NUMERICAL ANALYSIS OF THE SEISMIC RESPONSE OF BASINS USING A MODIFIED RICKER WAVELET

Abstract

This study aims to investigate the seismic response of sedimentary basins under linear elastic conditions through a parametric approach. For this purpose, a modified Ricker wavelet with controlled frequency content and a flat amplitude spectrum in the 0–10 Hz range is used. The proposed wavelet is constructed by superimposing 18 Ricker components with varying central frequencies and amplitudes, resulting in a synthetic ground motion that minimizes period dependency. All soils used in the study are assumed to behave linearly elastic, which not only allows for a more straightforward identification of the factors influencing the aggravation factor but also eliminates possible over-damping effects that may arise from nonlinear behavior. The aggravation behavior observed with the modified Ricker wavelet is compared against that produced by applying 29 scaled earthquake records to a reference model. It is observed that, in linear elastic dynamic analyses, the amplitude of the input earthquake does not significantly influence the aggravation, whereas the synthetic wavelet serves as a highly useful input form. As a result of the parametric studies performed using the FLAC finite difference software, the effects of parameters such as basin width, rock interface slope, soil stiffness, and depth on aggravation have been individually evaluated. It has been revealed that edge effects dominate in short periods, while aggravation at longer periods tends to spread toward the central regions of the basin. The two-dimensional oscillation period at which maximum aggravation is observed has been shown to correlate with the one-dimensional resonance period. While the methods and analyses presented in this study offer a preliminary framework for accurately simulating the seismic response of a given site, they also provide a foundation for more advanced studies aimed at understanding basin effects and reflecting them in design spectra.

Keywords

• Basin Effect
• Spectral Aggravation
• Two-Dimensional Site Response
• Ricker Wavelet
• Finite Difference Method

Havzaların Sismik Tepkisinin Modifiye Ricker Dalgacığı ile Nümerik Analizi

Öz

Bu çalışma, sedimanter havzaların sismik tepkisinin doğrusal elastik koşullar altında parametrik olarak incelenmesini amaçlamaktadır. Bu amaçla, frekans içeriği kontrollü ve genlik spektrumu 0–10 Hz arasında yatay genliğe sahip modifiye bir Ricker dalgacığı kullanılmıştır. Söz konusu dalga formu, farklı merkez frekansa ve genliğe sahip 18 adet Ricker bileşeninin süperpozisyonu ile oluşturulmuş, böylece periyot bağımlılığını minimize eden bir sentetik yer hareketi elde edilmiştir. Çalışmada kullanılan tüm zeminler doğrusal elastik kabul edilerek, şiddetlendirme faktörünün değişimindeki etkenler hem daha yalın şekilde tespit edilmiş hem de doğrusal olmayan davranışın sebep olabileceği muhtemel aşırı sönümlemeler bertaraf edilmiştir. 29 adet ölçeklenmiş gerçek deprem kaydının referans model üzerinde uygulanmasıyla modifiye Ricker dalgası ile gözlemlenen şiddetlendirme davranışı karşılaştırılmış, doğrusal elastik dinamik analizlerde depremin ivme genliğinin, şiddetlendirme üzerinde etkili olmadığı, sentetik dalga formu girdisinin ise son derece kullanışlı bir araç olduğu gözlemlenmiştir. FLAC sonlu farklar yazılımında gerçekleştirilen parametrik çalışmalar sonucunda, havza genişliği, kenar eğimi, zemin rijitliği ve derinlik gibi parametrelerin şiddetlendirme üzerindeki etkisi ayrı ayrı değerlendirilmiştir. Özellikle kısa periyotlarda kenar etkisinin baskın olduğu, daha uzun periyotlardaki şiddetlendirmenin ise havzanın orta bölgelerine yayıldığı, en yüksek şiddetlendirmenin tespit edildiği iki boyutlu salınım periyodunun ise bir boyutlu salınım periyodu ile ilişki olduğu ortaya koyulmuştur. Çalışmada kullanılan yöntem ve analizler belirli bir sahanın sismik tepkisini doğru şekilde simüle etmek adına ilksel bir yaklaşım sunmakla birlikte havzaların sismik tepkisinin anlaşılmasında ve bu etkilerin tasarım spektrumlarına yansıtılmasında daha ileri analizler için bir çerçeve oluşturmuştur.

