Rapid Finite Fault Inversion for Megathrust Earthquakes Roberto F. Benavente Bravo A thesis submitted for the degree of Doctor of Philosophy (PhD) The Australian National University March, 2016 ii c Roberto Benavente 2016 Declaration This thesis is an account of research undertaken between December 2011 and December 2015 at the Research School of Earth Sciences, College of Physical & Mathematical Sciences, The Australian National University, Canberra, Australia. Except where acknowledged in the text, the material presented in this thesis is, to the best of my knowledge, original and has not been submitted in whole or part for a degree in any university. Roberto Benavente July, 2016 iii iv Acknowledgements Many people have contributed to this research both directly by providing me with some advice and knowledge and indirectly with moral support and encouragement. I will do my best to include everyone in this list. Firstly, I would like to thank my supervisor Phil Cummins whose guidance and support were fundamental for this research. He introduced me to the topic of finite fault inversion, which I find fascinating, and showed me how it relates to natural hazards. His acute scientific insight was crucial every time I was stuck in my work, assisting me in resolving the issues and finding new directions for my research when pertinent. He was also extremely supportive when I was struggling with personal issues which is something I sincerely appreciate. Big thanks to Jan Dettmer who came to RSES when I was half way through my PhD. I have learned a lot from him, especially about inversion theory and statistics which turned out to be the core aspects of my research. His meticulous and rigorous approach to inverse problems substantially improved my first inversion methods and greatly motivated the introduction of the Bayesian framework I discuss in Chapter 5. Prof. Malcolm Sambridge was also very supportive and was always willing to share some insights about the inverse problem theory. I also benefited from discussions and advice from Hrvoje Tkalˇci´cand Brian Kennett. The calculations of the forward model in all the applications in this thesis were made using a Green Function database kindly provided by Luis Rivera, Hiroo Kanamori and Zacharie Duputel. I would particularly like to thank prof. Rivera who gave me useful information about the computation of the database. My short research stay at ETH was made possible through the efforts of Andreas Fichtner who also instructed me how to use SES3D software. Stan Dosso reviewed a pre- liminary version of the manuscript presented in Chapter 5 providing helpful insights. At RSES we are fortunate enough to have an excellent professional staff. The IT support team is outstanding and I always got timely assistance when required. Maree Coldrick, Sherryl Kluver and Mary Hapel were always keen to help me with all the administrative issues I came across. The vast majority of software I v vi developed relies on open source applications such as Python, NumPy, SciPy, Obspy, Matplotlib and OpenQuake. Thank you to all those developers for such an amazing work. I am also grateful to all the students and post docs of the Earth Physics group at RSES. Not only have I solved many research problems thanks to them but also they helped in hard times and offered me sincere friendship. I will miss you guys! My PhD was supported by the Chilean scholarship program \Becas Chile", this whole experience would not be possible without their financial support. Finally, I want to thank my family for their unconditional support. My wife Carolina has been supportive throughout this adventure. I feel very lucky to share my life with such an amazing person. My parents encouraged me to work hard and pursue my dreams with passion. Thanks to all my family and friends in Chile, I truly think you are all part of this achievement. Abstract The largest earthquakes take place at subduction zones, and their devastating impact in populated regions is often exacerbated by their ability to excite powerful tsunamis. Today, we understand that large subduction earthquakes, known as megathrust events, are caused by the sudden release of elastic strain energy stored at the plate boundaries where a localized, previously locked, section of the megathrust ruptures. The rupture process can propagate over hundreds of kilometres and slip on the fault can be tens of meters. Using ground motion data to image the spatio-temporal spread of slip over the fault surface is known as finite fault inversion (FFI). Over the past decade FFI has become almost routine, so that results produced by different groups are available within several days or even hours after a large event. However, these results typically require manual processing of the data, and are not accompanied by appraisals of uncertainty. My PhD research has focused on