A Bayesian model for truncated regression for the estimation of empirical ground-motion models
Tóm tắt
We present a Bayesian model for the estimation of ground-motion models that allows one to account for truncated data. Truncated data occurs in ground-motion model development because instruments do not record continuously, but only when triggered. The model is formulated as a multi-level model and incorporates event and station terms. The model considers truncation on one variable [e.g., peak ground acceleration (PGA)], and models the joint occurrence of PGA and other ground-motion intensity measures, while conditioning on the truncation for PGA. Initially, we perform numerical experiments on simulated data sets and show that not taking data truncation into account leads to biased models. Regressions using the proposed truncated model can recapture the functions used in the simulation well, and perform comparable to alternative approaches used in the past. Subsequently, we show the impact of the truncated model on observed ground-motion data representing moderate and high trigger levels, 2–4 gal and 10 gal, respectively. Differences to a model that does not take truncation into account occur at larger distances, and are more severe for the high trigger level data. For untruncated regression, the values of the standard deviations are underestimated.
Tài liệu tham khảo
Abrahamson NA, Silva WJ, Kamai R (2014) Summary of the ASK14 ground motion relation for active crustal regions. Earthq Spectra 30(3):1025–1055
Abrahamson NA, Youngs RR (1992) A stable algorithm for regression analysis using the random effects model. Bull Seismol Soc Am 82(1):505–510
Al-Atik L, Abrahamson N, Bommer JJ, Scherbaum F, Cotton F, Kuehn N (2010) The variability of Ground-Motion prediction models and its components. Seismol Res Lett 81(5):794–801
Aldama-Bustos G, Bommer JJ, Fenton CH, Stafford PJ (2009) Probabilistic seismic hazard analysis for rock sites in the cities of Abu Dhabi, Dubai and Ra’s Al Khaymah, United Arab Emirates. Georisk 3(1):1–29
AlHamaydeh M, Aly N, Galal K (2017) Impact of seismicity on performance and cost of RC shear wall buildings in Dubai, United Arab Emirates. J Perform Constr Facil 31(5):04017083
AlHamaydeh M, Aly N, Galal K (2018) Seismic response and life-cycle cost of reinforced concrete special structural wall buildings in Dubai UAE. Struct Concrete 19(3):771–782
Aly N, AlHamaydeh M, Galal K (2020) Quantification of the impact of detailing on the performance and cost of RC shear wall buildings in regions with high uncertainty in seismicity hazards. J Earthq Eng 24(3):421–446
Amiri GG, Mahdavian A, Dana FM (2007) Attenuation relationships for Iran. J Earthq Eng 11(4):469–492
Ancheta TD, Darragh RB, Stewart JP, Seyhan E, Silva WJ, Chiou BS-J, Wooddell KE, Graves RW, Kottke AR, Boore DM, Kishida T, Donahue JL (2014) NGA-West2 database. Earthq Spectra 30(3):989–1005
Aoi S, Kunugi T, Fujiwara H (2004) Strong-motion seismograph network operated by nied: k-net and kik-net shin. J Jpn Assoc Earthq Eng 4(3):65–74
Betancourt M (2017) A conceptual introduction to Hamiltonian Monte Carlo. PreprintArXiv:1701.02434. Columbia University, New York
Betancourt M, Girolami M (2015) Hamiltonian Monte Carlo for hierarchical models. Current trends in Bayesian methodology with applications. Chapman and Hall, London, pp 79–101
Bommer JJ, Abrahamson NA (2006) Why do modern probabilistic seismic-hazard analyses often lead to increased hazard estimates? Bull Seismol Soc Am 96(6):1967–1977
Boore DM (2010) Orientation-independent, nongeometric-mean measures of seismic intensity from two horizontal components of motion. Bull Seismol Soc Am 100(4):1830–1835
Boore DM, Stewart JP, Seyhan E, Atkinson GM (2014) NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes. Earthq Spectra 30(3):1057–1085
