Ground motion models for Arias intensity, cumulative absolute velocity, peak incremental ground velocity, and significant duration in New Zealand
This study proposes empirical ground motion models for a variety of non-spectral intensity measures and significant durations in New Zealand. Equations are presented for the prediction of the median and maximum rotated components of Arias intensity, cumulative absolute velocity, cumulative absolute velocity above a 5 cm/s2 acceleration threshold, peak incremental ground velocity, and the 5% to 75% and 5% to 95% significant durations. Recent research has highlighted the usefulness of these parameters in both structural and geotechnical engineering. The New Zealand Strong Motion Database provides the database for regression and includes many earthquakes from all regions of New Zealand with the exceptions of Auckland and Northland, Otago and Southland, and Taranaki. The functional forms for the proposed models are selected using cross validation. The possible influence of effects not typically included in ground motion models for these intensity measures is considered, such as hanging wall effects and basin depth effects, as well as altered attenuation in the Taupo Volcanic Zone. The selected functional forms include magnitude and rupture depth scaling, attenuation with distance, and shallow site effects. Finally, the spatial autocorrelation of the models’ within-event residuals is considered and recommendations are made for developing correlated maps of intensity predictions stochastically.
Cornell CA (1968). “Engineering seismic risk analysis”. Bulletin of the Seismological Society of America, 58(5): 1583-1606.
Abrahamson NA, Silva WJ and Kamai R (2013). “Update of the AS08 ground-motion prediction equations based on the NGA-West2 data set”. Pacific Earthquake Engineering Research Center.
Atkinson GM and Boore DM (2003). “Empirical ground-motion relations for subduction-zone earthquakes and their application to Cascadia and other regions”. Bulletin of the Seismological Society of America, 93(4), 1703-1729. DOI: https://doi.org/10.1785/0120020156
Boore DM, Stewart JP, Seyhan E and Atkinson GM (2014). “NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes”. Earthquake Spectra, 30(3): 1057-1085. DOI: https://doi.org/10.1193/070113EQS184M
Campbell KW and Bozorgnia Y (2014). “NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra”. Earthquake Spectra, 30(3): 1087-1115. DOI: https://doi.org/10.1193/062913EQS175M
Chiou BSJ and Youngs RR (2014). “Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra”. Earthquake Spectra, 30(3): 1117-1153. DOI: https://doi.org/10.1193/072813EQS219M
Bommer JJ, Stafford PJ and Alarcón JE (2009). “Empirical equations for the prediction of the significant, bracketed, and uniform duration of earthquake ground motion”. Bulletin of the Seismological Society of America, 99(6): 3217-3233. DOI: https://doi.org/10.1785/0120080298
Foulser‐Piggott R and Goda K (2015). “Ground‐motion prediction models for Arias intensity and cumulative absolute velocity for Japanese earthquakes considering single‐station sigma and within‐event spatial correlation”. Bulletin of the Seismological Society of America, 105(4): 1903-1918. DOI: https://doi.org/10.1785/0120140316
Afshari K and Stewart JP (2016). “Physically parameterized prediction equations for significant duration in active crustal regions”. Earthquake Spectra, 32(4): 2057-2081. DOI: https://doi.org/10.1193/063015EQS106M
Bullock Z, Dashti S, Liel A, Porter K, Karimi Z and Bradley B (2017). “Ground‐motion prediction equations for Arias intensity, cumulative absolute velocity, and peak incremental ground velocity for rock sites in different tectonic environments”. Bulletin of the Seismological Society of America, 107(5): 2293-2309. DOI: https://doi.org/10.1785/0120160388
Stafford PJ, Berrill JB and Pettinga JR (2009). “New predictive equations for Arias intensity from crustal earthquakes in New Zealand”. Journal of Seismology, 13(1): 31-52. DOI: https://doi.org/10.1007/s10950-008-9114-2
Van Houtte C, Larkin T and Holden C (2018). “On durations, peak factors, and non-stationarity corrections in Seismic Hazard Applications of Random Vibration Theory”. Bulletin of the Seismological Society of America, 108(1): 418-436. DOI: https://doi.org/10.1785/0120170076
Van Houtte C, Bannister S, Holden C, Bourguignon S and McVerry G (2017). “The New Zealand strong motion database”. Bulletin of the New Zealand Society for Earthquake Engineering, 50(1): 1-20. DOI: https://doi.org/10.5459/bnzsee.50.1.1-20
Arias A (1970). “A measure of earthquake intensity” in Seismic Design for Nuclear Power Plants. The MIT Press, Cambridge, Massachusetts, 438–483.
