Assessing Site Response Complexity Using Single Station HVSR: Mexico City Case Study A master’s thesis submitted by Marshall A. Pontrelli In partial fulfillment of the requirements for the degree of Master of Science In Civil and Environmental Engineering Tufts University August 2019 Adviser: Dr. Laurie Baise Committee Members: Dr. Dick Plumb, Dr. Juan Pestana and Dr. Jon Lamontagne i Purpose: Use the horizontal to vertical spectral ratio (HVSR) to characterize site response in high impedance basin environments. Test the applicability of the Thompson et al. (2012) statistics to the HVSR. Demonstrate that the shape of the HVSR can be used to characterize site response and potentially identify site response complexity, the shape being characterized by: the total number of peaks, and the frequency, amplitude, half power bandwidth and interevent variability of the fundamental peak. ii “As an earthquake wave travels from strata to strata, if we study its reflection and changing velocity in transit, we may often be led to the discovery of certain rocky structures buried deep beneath our view, about which without the help of such waves it would be hopeless ever to attain any knowledge… Earthquakes are gigantic experiments which tell the elastic moduli of rocks as they exist in nature, and when properly interpreted may lead to the proper comprehension of many ill-understood phenomena.” -John Milne 1898 iii ABSTRACT Sedimentary basins with high impedance contrasts can lead to significant shaking due to local site response during earthquakes and, as a result, pose a significant risk to infrastructure and local populations. The site response transfer function is most often modeled as the response of a soil column to a forcing function assuming vertically propagating shear waves through horizontal, laterally homogenous soil systems. In real soil systems, however, these assumptions tend to collapse due to wave scattering through heterogenous materials, significant attenuation, non- vertical incidence, and other complexities in the subsurface. In work by Thompson et al. (2012), the authors develop a taxonomy using surface-downhole spectral ratios from weak ground motions for classifying a site’s resonant behavior referenced to the SH1D condition. We attempt to apply this taxonomy to single station recordings in Mexico City, a case study where basin effects are well documented, by using the horizontal to vertical spectral ratio (HVSR) (Nakamura, 1989) as a first estimate of the site empirical transfer function (Lermo and Chávez-Garcia, 1994b), and using a theoretical transfer function derived from inversion. The HVSR clearly identifies a fundamental resonance peak and even higher resonance modes at some stations in the basin; however, the shape of the HVSR changes from the transition zone (at the edge of the basin) into the lake bed sediments (within the basin). The inverted theoretical transfer function also exhibits limitations mapping onto the HVSR. We extend the taxonomy by proposing a set of statistics describing the shape of the HVSR to assess site response complexity: the number of significant peaks, and the frequency, amplitude, half power bandwidth and interevent variability of the fundamental peak. We observe that these statistics vary spatially across the extent of the Mexico City basin in quantifiable patterns, reflecting variations in subsurface properties and providing indications of complex site response. iv TABLE OF CONTENTS Abstract………………………………………………………………………………………...iv Table of contents…………………………………………………………………………….…..v List of figures…………………………………………………………………………………..vii List of tables…………………………………………………………………………………....ix List of equations…………………………………………………………………………….…...x 1.0 Introduction 1.1 Background……………………………………………………………………………1 1.1.1 Site response definition…………………………………………...…………1 1.1.2 Theoretical transfer function……………………………………………...…3 1.1.3 Empirical transfer function……………………………………….…………6 1.1.3.1 Surface-borehole ETF……………………………………………..7 1.1.3.2 Simple spectral Ratio ETF………………………………………...7 1.1.3.3 HVSR…………………………………………………………...…8 1.2 Motivation……………………………………………………………………………10 1.3 Hypothesis……………………………………………………………………………14 2.0 Data 2.1 Mexico City RACM network……………………………………………………...…17 2.1.1 Background……………………………………………………...…………17 2.1.2 Earthquake details and tectonic setting… ...……………………………….18 2.2 Geologic and geotechnical Properties…..…………………………………………....19 2.2.1 Geology………………………………………………………………….…19 2.2.2 Geotechnical zones……..……..……..……..…….....……..……..……..…22 2.2.3 Basin structure…..……..……..……..……..……..……..…………..……..23 3.0 Methods 3.1 HVSR……………………………………………………………………………...…26 3.1.1 Signal processing, magnitude responses and HVSR..…..……..…..…..…....26 3.1.2 Computing median, standard deviation and 95% confidence interval……...27 3.2 TTF inversion…..