Spatial variation model of seismic ground motion for Istanbul
Year 2021,
Volume: 12 Issue: 1, 111 - 131, 13.01.2021
Ebru Harmandar
,
Eser Çaktı
,
Mustafa Erdik
Abstract
Earthquake induced base motions of elongated structures will not be uniform. This variation of ground motion has a nonnegligible effect on the dynamic response of lifelines that has led to investigations of characterization and modelling of the spatially varying earthquake ground motion within the last decade. In this context, spatial variation of seismic ground motion in Istanbul is analysed. After the introduction of the concept of coherency function and its conventional estimation procedure, estimation of coherency from recorded data and its interpretation are presented. The lagged coherency is calculated by the conventional coherency estimation scheme applied to six earthquakes registered by the Istanbul Earthquake Rapid Response System. A coherency model for Istanbul is derived that will enable to simulate spatially variable ground motion needed as input in the design of extended structures. Simulation of ground motion at pairs of closely spaced locations is presented that consider the derived coherencies in their scheme. The results are compared with actual recordings from the same locations. Simulation of spatially variable ground motion consistent with a coherency function is stated.
References
- 1. Schneider, J.F.; Abrahamson, N.A.; Somerville, P.G.; Stepp, J.C. Spatial Variability of Ground Motion from EPRI’s Dense Acceleragraph Array at Parkfield, California. Proc Fourth U. S. National Conf Earthq Eng, EERI, Palm Springs, 375-384, 1990.
- 2. Abrahamson, N.A.; Sykora, D. Variations of Ground Motions Across Individual Sites. Proc Fourth DOE Natl Phenom Hazards Mitig Conf, 9192-9198, Atlanta, Georgia, 1993.
- 3. Joyner, W.B.; Boore, D.M. Peak Horizontal Acceleration and Velocity from Strong-Motion Records Including Records from the 1979 Imperial Valley, California, Earthquake. Bull Seism Soc Am 1981, 71, 2011-2038.
- 4. Abrahamson, N.A. Statistical Properties of Peak Ground Accelerations Recorded by the Smart 1 Array. Bull Seismol Soc Am 1988, 78, 26-41.
- 5. Kawakami, H.; Mogi, H. Analyzing Spatial Intraevent Variability of Peak Ground Accelerations as a Function of Separation Distance. Bull Seism Soc Am 2003, 93, 1079-1090.
- 6. Field, H.E.; Hough, S.E. The Variability of PSV Response Spectra across a Dense Array Developed During the Northridge Aftershock Sequence. Earthq Spectra 1997, 13, 243-257.
- 7. Evans, J.R.; Hamstra, R.H.; Spudich, Jr.P.; Kündig , C.; Camina, P.; Rogers, J.A. TREMOR: A Wireless, MEMS Accelerograph for Dense Arrays. U.S.G.S. Open File Report 2003, 03-159.
- 8. Loh, C.H. Analysis of the Spatial Variation of Seismic Waves and Ground Movements from SMART-1 Array Data. Earthq Eng Struct Dyn 1985, 13, 561–581.
- 9. McLaughlin, K.L. Spatial Coherency of Seismic Waveforms, PhD Thesis, University of California, Berkeley, 1983.
- 10. Abrahamson, N.A. Estimation of Seismic Wave Coherency and Rupture Velocity Using the SMART-1 Strong Motion Array Recordings. EERC Report No. EERC/UCB/85-02 1985, Earthquake Engineering Research Center, University of California.
- 11. Abrahamson, N.A. Spatial Variation of Multiple Support Inputs. Proc the First U.S. Semin Seism Eval Retrofit Steel Bridges, San Francisco, 1993.
- 12. Harichandran, R.S; Vanmarcke, E. Stochastic Variation of Earthquake Ground Motion in Space and Time. J Eng Mech ASCE 1986, 112, 154-174.