Travasarou T, Bray JD and Abrahamson NA (2003). “Empirical attenuation relationship for Arias intensity”. Earthquake Engineering and Structural Dynamics, 32(7): 1133-1155. DOI: https://doi.org/10.1002/eqe.270
Electric Power Research Institute (1988). “A Criterion for Determining Exceedances of the Operating Basis Earthquake”. EPRI Report NP-5930, Electric Power Research Institute, Palo Alto, CA.
Karimi Z and Dashti S (2017). “Ground motion intensity measures to evaluate II: the performance of shallow-founded structures on liquefiable ground”. Earthquake Spectra, 33(1): 277-298. DOI: https://doi.org/10.1193/103015EQS163M
Bullock Z, Karimi Z, Dashti S, Porter K, Liel AB and Franke KW (2018). “A Physics-Informed Semi-Empirical Probabilistic Model for the Settlement of Shallow-Founded Structures on Liquefiable Ground”. Géotechnique, 69(5): 406-419. DOI: https://doi.org/10.1680/jgeot.17.P.174
Bullock Z, Dashti S, Karimi Z, Liel AB, Porter K and Franke KW (2019). “Probabilistic Models for Residual and Peak Transient Tilt of Mat-Founded Structures on Liquefiable Soils”. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 145(2): 04018108.
Bullock Z, Dashti S, Liel AB, Porter K and Karimi Z (2019). “Evaluation of Intensity Measures for Predicting Consequences of Soil Liquefaction on Shallow-Founded Structures”. Earthquake Spectra, 35(4): 1899-1926. DOI: https://doi.org/10.1193/041618EQS094M
Kramer SL and Mitchell RA (2006). “Ground motion intensity measures for liquefaction hazard evaluation”. Earthquake Spectra, 22(2): 413-438. DOI: https://doi.org/10.1193/1.2194970
Electric Power Research Institute (2006). “Program on technology innovation: Use of cumulative absolute velocity (CAV) in determining effects of small magnitude earthquakes on seismic hazard analyses”. EPRI Report 1014099, EPRI, Palo Alto, CA, and the US Department of Energy, Germantown, MD.
Campbell KW and Bozorgnia Y (2011). “Prediction equations for the standardized version of cumulative absolute velocity as adapted for use in the shutdown of US nuclear power plants”. Nuclear Engineering and Design, 241(7): 2558-2569. DOI: https://doi.org/10.1016/j.nucengdes.2011.04.020
Jampole E, Deierlein G, Miranda E, Fell B, Swensen S and Acevedo C (2016). “Full-Scale Dynamic Testing of a Sliding Seismically Isolated Unibody House”. Earthquake Spectra, 32(4): 2245-2270. DOI: https://doi.org/10.1193/010616EQS003M
Bommer JJ and Martinez-Pereira A (1999). “The effective duration of earthquake strong motion”. Journal of Earthquake Engineering, 3(02): 127-172. DOI: https://doi.org/10.1080/13632469909350343
Bommer JJ, Magenes G, Hancock J and Penazzo P (2004). “The influence of strong-motion duration on the seismic response of masonry structures”. Bulletin of Earthquake Engineering, 2(1): 1-26. DOI: https://doi.org/10.1023/B:BEEE.0000038948.95616.bf
Raghunandan M and Liel AB (2013). “Effect of ground motion duration on earthquake-induced structural collapse”. Structural Safety, 41: 119-133.
Chandramohan R, Baker JW and Deierlein GG (2016). “Quantifying the influence of ground motion duration on structural collapse capacity using spectrally equivalent records”. Earthquake Spectra, 32(2): 927-950. DOI: https://doi.org/10.1193/122813EQS298MR2
Rogan M (1982). “A geophysical study of the Taupo Volcanic Zone New Zealand”. Journal of Geophysical Research: Solid Earth, 87(B5): 4073-4088.
Wilson CJN, Rogan AM, Smith IEM, Northey DJ, Nairn IA and Houghton BF (1984). “Caldera volcanoes of the Taupo Volcanic Zone, New Zealand”. Journal of Geophysical Research: Solid Earth, 89(B10): 8463-8484.