Bozorgnia Y, Abrahamson NA, Atik LA, Ancheta TD, Atkinson GM, Baker JW, Baltay A, Boore DM, Campbell KW, Chiou BS-J, Darragh R, Day S, Donahue J, Graves RW, Gregor N, Hanks T, Idriss IM, Kamai R, Kishida T, Kottke A, Mahin SA, Rezaeian S, Rowshandel B, Seyhan E, Shahi S, Shantz T, Silva W, Spudich P, Stewart JP, Watson-Lamprey J, Wooddell K, Youngs R (2014) NGA-West2 research project. Earthq Spectra 30(3):973–987
Bozorgnia Y, Kishida T, Abrahamson NA, Ahdi SK, Ancheta TD, Archuleta J, Atkinson G, Boore DM, Campbell KW, Chiou B, Contreras V, Darragh R, Gregor N, Gulerce Z, Idriss IM, Ji C, Kamai R, Kuehn N, Kwak DY, Kwok A, Lin P-s, Magistrale H, Mazzoni S, Muin S, Parker G, Si H, Silva WJ, Stewart JP, Walling M, Katie E, Youngs RR (2018) NGA-subduction research program NGA-subduction research program. In: Proceedings of the 11th national conference on earthquake engineering
Bradley BA (2011) Empirical correlation of PGA, spectral accelerations and spectrum intensities from active shallow crustal earthquakes. Earthq Eng Struct Dyn 40(15):1707–1721
Bragato PL (2004) Regression Analysis with Truncated Samples and Its Application to Ground-Motion Attenuation Studies. Bull Seismol Soc Am 94(4):1369–1378
Carpenter B, Gelman A, Hoffman MD, Lee D, Goodrich B, Betancourt M, Brubaker M, Guo J, Li P, Riddell A (2017) Stan : a probabilistic programming language. J Stat Softw 76(1):1–32
Chao S-H, Chen Y-H (2019) A novel regression analysis method for randomly truncated strong-motion data. Earthq Spectra 35(2):977–1001
Chao S-H, Chiou B, Hsu C-C, Lin P-S (2020) A horizontal ground-motion model for crustal and subduction earthquakes in Taiwan. Earthquake Spectra 36(2):463–506
Chiou BS-J, Youngs RR (2014) Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthq Spectra 30(3):1117–1153
Contreras V, Stewart JP, Kishida T, Darragh RB, Chiou BSJ, Mazzoni S, Kuehn N, Ahdi SK, Wooddell K, Youngs RR, Bozorgnia Y, Boroschek R, Rojas F, Órdenes J (2020) Chapter 4: source and path metadata. In: Stewart JP (ed) Data Resources for NGA-Subduction Project, PEER Report 2020/02. Pacific Earthquake Engineering Research Center, UC Berkeley (Headquarters)
Darzi A, Zolfaghari MR, Cauzzi C, Fäh D (2019) An empirical ground-motion model for horizontal PGV, PGA, and 5% damped elastic response spectra (0.01–10 s) in Iran. Bull Seismol Soc Am 109(3):1041–1057
Fukushima Y (1997) Comment on ground motion attenuation relations for subduction zones. Seismol Res Lett 68(6):947–949
Fukushima Y, Tanaka T (1990) A new attenuation relation for peak horizontal acceleration of strong earthquake ground motion in Japan. Bull Seismol Soc Am 80(4):757–783
Gelman A, Hill J (2006) Data Analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge
Ghasemi H, Zare M, Fukushima Y, Koketsu K (2008) An empirical spectral ground-motion model for Iran. J Seismol 13(4):499–515
Hamzehloo H, Mahood M (2012) Ground-Motion attenuation relationship for East Central Iran. Bull Seismol Soc Am 102(6):2677–2684
Joyner WB, Boore DM (1993) Methods for regression analysis of strong-motion data. Bull Seismol Soc Am 83(2):469–487
Joyner WB, Boore DM (1994) Erratum to methods for regression analysis of strong-motion data. Bull Seismol Soc Am 84(3):955–956
Kale O, Akkar S (2013) A New procedure for selecting and ranking ground-motion prediction equations (GMPEs): the Euclidean distance-based ranking (EDR) method. Bull Seismol Soc Am 103(2A):1069–1084
Kale O, Akkar S, Ansari A, Hamzehloo H (2015) A Ground-Motion predictive model for Iran and Turkey for horizontal PGA, PGV, and 5% damped response spectrum: investigation of possible regional effects. Bull Seismol Soc Am 105(2A):963–980
Kishida T, Darragh RB, Chiou BSJ, Bozorgnia Y, Mazzoni S, Contreras V, Boroschek R, Rojas F, Stewart JP (2020) Chapter 3: ground motions and intensity measures, PEER Report 2020/xx, J.P. Stewart (editor), Pacific Earthquake Engineering Research Center, UC Berkeley (Headquarters)
Kuehn NM, Kishida T, AlHamaydeh M, Lavrentiadis G, Bozorgnia Y (2020) nikuehn/BayesTruncRegGMM: pre-review (Version v0.0.1). Zenodo. https://doi.org/10.5281/zenodo.3738494