- 13. Harichandran, R.S. Local Spatial Variation of Earthquake Ground Motion. In Earthquake Engineering and Soil Dynamics II - Recent Advances in Ground-Motion Evaluation; Von Thun, J. L. (editor),. American Society of Civil Engineers, New York, 1988; pp. 203-217.
- 14. Harichandran, R.S. Estimating the Spatial Variation of Earthquake Ground Motion from Dense Array Recordings. Struct Saf 1991, 10, 219-233.
- 15. Loh, C.H.; Yeh, Y.T. Spatial Variation and Stochastic Modeling of Seismic Differential Ground Movement. Earthq Eng Struct Dyn 1988, 16, 583–596.
- 16. Loh, C.H.; Lin, S.G. Directionality and Simulation in Spatial Variation of Seismic Waves. Eng Structs 1990, 12, 134–143.
- 17. Novak, M. Discussion on Stochastic Variation of Earthquake Ground Motion in Space and Time by R. S. Harichandran and E. H. Vanmarcke. J Eng Mech Div 1987, 113, 1267–1270.
- 18. Oliveira, C.S.; Hao, H.; Penzien, J. Ground Motion Modeling for Multiple-Input Structural Analysis. Struct Saf 1991, 10, 79–93.
- 19. Ramadan, O.; Novak, M. Coherency Functions for Spatially Correlated Seismic Ground Motions. Geotechnical Research Center Report No. GEOT-9-93, 1993;University of Western Ontario, London, Canada.
- 20. Vernon, F.; Fletcher, J.; Carroll Chave, A.; Sembera, E. Coherence of Seismic Body Waves as Measured by a Small Aperture Array. J Geophys Res 1991, 96, 11981–11996.
- 21. Zerva, A.; Zhang, O. Correlation Patterns in Characteristics of Spatially Variable Seismic Ground Motions. Earthq Eng Struct Dyn 1997, 26, 19–39.
- 22. Cacciola, P.; Deodatis, G. A method for generating fully non-stationary and spectrum-compatible ground motion vector processes. Soil Dyn Earthq Eng 2011, 31, 351-360.
- 23. Zerva, A.; Zervas, V. Spatial Variation of Seismic Ground Motions: An Overview. Appl Mech Rev 2002, 55, (3): 271-297.
- 24. Zerva, A. Spatial Variation of Seismic Ground Motions. CRS Press, New York: 2009.
- 25. Song, S.G.; Pitarka, A.; Somerville, P. Exploring Spatial Coherence between Earthquake Source Parameters. Bull Seism Soc Am 2009, 99 (4): 2564-2571.
- 26. Harmandar, E.; Durukal, E.,; Erdik, M.; Özel, O. Spatial Variation Strong Ground Motion in Istanbul: Preliminary Results based on Data from the Istanbul Earthquake Rapid Response System. European Geosciences Union (EGU) General Assembly, Vienna, Austria, 2006.
- 27. Harmandar, E.; Durukal, E.; Erdik, M.; Ozel, O. Spatial Variation of Strong Ground Motion in Istanbul. First European Conf Earthq Eng Seism, Geneva, 2006.
- 28. Harmandar, E.; Durukal, E.; Erdik, M. A method for spatial estimation of peak ground acceleration in dense arrays. Geophys J Int 2012, 191, 1272–1284.
- 29. Rice, S.O. Mathematical Analysis of Random Noise. Bell Syst Technical J 1944, 23, 282–332.
- 30. Shinozuka, M. Monte Carlo Solution of Structural Dynamics. Computers and Structs 1972, 2, 855–874.
- 31. Conte, J.P.; Pister, K.S.; Mahin, S.A. Non-Stationary ARMA Modeling of Seismic Ground Motions. Soil Dyn Earthq Eng 1992, 11, 411-426.
- 32. Ellis, G.W.; Cakmak, A.S. Time Series Modeling of Strong Ground Motion from Multiple Event Earthquakes. Soil Dyn Earthq Eng 1991, 10, 42-54.