Anahtar Kelimeler

• Basen etkisi
• Spektral Şiddetlendirme
• İki Boyutlu Zemin Tepkisi
• Ricker Dalgacığı
• Sonlu Farklar Yöntemi

Kaynakça

1. [1] P. Y. Bard, M. Bouchon, The two-dimensional resonance of sediment-filled valleys. Bulletin of the Seismological Society of America, 75: 2 (1985) 519–541.
2. [2] A. S. Papageorgiou, J. Kim, Oblique incidence of SV-waves on sediment-filled valleys: Implications for seismic zonation. In Proceedings of the Fourth International Conference on Seismic Zonation (Vol. 3), Stanford, CA (1991) 545–552.
3. [3] F. J. Chávez-García, E. Faccioli, Complex site effects and building codes: Making the leap. Journal of Seismology, 4: 1 (2000) 23–40.
4. [4] D. Komatitsch, Q. Liu, J. Tromp, P. Süss, C. Stidham, J. H. Shaw, Simulations of ground motion in the Los Angeles basin based upon the spectral-element method. Bulletin of the Seismological Society of America, 94: 1 (2004) 187–206.
5. [5] M. P. Moschetti, D. Churchwell, E. M. Thompson, J. M. Rekoske, E. Wolin, O. S. Boyd, Seismic wave propagation and basin amplification in the Wasatch Front, Utah. Seismological Research Letters, 92: 6 (2021) 3626–3641.
6. [6] B. Zhang, A. S. Papageorgiou, Simulation of the response of the Marina District Basin, San Francisco, California, to the 1989 Loma Prieta earthquake. Bulletin of the Seismological Society of America, 86: 5 (1996) 1382–1400.
7. [7] H. Kawase, The cause of the damage belt in Kobe: 'The basin-edge effect,' constructive interference of the direct S-wave with the basin-induced diffracted Rayleigh waves. Seismological Research Letters, 67: 5 (1996) 25–34.
8. [8] M. E. Hasal, R. Iyisan, A numerical study on comparison of 1D and 2D seismic responses of a basin in Turkey. American Journal of Civil Engineering, 2: 5 (2014) 123–133.

9. [9] Amini, D., Maghoul, P., Perret, D., & Gatmiri, B. (2022). Two-dimensional basin-scale seismic site effects in the Kitimat Valley, British Columbia, Canada: A practical example of using a fast hybrid FE/BE method. Engineering Geology, 311, 106872.
10. [10] Makra, K., Rovithis, E., Riga, E., Raptakis, D., & Pitilakis, K. (2021). Amplification features and observed damages in İzmir (Turkey) due to 2020 Samos (Aegean Sea) earthquake: identifying basin effects and design requirements. Bulletin of Earthquake Engineering, 19(12), 4773–4804.
11. [11] R. Rodriguez-Plata, A. G. Özcebe, C. Smerzini, C. G. Lai, Aggravation factors for 2D site effects in sedimentary basins: The case of Norcia, central Italy. Soil Dynamics and Earthquake Engineering, 149 (2021) 106854.
12. [12] K. Makra, F. J. Chávez-García, D. Raptakis, K. Pitilakis, Parametric analysis of the seismic response of a 2D sedimentary valley: Implications for code implementations of complex site effects. Soil Dynamics and Earthquake Engineering, 25: 4 (2005) 303–315.
13. [13] L. F. Bonilla, R. J. Archuleta, D. Lavallée, Hysteretic and dilatant behavior of cohesionless soils and their effects on nonlinear site response: Field data observations and modeling. Bulletin of the Seismological Society of America, 95: 6 (2005) 2373–2395.
14. [14] J. Zhang, C. Zhao, Response spectral amplification ratios from 1-D and 2-D nonlinear soil site models. Soil Dynamics and Earthquake Engineering, 28: 10 (2008) 728–740.
15. [15] H. Khanbabazadeh, R. Iyisan, A numerical study on the 2D behavior of single and layered clayey basins. Bulletin of Earthquake Engineering, 12: 4 (2016) 1515–1539.
16. [16] B. Ozaslan, R. Iyisan, Gemlik Havzası’nda 2B doğrusal olmayan analizlerle tasarım spektrumunun değerlendirilmesi. Proceedings of the 2022 Türkiye Deprem Mühendisliği Konferansı (2022).
17. [17] Chen, W., Liu, Y., & Zhang, J. (2023). Nonlinear seismic response and amplification effect of 3D sedimentary basin based on bounding surface constitutive model. Soil Dynamics and Earthquake Engineering, 158, 107292.
18. [18] E. Riga, K. Makra, K. Pitilakis, Aggravation factors for seismic response of sedimentary basins: A code-oriented parametric study. Soil Dynamics and Earthquake Engineering, 90 (2016) 242–264.
19. [19] N. Ricker, The form and laws of propagation of seismic wavelets. Geophysics, 18: 1 (1953) 10–40.
20. [20] Aki, K., & Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books.
21. [21] Itasca Consulting Group, Inc. (2019). FLAC — Fast Lagrangian Analysis of Continua, Version 8.1. Minneapolis, MN: Itasca.
22. [22] Cundall, P. A., Hart, R. D., & Lemos, J. V. (1980). NESSI: A continuum code for nonlinear geomechanical modeling. In Proceedings of the International Symposium on Numerical Models in Geomechanics (NUMOG) (pp. 163–172). Zurich, Switzerland.
23. [23] J. Lysmer, R. L. Kuhlemeyer, Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, ASCE, 95: EM4 (1969) 859–877.