). “Off- fault damage patterns due to supershear ruptures with application to the 2001 Mw 8.1 Kokoxili (Kunlun) Tibet earthquake”. J. Geophys. Res. DOI: 10.1029/2006JB004425. ACKNOWLEDGEMENTS We are nothing but a sum total of our experiences. We carry these expe- riences from our past to build a better future for ourselves. Many of these experiences are mere reflections of the people who have made profound in- fluences in our lives. I would thus like to acknowledge these individuals who have made me into who I am today. I cherish each one of you and am lucky to have encountered you. From the bottom of my heart, thank you Amma and Appa. I am forever grateful, and mindful, to the sacrifices you have made to ensure that I could carve out my own life. You have protected me from the enormous societal pressures to conform and have always encouraged me in sating my thirst to learn. In your twilight years, my only regret is that I am unable to recipro- cate as much as I should. Some were out of my hand and some were not. I hope you forgive me for the latter. To Deepti, my constant. True to your name, you have been a shining light in my life. Your unwavering love keeps this crazy train on its tracks. To Chikkamma, how apt it is that an aunt is called ‘Little Mother’. My fond memories of learning start with you. I am eternally grateful to my advisors Jim and Renata, my parents in America. Thank you for taking on a twenty one year old boy from small town India under your tutelage. Your profound influence in my life is aptly summarised by a Kannada poet called Kuvempu. Thank you from the bot- tom of my heart. ಮನುಜ ಮತ, ಶ ಪಥ, ಾನ ದೃ, ಾರ ಬು ಇವ ನಮ ಹೃದಯದ ತಮಂತಗಾಗೇಕು Humanism, universalism, scientific outlook, a spirit of inquiry These ought to be our daily hymns – ಕುೆಂಪ To Virginia, Barbara and Chris for mothering me at Harvard. To Ares, who instilled a sense of self-confidence that was severely battered for almost a decade. Thank you my friend. To Charlie, for taking me on as a postdoc and sharing with me your unflappable enthusiasm. To Pritika who took a naive twenty one year old, fresh off the boat in America, under her wings and began his re-education as a social being. 8 When I took on another wild adventure of coming to work in France, a country whose language and culture were alien to me, I didn’t imagine that I would make it this far. For this, I am eternally grateful to Claude Jaupart, Yann Klinger, Nobuaki Fuji, Djimédo Kondo, Ioanna Hélou and Yves Guéguen. To Geoff, my dear friend. Thank you for your support, your friendship and for those moments of discussing our shared love of an Eng- land of the yesteryears. I am especially grateful to Alex for encouraging me here in France and for giving a kick-start to my career that had flagged for almost half a decade. I was fumbling in the dark and in the pits about my future when you extended your friendly hand and pulled me out of it. Thank you Lolo my true friend. From the moment you helped me af- ter my accident to helping me through the vicissitudes of life in France, for a non-European non-American non-white foreigner, you have been the beach in the horizon when I thought I was floundering. Thank you Marion for your friendship and your constant love. Every moment I share with you is cherished and savoured. Do not change. To all my students and postdocs. I have truly learnt a lot from you and my experience with each and everyone of you has left a positive, indelible mark on me. Thank you. To the two true loves of my life. Aziliz and Kiara. You and my science are the only things that matter to me. I love you both and will love you forever and ever and ever ... काममया एवायं पषु इित सा यथाकामो भवित ततरु भवित यातरु भवित तत कम कुते यत कम कुते तद अिभसम पते You are what your deep, driving desire is As your desire is, so is your will As your will is, so is your deed As your deed is, so is your destiny – उपिनषद ् CONTENTS Introduction 11 • A Brief History of Earthquake Source Mechanics 11 • Supershear Earthquake Ruptures 15 Theory 21 • Classification and Stability of Ruptures 21 • 2D Steady State Singular Elastic Model 22 • 2D Steady State Cohesive Zone Models 31 • Far Field Stresses Along Mach Fronts 45 • 2D Spontaneous Rupture Models 47 • 3D Steady State Cohesive Zone Model 50 • Transition to Supershear Speed 72 • Scaling Relationship for Laboratory Earthquakes 79 • Mach Envelopes for Arbitrary Ruptures 81 Experiments 83 • Caltech Laboratory Earthquake Experiment 83 • ENS Laboratory Earthquake Experiment 111 Observations 117 • Ground Motion 117 2002 Denali earthquake 117 2018 Palu earthquake 128 • Far-Field Damage 129 2001 Kunlun earthquake 129 • Off-fault Damage at Transition 132 1999 Izmit ; 2001 Kunlun ; 2002 Denali & 2013 Craig earthquakes 132 • Supershear Tsunamis 136 2018 Palu earthquake 136 Conclusions 143 1 INTRODUCTION 1.1 A Brief History of Earthquake Source Mechanics One of the perennial mysteries of humankind, earthquakes have always fas- cinated, shocked and awe-inspired us. The earliest attempt to provide close to a scientific explanation, as always, dates back to the ancient Greeks. The most famous of these explanations was provided by Aristotle (384–322 B.C.) in his revolutionary treatise titled Meteorologica (Aristotle, 350 B.C.E.). In it he introduced the notion of the four elements (water, fire, air, earth) that compose all terrestrial elements. Aristotle proposed that the cause of earth- quakes consisted in the shaking of the earth by dry heated underground exhalations of winds trapped in cavities of its interior, as they attempt to es- cape toward the exterior (Udias, 1999; Udías et al., 2014). It is worth noting that the Aristotelian idea of earth, “The earth is surrounded by water, just as that is by the sphere of air, and that again by the sphere called that of fire”, still describes the broad sections of earth and atmospheric sciences. It is also worth noting that this theory survived for twenty centuries until the seventeenth century, the era of the birth of modern scientific revolution! The great Lisbon earthquake of 1755, estimated to have a moment mag- nitude of 8.5 ± 0.3 (Solares & Arroyo, 2004), occurred on November 1 on the day of the feast of all saints. It caused the death of tens of thousands of people and turned Voltaire into a pessimist. He was finally forced to reject Leibniz’s notion of “the best of all possible worlds” argument. This earth- quake resulted in Candide and his “Poème sur le désastre de Lisbonne”. It also launched a vigorous scientific inquiry taking earthquakes from the su- pernatural to the natural realm. It is now accepted that this earthquake led to the birth of modern seismology. The pioneering text of Revered John Michell, ‘Conjectures concerning the cause, and observations upon the phe- nomena, of earthquakes’, read at the Royal Society in 1760 firmly estab- lished the notion of an earthquake focus and that waves, traveling at a speed of about 0.5 km/s, propagated out of this focus all over the world.