- 33. Mignolet, M.P.; Spanos, P.D. Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models. J Appl Mech 1992, 59, 260–269.
- 34. Shama, A. Simplified Procedure for Simulating Spatially Correlated Earthquake Ground Motions. Eng Structs 2007, 29, 248-258.
- 35. Fenton, G.A.; Vanmarcke, E.H. Simulations of Random Fields via Local Average Subdivision. J Eng Mech 1990, 116, 1733-1749.
- 36. Hao, H.; Oliveira, C.S.; Penzien, J. Multiple-Station Ground Motion Processing and Simulation based on SMART-1 Array Data. Nuclear Eng Des 1989, 111, 293-310.
- 37. Zerva, A,; Katafygiotis, L.S. Selection of Simulation Scheme for the Nonlinear Seismic Response of Spatial Structures. Proc Fourth Int Colloq Computation of Shell and Spatial Structs, Chania, Greece, 2000.
- 38. Abrahamson, N.A. Generation of Spatially Incoherent Strong Motion Time Histories. Proc Tenth World Conf Earthq Eng, Madrid, Spain, 1992.
- 39. Ramadan, O.; Novak, M. Simulation of Multidimensional Anisotropic Ground Motions. J Eng Mechs 1994, 120, 1773–1785.
- 40. Yamamoto, Y. Stochastic model for earthquake ground motion using wavelet packets. PhD Thesis, Stanford University, 2011.
- 41. Mirrashid, M.; Givehchi, M.; Miri, M,; Madandoust, R. Performance investigation of neuro-fuzzy system for earthquake prediction. Asian J Civ Eng (BHRC) 2016, 17, 213–223.
- 42. Matsushima, Y. Stochastic Response of Structure due to Spatially Variant Earthquake Excitations. Proc Sixth World Conf Earthq Eng, Vol. II, 1077-1082, Sarita Prakashan, Meerut, India, 1977.
- 43. Abrahamson, N.A.; Schneider, JF, and Stepp C. Spatial Variation of Strong Ground Motion for Use in Soil-Structure Interaction Analyses. Proc Fourth U.S. Natl Conf Earthq Eng, Palm Springs, California, 1990.
- 44. Abrahamson, N.A.; Schneider, J.F.; Stepp; J.C. Empirical Spatial Coherency Functions for Applications to Soil-Structure Interaction Analyses. Earthq Spectra 1991, 7, 1-27.
- 45. Erdik, M.; Fahjan, Y.; Ozel, O.; Alcik, H.; Mert, A.; Gul, M. Istanbul Earthquake Rapid Response and the Early Warning System. Bull Earthq Eng 2003, 1, 157-163.
- 46. Boissieres, H.P.; Vanmarcke, E.H. Estimation of Lags for a Seismograph Array: Wave Propagation and Composite Correlation. Soil Dyn Earthq Eng 1995, 14, 5-22.
- 47. Parolai, S.; Ansal, A.; Kurtulus, A.; Strollo, A.; Wang, R.; Zschau, J. The Ataköy vertical array (Turkey): Insights into seismic wave propagation in the shallow-most crustal layers by waveform deconvolution. Geophysical Journal International 2009, 178, 3, 1649–1662.
https://doi.org/10.1111/j.1365-246X.2009.04257.x.
- 48. Bolt, B.A.; Tsai Y.B.; Yeh. K.; Hsu, M.K. Earthquake strong ground motion recorded by a large near-source array of digital seismographs. Earthq Eng Struct Dyn 1982, 10, 561-573.
- 49. Porter, K.A. An Overview of PEER’s Performance-based Earthquake Engineering Methodology. Proc Ninth Intern Conf Appls Stat Probab Civil Eng, San Francisco, California, 2003.
- 50. Songtao, L. Physical Characterization of Seismic Ground Motion Spatial Variation and Conditional Simulation for Performance-Based Design. PhD Thesis, Drexel University, 2006.
