Earthquake Forecasts: The Life-Saving Potential of Last-Minute Warnings by Armann Ing61fsson B.S.. Industrial Engineering, University at Buffalo, 1989 and S.M., Operations Research, MIT, 1991 Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degrees of Doctor of Philosophy in Operations Research at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 1994 @ Massachusetts Institute of Technology 1994. All rights reserved. A Au th o r ................ ... .. ......... .................... Department of Electrical ngineering and Computer Science 30 August 1994 /'2 I'm Certified by... ........ .. .... ...... .......... .. ... ... Arnold I. Barnett Professor of Operations Research and Management Thesis Supervisor Accepted by.............. ................ .. ........................... Robert M. Freund Acting Co-Director, Operations Research Center Earthquake Forecasts: The Life-Saving Potential of Last-Minute Warnings by Armann Ing6lfsson Submitted to the Department of Electrical Engineering and Computer Science on 30 August 1994, in partial fulfillment of the requirements for the degrees of Doctor of Philosophy in Operations Research Abstract An attempt was made to estimate how many lives could be saved if unequivocal earthquake warnings were possible before major earthquakes. The estimates are for urban areas in California and are contingent on the best-case assumptions that (1) the best available communication strategies are used and (2) individuals react to the warnings by immediately taking the most beneficial action (e.g., exit the building), under the circumstances. The results of a survey of experts were combined with estimates of population fractions for each of a set of categories (e.g., "people at home, awake") and simple mathematical models to arrive at the estimates. On taking the expert judgment at face-value, we estimate that 3 minutes are needed to halve the death toll and an additional 22 minutes reduce the remaining death toll by 510%. Under a model-based procedure, where the expert judgment was used to calibrate a set of first-principles based models, the corresponding halving times were estimated to be 1.5 and 28.5 minutes. With one minute of warning, we estimate that 45% of the deaths could be avoided, under both the face-value and model-based approaches. This scenario is of particular interest because with real-time earthquake monitoring such lead-times are thought to be possible for some regions. The implications of three recent earthquakes were examined. Based on mortality pat- terns in the 1994 Northridge and 1989 Loma Prieta quakes we conclude that commonly quoted death toll estimates for "the Big One" expected to strike California may overes- timate both the number of deaths (by a factor of 4 to 15) and the time-of-day variation (by a factor of two) in the death toll. The consequences of the 1988 Armenia earthquake lead us to believe that unequivocal earthquake warnings - were they possible - have greater life-saving potential in the third world in both absolute and percentage terms. Thesis Supervisor: Arnold I. Barnett Title: Professor of Operations Research and Management Acknowledgements On August 30th, the day of my thesis defense, I read in the Tech that a ribbon-cutting ceremony for the new Biology building (building 68) was scheduled for sometime in October. This news was important to me, because for the last three years I have been measuring my progress on this thesis against the pace at which this building has risen from the ground. For a. while, it looked as if the building would be completed before my thesis. To console myself I first reasoned that the comparison was unfair, since many more people were involved in the construction of the biology building, whereas I was laboring alone on my thesis. Then, I came up with a much better rationalization: I should be comparing the date at which I defend my thesis with the date at which the Biology building is officially opened; not the date at which the first tenants move in. Of course, my first rationalization was not very good: I was not alone. Many people have helped me complete this thesis and I would like to thank some of them. I would like to thank Arnie Barnett for supervising my thesis: thank you! I have learned many valuable lessons from you during the last three years; sometimes concerning matters that I thought I had nothing more to learn about. Working with you has been thoroughly enjoyable. The other members of my thesis committee - Professors Al Drake, Amedeo Odoni, and Robert Whitman - all nudged the thesis in directions that cause me to be happier with the final product. I thank Professor Whitman for sharing his wealth of knowledge about earthquakes with me. I thank Al Drake and