……..……..……..……..……..……..……..……..……..…..…….28 3.3 Thompson et al. (2012) statistics……………………………….…………………….31 3.4 Peak identification…………………………………………………………………....31 3.5 Peak shape statistics……………………………………………………………….....34 3.6 Peak finding and statistics system design..………………………………………..…35 4.0 Results 4.1 Inversion results……………………………………………………………………...38 4.2 Thompson et al. (2012) statistics..…..…..……..……..…..……..……...……..……..39 4.2.1 Transition zone stations…………………………………………………....43 4.2.2 Lake zone stations………………………………………………………….44 4.3 Transect using HVSR shape statistics...……..……..……..……..……...……...…….49 4.4 Spatial statistics..……..……..……..……..……..……..……..……….…..…….....…53 4.4.1 Number of peaks.……..……..……..……..……..……..……..………..…..53 v 4.4.2 Fundamental peak statistics fn, a, HPB and σi …….…..……….……..……56 5.0 Discussion 5.1 Thompson et al. (2012) statistics…………………………………….……...……….60 5.2 Number of peaks in the HVSR………………………………………………………60 5.3 Shape statistics…………………………………………….……..……..……………61 5.3.1 Fundamental frequency…………………………………………………….61 5.3.2 Amplification………………………………………………………………63 5.3.3 Half power bandwidth………………………………………………….…..67 5.3.4 Interevent variability………………………………………………...……..71 6.0 Conclusions…..……..……..………..……..……..……..……………..……..……..……..…76 Acknowledgements …..……..……..……..……..……..…….....……..……..……..……..…..80 References…..……..……..……..……..……..…………....……..……..……..……..……..…81 Appendix…..……..……..……..……..……..……..……..……..……..……..……..…………86 Tables…..……..……..……..……..……..……..……..……..……..……..……..……..….....109 vi LIST OF FIGURES 1. Puebla Earthquake waveforms……………………………………………………………...2 2. TTF examples……………………………………………………………………………….3 3. Site response model…………………………………………………………………………5 4. Basin cartoon………………………………………………………………………………..7 5. HVSR Rayleigh wave derivation…………………………………………………………..10 6. Thompson et al. (2009) example..………………………………………………………….13 7. Thompson et al. (2009) example..………………………………………………………….13 8. HVSR-TTF example………………………………………………………………………15 9. Mexico City HVSR shapes………………………………………………………………...16 10. RACM network stations………………………………………………………………..….18 11. Earthquake events used in this study……………………………………………………….19 12. Geologic profile……………………………………………………………………………20 13. Shear wave velocity profile………………………………………………………………..21 14. Geotechnical zones………………………………………………………………………...23 15. Fundamental period map and basin structure……………………………………………....25 16. HVSR magnitude response example………………………………………………………27 17. HVSR averaging example…………………………………………………………………28 18. Objective function demonstration…………………………………………………………30 19. Peak finder example……………………………………………………………………….33 20. HPB and σi computation example………………………………………………………….35 21. Shape statistics example…………………………………………………………….……..36 22. System workflow…………………………………………………………………………..37 23. Inversion depth and damping maps………………………………………………………..39 24. Thompson et al. (2012) statistics…………………………………………………………..40 25. LG stations………………………………………………………………………………...41 26. LP stations with r > 0.55…………………………………………………………………...42 27. Transition zone stations……………………………………………………………………44 28. Lake zone stations…………………………………………………………………………46 29. Box and whisker plot of Thompson et al. (2012) statistics…………………………………47 30. Map of classifications……………………………………………………………………...48 31. Transect station locations………………………………………………………………….50 32. Transect station HVSRs……………………………………………………………………51 33. Transect number of peaks………………………………………………………………….52 34. Transect fundamental peak statistics………………………………………………………53 35. Number of peaks across all stations bar chart………………………………………………54 36. Number of peaks across all stations map…………………………………………………...55 37. Shape statistics map………………………………………………………………………..57 38. Shape statistics box and whisker…………………………………………………………...58 39. Shape statistics vs fn………………………………………………………………………..59 40. fn and depth………………………………………………………………………………...62 41. Depth to DD from Moisés et al. (2016)…………………………………………………….63 42. Magnitude responses from the lake zone…………………………………………………..65 43. Magnitude responses from the transition zone……………………………………………..66 44. HPB vs. fn linear relationship………………………………………………………………68 vii 45. HPB vs. fn using ζ values from inversion…………………………………………………..69 46. HPB vs. fn from HVSR…………………………………………………………………….70 47. HPB vs. fn for all three realizations………………………………………………………...70 48. σi comparison………………………………………………………………………………72 49. Sigma vectors in the transition zone……………………………………………………….73 50. Sigma vectors in the lake zone……………………………………………………………..74 viii LIST OF TABLES 1. Station information*……………………………………………………………………….109 2. Event information*……………………………………………………………………...…111 3. Peak finding example………………………………………………………………………..34 4. Peak statistics along transect…………………………………………………………..…….52