- 51. Das, S.; Gupta, V.K. Wavelet-Based Simulation of Spectrum-Compatible Aftershock Accelerograms. Earthq Eng Struct Dyn 2008, 37, 1333-1348.
- 52. Bi, K.; Hao, H. Simulation of Spatially Varying Ground Motions with Non-Uniform Intensities and Frequency Content. Earthq Eng Aust Conf, Ballarat, Australia, 2003.
- 53. Abrahamson, N.A. Non-stationary spectral matching program RSPMATCH. Pacific Gas and Electric Company Internal Report, 1998.
- 54. Hancock, J.; Watson-Lamprey, J.; Abrahamson, N.A.; Bommer, J.J.; Markatis, A.; McCoy, E.; Mendis, E. An improved method of matching response spectra of recorded earthquake ground motion using wavelets. J Earthq Eng 2006, 10, Special Issue I, 67-89.
- 55. Liu, T.J.; Hong, H.P. Application of spatially correlated and coherent records of scenario event to estimate seismic loss of a portfolio of buildings. Earthq Spectra 2015, 31.4: 2047-2068.
- 56. Chen, Z.; Liang, S.; He, C. Effects of different coherency models on utility tunnel through shaking table test. J Earthq Eng 2020, 24.4: 579-600.
- 57. Ahmed, K.; Kim, D.; Lee, S.H. Effect of the incoherent earthquake motion on responses of seismically isolated nuclear power plant structure. Earthq Struc 2018, 14.1: 33-44.
- 58. Papadopoulos, S.; Sextos, A.; Know, O.; Gerasimidis, S.; Deodatis, G. Impact of spatial variability of earthquake ground motion on seismic demand to natural gas transmission pipelines. Proccedings of the 16th World Conference on Earthquake, 16WCEE, 2017.
- 59. Wu, Y.; Gao, Y.; Zhang, N.; Zhang, F. Simulation of spatially varying non-Gaussian and nonstationary seismic ground motions by the spectral representation method. J Eng Mech 2018, 144.1: 04017143.
Spatial variation model of seismic ground motion for Istanbul
Year 2021,
Volume: 12 Issue: 1, 111 - 131, 13.01.2021
Ebru Harmandar
,
Eser Çaktı
,
Mustafa Erdik
Abstract
Earthquake induced base motions of elongated structures will not be uniform. This variation of ground motion has a nonnegligible effect on the dynamic response of lifelines that has led to investigations of characterization and modelling of the spatially varying earthquake ground motion within the last decade. In this context, spatial variation of seismic ground motion in Istanbul is analysed. After the introduction of the concept of coherency function and its conventional estimation procedure, estimation of coherency from recorded data and its interpretation are presented. The lagged coherency is calculated by the conventional coherency estimation scheme applied to six earthquakes registered by the Istanbul Earthquake Rapid Response System. A coherency model for Istanbul is derived that will enable to simulate spatially variable ground motion needed as input in the design of extended structures. Simulation of ground motion at pairs of closely spaced locations is presented that consider the derived coherencies in their scheme. The results are compared with actual recordings from the same locations. Simulation of spatially variable ground motion consistent with a coherency function is stated.
References
- 1. Schneider, J.F.; Abrahamson, N.A.; Somerville, P.G.; Stepp, J.C. Spatial Variability of Ground Motion from EPRI’s Dense Acceleragraph Array at Parkfield, California. Proc Fourth U. S. National Conf Earthq Eng, EERI, Palm Springs, 375-384, 1990.
- 2. Abrahamson, N.A.; Sykora, D. Variations of Ground Motions Across Individual Sites. Proc Fourth DOE Natl Phenom Hazards Mitig Conf, 9192-9198, Atlanta, Georgia, 1993.
- 3. Joyner, W.B.; Boore, D.M. Peak Horizontal Acceleration and Velocity from Strong-Motion Records Including Records from the 1979 Imperial Valley, California, Earthquake. Bull Seism Soc Am 1981, 71, 2011-2038.