obtaining slip models for such events in near real time. I divided my analysis into three main projects that are discussed in this thesis. First, I evaluated the performance of a long period seismic wave, the W-phase, which arrives between P and S waves, in a classic FFI scheme for the Maule (2010, Mw = 8.8) and Tohoku (2011, Mw = 9.1) events. I found that, despite its long period, the W-phase can resolve first order features of the rupture for both events. Since the W-phase is not very sensitive to 3D structure, the processing of data for the W-phase is generally simpler than it is for the body and surface waves that are commonly used for FFI. In addition, the W-phase is fast and can be obtained soon after the arrival of the P-wave. Second, I improve the classic inversion scheme to increase robustness and rigour for rapid inversions. The most remarkable aspects of this inversion approach are that the faulting surface is constrained to follow the 3D subducting slab geometry and that the smoothness of the rupture is objectively determined. I used this approach for the recent Illapel event (2015, Mw = 8.3) and showed that a meaningful preliminary model can be obtained within 25 minutes from rupture onset. A refined solution can be obtained 1 hour from the origin time, which is still useful for the management of the disaster. vii viii Finally, I have developed a novel linearized inversion method that allows slip uncertainties to be estimated during rapid finite fault inversion. This is an intrinsically complex problem as normally positivity constraints are imposed on finite fault models to ensure well behaved solutions. Uncertainties are typically unavailable for FFI results, but they can be crucial for meaningful interpretation of the slip models. To estimate them, I follow a probabilistic Bayesian framework but avoiding the computationally demanding Bayesian sampling. Instead, by using a coordinate transformation, the posterior distribution is approximated and obtained by linearized inversion. This inversion scheme was tested employing both simulated and real W-phase data, showing that meaningful uncertainty estimates can be inferred. Comparison with Bayesian sampling is also performed suggesting that the error of approximating the posterior is small. Including uncertainty estimates in early finite fault models will reduce the risk of working with misleading solutions. The rigour, objectivity and robustness of the inversion techniques devised in this thesis can be a valuable contribution to the FFI community. Since I have utilized mostly open source software and a desktop computer to carry out this research, the tools I have developed can be easily used for early warning in most seismic observatories. I believe that, when facing such disastrous events, the methods developed here can be important to assist authorities with emergency response. Contents Declaration iii Acknowledgements v Abstract vii 1 Introduction 1 1.1 Thesis Outline . 4 1.2 Publication Schedule . 6 2 Background 9 2.1 Basic Theory in Source Studies . 9 2.2 Point Source Approximation . 13 2.2.1 Rapid determination of the moment tensor: Application to Geoscience Australia (GA) and Centro Sismol´ogicoNacional (CSN, Chile) . 20 2.3 Finite Fault Problem . 22 2.4 The Multiple-time-window Method . 25 3 W-phase Finite Fault Inversion 29 3.1 Abstract . 29 3.2 The W-phase and Rapid Source Characterization . 30 3.3 Approach . 32 3.4 Models for the Maule and Tohoku Earthquakes . 37 3.4.1 Maule earthquake . 38 3.4.2 Tohoku earthquake . 39 3.5 Conclusion . 40 4 Automated Algorithm for Finite Fault Inversion in Megathrust Events 43 4.1 Abstract . 43 4.2 Introduction . 44 4.3 Inversion scheme . 45 4.4 Preliminary Rapid W-phase point source solution . 48 ix x Contents 4.5 Estimation of required parameters . 50 4.6 Inversion Results . 54 4.7 Conclusion and discussion . 58 5 Estimating Uncertainty from Rapid Finite Fault Models 67 5.1 Introduction . 67 5.2 Bayesian Inversion Framework . 70 5.2.1 Parametrization and Positivity Constraints . 71 5.2.2 Positivity by variable transformation . 73 5.2.3 Uncertainty estimation by linearization . 75 5.2.4 Inversion strategy . 76 5.3 Inversion for simulated data . 78 5.3.1 Effects of smoothing in logarithmic space . 79 5.3.2 Uncertainty estimation for different noise levels . 80 5.3.3 Comparison with nonlinear Bayesian sampling . 81 5.4 Application: Illapel great earthquake (2015, Mw=8.3), Chile . 84 5.5 Summary and Discussion . 85 6 Conclusion and Discussion 89 6.1 Discussion and future work . 90 A Computation of Hessian and gradient of the non-linear objective function 93 B Confidence intervals for log-normal distribution 97 List of Figures 1.1 Tsunami travel times for the Sumatra 2004 event. The seismic source region is indicated by a red ellipse and contours show the arrival time of the tsunami wave in hours.