Cole JW (1990). “Structural control and origin of volcanism in the Taupo Volcanic Zone, New Zealand.” Bulletin of Volcanology, 52(6): 445-459. DOI: https://doi.org/10.1007/BF00268925
McVerry GH, Zhao JX, Abrahamson NA and Somerville PG (2006). “Crustal and subduction zone attenuation relations for New Zealand earthquakes”. Bulletin of the New Zealand Society for Earthquake Engineering, 39(1). DOI: https://doi.org/10.5459/bnzsee.39.1.1-58
Bradley BA (2013). “A New Zealand‐specific pseudo-spectral acceleration ground‐motion prediction equation for active shallow crustal earthquakes based on foreign models”. Bulletin of the Seismological Society of America, 103(3): 1801-1822. DOI: https://doi.org/10.1785/0120120021
Cousins WJ, Zhao JX and Perrin ND (1999). “A model for the attenuation of peak ground acceleration in New Zealand earthquakes based on seismograph and accelerograph data”. Bulletin of the New Zealand National Society for Earthquake Engineering, 32(4): 193-220. DOI: https://doi.org/10.5459/bnzsee.32.4.193-220
Pinheiro J, Bates D, DebRoy S and Sarkar D (2014). “Linear and nonlinear mixed effects models”. R package, version 3.
Stafford PJ (2014). “Crossed and nested mixed‐effects approaches for enhanced model development and removal of the ergodic assumption in empirical ground‐motion models”. Bulletin of the Seismological Society of America, 104(2): 702-719. DOI: https://doi.org/10.1785/0120130145
Stafford PJ (2008). “Conditional prediction of absolute durations”. Bulletin of the Seismological Society of America, 98(3): 1588-1594. DOI: https://doi.org/10.1785/0120070207
Foulser‐Piggott R and Stafford PJ (2012). “A predictive model for Arias intensity at multiple sites and consideration of spatial correlations”. Earthquake Engineering and Structural Dynamics, 41(3): 431-451. DOI: https://doi.org/10.1002/eqe.1137
Cressie N and Huang HC (1999). “Classes of nonseparable, spatio-temporal stationary covariance functions”. Journal of the American Statistical Association, 94(448): 1330-1339. DOI: https://doi.org/10.1080/01621459.1999.10473885
Cressie N (1985). “Fitting variogram models by weighted least squares”. Journal of the International Association for Mathematical Geology, 17(5): 563-586. DOI: https://doi.org/10.1007/BF01032109
Mooney HM (1970). “Upper mantle inhomogeneity beneath New Zealand: seismic evidence”. Journal of Geophysical Research, 75(2): 285-309. DOI: https://doi.org/10.1029/JB075i002p00285
Haines AJ (1981). “A local magnitude scale for New Zealand earthquakes”. Bulletin of the Seismological Society of America, 71(1): 275-294.
Arlot S and Celisse A (2010). “A survey of cross-validation procedures for model selection”. Statistics Surveys, 4: 40-79.
Lilliefors HW (1967). “On the Kolmogorov-Smirnov test for normality with mean and variance unknown”. Journal of the American Statistical Association, 62(318): 399-402. DOI: https://doi.org/10.1080/01621459.1967.10482916
Eberhart-Phillips D and McVerry G (2003). “Estimating slab earthquake response spectra from a 3D Q model”. Bulletin of the Seismological Society of America, 93(6): 2649-2663. DOI: https://doi.org/10.1785/0120030036
Atik LA and Youngs RR (2014). “Epistemic uncertainty for NGA-West2 models”. Earthquake Spectra, 30(3): 1301-1318. DOI: https://doi.org/10.1193/062813EQS173M
Jayaram N and Baker JW (2009). “Correlation model for spatially distributed ground‐motion intensities”. Earthquake Engineering and Structural Dynamics, 38(15): 1687-1708. DOI: https://doi.org/10.1002/eqe.922
Cesca S, Zhang Y, Mouslopoulou V, Wang R, Saul J, Savage M, Heimann S, Kufner SK, Oncken O and Dahm T (2017). “Complex rupture process of the Mw 7.8, 2016, Kaikoura earthquake, New Zealand, and its aftershock sequence”. Earth and Planetary Science Letters, 478: 110-120.
Zhang H, Koper KD, Pankow K and Ge Z (2017). “Imaging the 2016 Mw 7.8 Kaikoura, New Zealand, earthquake with teleseismic P waves: A cascading rupture across multiple faults”. Geophysical Research Letters, 44(10): 4790-4798. DOI: https://doi.org/10.1002/2017GL073461