- 4. Abrahamson, N.A. Statistical Properties of Peak Ground Accelerations Recorded by the Smart 1 Array. Bull Seismol Soc Am 1988, 78, 26-41.
- 5. Kawakami, H.; Mogi, H. Analyzing Spatial Intraevent Variability of Peak Ground Accelerations as a Function of Separation Distance. Bull Seism Soc Am 2003, 93, 1079-1090.
- 6. Field, H.E.; Hough, S.E. The Variability of PSV Response Spectra across a Dense Array Developed During the Northridge Aftershock Sequence. Earthq Spectra 1997, 13, 243-257.
- 7. Evans, J.R.; Hamstra, R.H.; Spudich, Jr.P.; Kündig , C.; Camina, P.; Rogers, J.A. TREMOR: A Wireless, MEMS Accelerograph for Dense Arrays. U.S.G.S. Open File Report 2003, 03-159.
- 8. Loh, C.H. Analysis of the Spatial Variation of Seismic Waves and Ground Movements from SMART-1 Array Data. Earthq Eng Struct Dyn 1985, 13, 561–581.
- 9. McLaughlin, K.L. Spatial Coherency of Seismic Waveforms, PhD Thesis, University of California, Berkeley, 1983.
- 10. Abrahamson, N.A. Estimation of Seismic Wave Coherency and Rupture Velocity Using the SMART-1 Strong Motion Array Recordings. EERC Report No. EERC/UCB/85-02 1985, Earthquake Engineering Research Center, University of California.
- 11. Abrahamson, N.A. Spatial Variation of Multiple Support Inputs. Proc the First U.S. Semin Seism Eval Retrofit Steel Bridges, San Francisco, 1993.
- 12. Harichandran, R.S; Vanmarcke, E. Stochastic Variation of Earthquake Ground Motion in Space and Time. J Eng Mech ASCE 1986, 112, 154-174.
- 13. Harichandran, R.S. Local Spatial Variation of Earthquake Ground Motion. In Earthquake Engineering and Soil Dynamics II - Recent Advances in Ground-Motion Evaluation; Von Thun, J. L. (editor),. American Society of Civil Engineers, New York, 1988; pp. 203-217.
- 14. Harichandran, R.S. Estimating the Spatial Variation of Earthquake Ground Motion from Dense Array Recordings. Struct Saf 1991, 10, 219-233.
- 15. Loh, C.H.; Yeh, Y.T. Spatial Variation and Stochastic Modeling of Seismic Differential Ground Movement. Earthq Eng Struct Dyn 1988, 16, 583–596.
- 16. Loh, C.H.; Lin, S.G. Directionality and Simulation in Spatial Variation of Seismic Waves. Eng Structs 1990, 12, 134–143.
- 17. Novak, M. Discussion on Stochastic Variation of Earthquake Ground Motion in Space and Time by R. S. Harichandran and E. H. Vanmarcke. J Eng Mech Div 1987, 113, 1267–1270.
- 18. Oliveira, C.S.; Hao, H.; Penzien, J. Ground Motion Modeling for Multiple-Input Structural Analysis. Struct Saf 1991, 10, 79–93.
- 19. Ramadan, O.; Novak, M. Coherency Functions for Spatially Correlated Seismic Ground Motions. Geotechnical Research Center Report No. GEOT-9-93, 1993;University of Western Ontario, London, Canada.
- 20. Vernon, F.; Fletcher, J.; Carroll Chave, A.; Sembera, E. Coherence of Seismic Body Waves as Measured by a Small Aperture Array. J Geophys Res 1991, 96, 11981–11996.
- 21. Zerva, A.; Zhang, O. Correlation Patterns in Characteristics of Spatially Variable Seismic Ground Motions. Earthq Eng Struct Dyn 1997, 26, 19–39.
- 22. Cacciola, P.; Deodatis, G. A method for generating fully non-stationary and spectrum-compatible ground motion vector processes. Soil Dyn Earthq Eng 2011, 31, 351-360.