Kuehn NM, Scherbaum F (2015) Ground-motion prediction model building: a multilevel approach. Bull Earthq Eng 13(9):2481–2491
Kuehn NM, Scherbaum F (2016) A partially non-ergodic ground-motion prediction equation for Europe and the Middle East. Bull Earthq Eng 14(10):2629–2642
Kuehn NM, Abrahamson NA (2018) The effect of uncertainty in predictor variables on the estimation of Ground-Motion prediction equations. Bull Seismol Soc Am 108(1):358–370
Kuehn NM, Abrahamson NA (2020) Spatial correlations of ground motion for non-ergodic seismic hazard analysis. Earthq Eng Struct Dyn 49(1):4–23
Lewandowski D, Kurowicka D, Joe H (2009) Generating random correlation matrices based on vines and extended onion method. J Multivar Anal 100(9):1989–2001
Lunn D, Spiegelhalter D, Thomas A, Best N (2009) The BUGS project: evolution, critique and future directions. Stat Med 28(25):3049–3067
Moss RES (2011) reduced sigma of Ground-Motion prediction equations through uncertainty propagation. Bull Seismol Soc Am 101(1):250–257
Neal R (2011) MCMC using hamiltonian dynamics. In: Brooks S, Gelman A, Jones GL, Meng X-L (eds) Hand- book of Markov Chain Monte Carlo. CRC Press, New York
National Center for Research on Earthquake Engineering (NCREE) (2015) Web page for reevaluation of probabilistic seismic hazard of nuclear facilities in Taiwan using SSHAC level 3 methodology project. http://sshac.ncree.org.tw
Plummer M (2003) JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In: Hornik K, Leisch F, and Zeileis A. (eds) 3rd International workshop on distributed statistical computing (DSC 2003), Vienna (1)
Rhoades DA (1997) Estimation of attenuation relations for strong-motion data allowing for individual earthquake magnitude uncertainties. Bull Seismol Soc Am 87(6):1674–1678
Saffari H, Kuwata Y, Takada S, Mahdavian A (2012) Updated PGA, PGV, and spectral acceleration attenuation relations for Iran. Earthq Spectra 28(1):257
Sawires R, Peláez JA, AlHamaydeh M, Henares J (2019) A state-of-the-art seismic source model for the United Arab Emirates. J Asian Earth Sci 186:104063
Sawires R, Peláez JA, AlHamaydeh M, Henares J (2020) Up-to-date earthquake and focal mechanism solutions datasets for the assessment of seismic hazard in the vicinity of the United Arab Emirates. Data Brief 28:104844
Scherbaum F, Delavaud E, Riggelsen C (2009) Model selection in seismic hazard analysis: an information-theoretic perspective. Bull Seismol Soc Am 99(6):3234–3247
Sedaghati F, Pezeshk S (2017) Partially nonergodic empirical ground-motion models for predicting horizontal and vertical PGV, PGA, and 5% damped linear acceleration response spectra using data from the Iranian Plateau. Bull Seismol Soc Am 107(2):934–948
Sorensen T, Hohenstein S, Vasishth S (2016) Bayesian linear mixed models using Stan: a tutorial for psychologists, linguists, and cognitive scientists. Quant Methods Psychol 12(3):175–200
Spiegelhalter D, Rice K (2009) Bayesian statistics. Scholarpedia 4(8):5230
Stafford PJ (2008) Conditional prediction of absolute durations. Bull Seismol Soc Am 98(3):1588–1594
Stafford PJ (2014) Crossed and nested mixed-effects approaches for enhanced model development and removal of the ergodic assumption in empirical Ground-Motion models. Bull Seismol Soc Am 104(2):702–719
Stafford PJ (2019) Continuous integration of data into ground-motion models using Bayesian updating. J Seismol 23(1):39–57
Stewart JP (ed) (2020) Data resources for NGA-subduction project. PEER report 2020/02
Wang Z, Zentner I, Zio E (2020) Accounting for uncertainties of magnitude- and site-related parameters on neural network-computed ground-motion prediction equations. Bull Seismol Soc Am 110:629–646
Zafarani H, Luzi L, Lanzano G, Soghrat MR (2018) Empirical equations for the prediction of PGA and pseudo spectral accelerations using Iranian strong-motion data. J Seismol 22(1):263–285
Zafarani H, Rahpeyma S, Mousavi M (2017) Regional adjustment factors for three NGA-West2 ground-motion prediction equations to be applicable in northern Iran. J Seismol 21(3):473–493