Amedeo Odoni not only for taking an interest ini my thesis but also for providing me with financial support during its preparation. I would also like to thank Al for personal advice, which was not always solicited, but always appreciated. This thesis could not have been completed without the effort of the many experts that completed my questionnaire. Most of these people I have never met; this makes me all the more grateful for their efforts. I have had valuable conversations with Professors Norm Rasmussen, Leonard Morse-Fortier, Daniele Veneziano, and Dick Larson; I thank them all. I cannot think of a better environment to work in than the Operations Research Center. I thank Paulette, Laura, Cheryl, and other staff members before them. I know there are only two reasons why the place is not run perfectly: students and Professors. Even with those two groups around, you do a great job. I thank the many students I have met for their friendship; I hope it will continue long after we have all graduated from MIT. Raghu: It has been great having someone to share the trials and tribulations of the final stages of thesis-writing with. Rob: Thanks for letting me run past you once in a while. It's been fun strategizing about how to deal with ... Oops, I better not mention that yet! Joe, Kerry, Mitchell, Sungsu, Pieter, Michael, Ediel, Alan, Rama, Rich, Rodrigo, and many others that I don't mention but should: It has been my good fortune to know you; I hope we will stay in touch. Finally, I thank my parents, my brother, and my sister for their support. Dedication I dedicate this thesis to my grandfather, Armann Dalmannsson, who was born 100 years before it was finished. I did not know him for long, but long enough to recognize that lihe was a great man., Contents 1 Introduction 11 1.1 Can Earthquake Prediction Save Lives? A Rudimentary Model ...... 13 1.2 Outline of the Thesis and Its Findings ................... .. 15 2 Background and Literature Review 19 2.1 Earthquake Risk and How It Can Be Reduced . ................ 19 2.2 Is Earthquake Prediction a Realistic Future Possibility? . ....... .. 27 2.2.1 Real-Time Earthquake Monitoring . .................. 29 2.3 A Sociological Perspective: Risk Communication Theory . .......... 32 2.4 Cost-Benefit Frameworks for Earthquake Prediction . ............ 35 3 Gathering of Data 39 3.1 Estimates of the Population Fractions {Fi(t)} . ........... ... 40 3.1.1 Where People Were During the 1989 Loma Prieta Earthquake . 42 3.1.2 Household Travel Survey Data ..................... 43 3.1.3 Aggregate Data on Commuting Patterns . ............... 45 3.1.4 Data on Television Viewing . .................. .... 45 3.1.5 Fraction of Cars on Freeways that are On, Under, or Near an Overpass 46 3.1.6 Various Educated Guesses ................... ..... 47 3.2 Earthquake Loss Studies: Estimates of the Baseline Death Rates Di(O) . 50 3.2.1 The USGS/NOAA Studies ...................... .. 50 3.2.2 The ATC-13 Report ........................... 54 3.3 The Design and Administration of the Questionnaire . ............ 55 3.3.1 The List of Experts ........................... 56 3.3.2 The Design of the Questionnaire . .................. 56 Appendix 3A: User's Manual for the Questionnaire . ................ 66 4 Models of Reactions to Earthquake Warnings 69 4.1 Description of a Model for the Death Toll . .................. 69 4.1.1 Description of a Model for the Death Rates . ............. 71 4.1.2 Assum ptions ................... ... ........ 71 4.2 Models for Warning Propagation ............. .......... 74 4.2.1 Behavioral Assumptions ................... ...... 76 4.2.2 Solution of the Differential Equation . ................. 76 4.3 Models for the Time Needed to Complete the Best Action . ......... 79 4.4 Estimation of the Baseline and Revised Death Rates . ............ 82 4.5 Estimation of the Parameters in the Propagation Model . .......... 86 4.5.1 Least-Squares Estimation ............. ..... .. 86 4.5.2 Maximum Likelihood Estimation ................... 89 4.5.3 Bayesian Estimation ............... .. ....... .. 89 Appendix 4A: Properties of the Homogeneous Mixing Model . .......... 91 Appendix 4B: A Model that Incorporates Spatial Dependence . .......... 93 Appendix 4C: Estimating the Median of a Lognormal distribution . ....... 98 5 Results of the Survey of Experts 103 5.1 Introduction ........... ................ ... .... 103 5.1.1 The Questionnaire Data ......................... 103 5.2 Two Uses of Expert Opinion ........................ .. 104 5.3 Face-Value Analysis ....... ...... ... ............. 105 5.3.1 Baseline Death Rates .......... .. ......... .. 105 5.3.2 Relative Death Rates ........... .... ....... .. 110 5.3.3 Overall Relative Death Rates ...............