- 23. Zerva, A.; Zervas, V. Spatial Variation of Seismic Ground Motions: An Overview. Appl Mech Rev 2002, 55, (3): 271-297.
- 24. Zerva, A. Spatial Variation of Seismic Ground Motions. CRS Press, New York: 2009.
- 25. Song, S.G.; Pitarka, A.; Somerville, P. Exploring Spatial Coherence between Earthquake Source Parameters. Bull Seism Soc Am 2009, 99 (4): 2564-2571.
- 26. Harmandar, E.; Durukal, E.,; Erdik, M.; Özel, O. Spatial Variation Strong Ground Motion in Istanbul: Preliminary Results based on Data from the Istanbul Earthquake Rapid Response System. European Geosciences Union (EGU) General Assembly, Vienna, Austria, 2006.
- 27. Harmandar, E.; Durukal, E.; Erdik, M.; Ozel, O. Spatial Variation of Strong Ground Motion in Istanbul. First European Conf Earthq Eng Seism, Geneva, 2006.
- 28. Harmandar, E.; Durukal, E.; Erdik, M. A method for spatial estimation of peak ground acceleration in dense arrays. Geophys J Int 2012, 191, 1272–1284.
- 29. Rice, S.O. Mathematical Analysis of Random Noise. Bell Syst Technical J 1944, 23, 282–332.
- 30. Shinozuka, M. Monte Carlo Solution of Structural Dynamics. Computers and Structs 1972, 2, 855–874.
- 31. Conte, J.P.; Pister, K.S.; Mahin, S.A. Non-Stationary ARMA Modeling of Seismic Ground Motions. Soil Dyn Earthq Eng 1992, 11, 411-426.
- 32. Ellis, G.W.; Cakmak, A.S. Time Series Modeling of Strong Ground Motion from Multiple Event Earthquakes. Soil Dyn Earthq Eng 1991, 10, 42-54.
- 33. Mignolet, M.P.; Spanos, P.D. Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models. J Appl Mech 1992, 59, 260–269.
- 34. Shama, A. Simplified Procedure for Simulating Spatially Correlated Earthquake Ground Motions. Eng Structs 2007, 29, 248-258.
- 35. Fenton, G.A.; Vanmarcke, E.H. Simulations of Random Fields via Local Average Subdivision. J Eng Mech 1990, 116, 1733-1749.
- 36. Hao, H.; Oliveira, C.S.; Penzien, J. Multiple-Station Ground Motion Processing and Simulation based on SMART-1 Array Data. Nuclear Eng Des 1989, 111, 293-310.
- 37. Zerva, A,; Katafygiotis, L.S. Selection of Simulation Scheme for the Nonlinear Seismic Response of Spatial Structures. Proc Fourth Int Colloq Computation of Shell and Spatial Structs, Chania, Greece, 2000.
- 38. Abrahamson, N.A. Generation of Spatially Incoherent Strong Motion Time Histories. Proc Tenth World Conf Earthq Eng, Madrid, Spain, 1992.
- 39. Ramadan, O.; Novak, M. Simulation of Multidimensional Anisotropic Ground Motions. J Eng Mechs 1994, 120, 1773–1785.
- 40. Yamamoto, Y. Stochastic model for earthquake ground motion using wavelet packets. PhD Thesis, Stanford University, 2011.
- 41. Mirrashid, M.; Givehchi, M.; Miri, M,; Madandoust, R. Performance investigation of neuro-fuzzy system for earthquake prediction. Asian J Civ Eng (BHRC) 2016, 17, 213–223.
- 42. Matsushima, Y. Stochastic Response of Structure due to Spatially Variant Earthquake Excitations. Proc Sixth World Conf Earthq Eng, Vol. II, 1077-1082, Sarita Prakashan, Meerut, India, 1977.
- 43. Abrahamson, N.A.; Schneider, JF, and Stepp C. Spatial Variation of Strong Ground Motion for Use in Soil-Structure Interaction Analyses. Proc Fourth U.S. Natl Conf Earthq Eng, Palm Springs, California, 1990.
- 44. Abrahamson, N.A.; Schneider, J.F.; Stepp; J.C. Empirical Spatial Coherency Functions for Applications to Soil-Structure Interaction Analyses. Earthq Spectra 1991, 7, 1-27.
- 45. Erdik, M.; Fahjan, Y.; Ozel, O.; Alcik, H.; Mert, A.; Gul, M. Istanbul Earthquake Rapid Response and the Early Warning System. Bull Earthq Eng 2003, 1, 157-163.
- 46. Boissieres, H.P.; Vanmarcke, E.H. Estimation of Lags for a Seismograph Array: Wave Propagation and Composite Correlation. Soil Dyn Earthq Eng 1995, 14, 5-22.
- 47. Parolai, S.; Ansal, A.; Kurtulus, A.; Strollo, A.; Wang, R.; Zschau, J. The Ataköy vertical array (Turkey): Insights into seismic wave propagation in the shallow-most crustal layers by waveform deconvolution. Geophysical Journal International 2009, 178, 3, 1649–1662.
https://doi.org/10.1111/j.1365-246X.2009.04257.x.
- 48. Bolt, B.A.; Tsai Y.B.; Yeh. K.; Hsu, M.K. Earthquake strong ground motion recorded by a large near-source array of digital seismographs. Earthq Eng Struct Dyn 1982, 10, 561-573.
- 49. Porter, K.A. An Overview of PEER’s Performance-based Earthquake Engineering Methodology. Proc Ninth Intern Conf Appls Stat Probab Civil Eng, San Francisco, California, 2003.
- 50. Songtao, L. Physical Characterization of Seismic Ground Motion Spatial Variation and Conditional Simulation for Performance-Based Design. PhD Thesis, Drexel University, 2006.
- 51. Das, S.; Gupta, V.K. Wavelet-Based Simulation of Spectrum-Compatible Aftershock Accelerograms. Earthq Eng Struct Dyn 2008, 37, 1333-1348.
- 52. Bi, K.; Hao, H. Simulation of Spatially Varying Ground Motions with Non-Uniform Intensities and Frequency Content. Earthq Eng Aust Conf, Ballarat, Australia, 2003.
- 53. Abrahamson, N.A. Non-stationary spectral matching program RSPMATCH. Pacific Gas and Electric Company Internal Report, 1998.
- 54. Hancock, J.; Watson-Lamprey, J.; Abrahamson, N.A.; Bommer, J.J.; Markatis, A.; McCoy, E.; Mendis, E. An improved method of matching response spectra of recorded earthquake ground motion using wavelets. J Earthq Eng 2006, 10, Special Issue I, 67-89.
- 55. Liu, T.J.; Hong, H.P. Application of spatially correlated and coherent records of scenario event to estimate seismic loss of a portfolio of buildings. Earthq Spectra 2015, 31.4: 2047-2068.
- 56. Chen, Z.; Liang, S.; He, C. Effects of different coherency models on utility tunnel through shaking table test. J Earthq Eng 2020, 24.4: 579-600.
- 57. Ahmed, K.; Kim, D.; Lee, S.H. Effect of the incoherent earthquake motion on responses of seismically isolated nuclear power plant structure. Earthq Struc 2018, 14.1: 33-44.
- 58. Papadopoulos, S.; Sextos, A.; Know, O.; Gerasimidis, S.; Deodatis, G. Impact of spatial variability of earthquake ground motion on seismic demand to natural gas transmission pipelines. Proccedings of the 16th World Conference on Earthquake, 16WCEE, 2017.
- 59. Wu, Y.; Gao, Y.; Zhang, N.; Zhang, F. Simulation of spatially varying non-Gaussian and nonstationary seismic ground motions by the spectral representation method. J Eng Mech 2018, 144.1: 04017143.