مجله ژئوفیزیک ایران

مجله ژئوفیزیک ایران

بررسی عملکرد معادلات غیرخطی آب کم‌عمق در مدلسازی امواج سونامی

نوع مقاله : مقاله پژوهشی‌

نویسندگان
1 استادیار، گروه زلزله‌شناسی، موسسه ژئوفیزیک دانشگاه تهران، تهران، ایران
2 دانشیار، گروه زلزله‌شناسی، موسسه ژئوفیزیک دانشگاه تهران، تهران، ایران
چکیده
در این مقاله معادلات غیرخطی آب کم‌عمق در مدلسازی عددی امواج سونامی مورد بررسی و ارزیابی قرار داده می‌شود. مدلسازی سونامی شامل سه‌مرحله تولید، انتشار و بالاروی امواج سونامی است. در این مطالعه ابتدا از یک آزمون‌ محک برای ارزیابی کلی مدل غیرخطی آب کم‌عمق استفاده شد و پس از حصول اطمینان از عملکرد آن، شبیه‌سازی سه رویداد واقعی سونامی (2004 اقیانوس هند، 2011 ژاپن و 1945 مکران) انجام شد. همواره داده‌های واقعی یا آزمایشگاهی نقش مهمی در تنظیم و کالیبره‌کردن مدل‌های عددی ایفا می‌نمایند. تطبیق نتایج مدل‌سازی با داده‌های واقعی در این مطالعه حاکی از دقت قابل قبول مدلسازی عددی غیرخطی آب کم‌عمق در شبیه‌سازی امواج سونامی می‌باشد. این امر بخصوص در مورد سونامی 2011 ژاپن که شامل داده‌های مناسب و دقیق‌تر می‌باشد، بیشتر مشهود است. لازم به ذکر است که اختلاف بین خروجی مدلسازی و داده واقعی تنها ناشی از خطاهای دستگاهی و روش مدلسازی نمی‌باشد و عامل بسیار کلیدی دیگر درک ناقص از چشمه سونامی است. بدین جهت مدلسازی چشمه تولید سونامی دارای بیشترین عدم قطعیت و حیاتی‌ترین مرحله مدلسازی است. هرچند با وجود شناخته‌شده بودن معادلات موج آب، نیاز به بهبود و پیشرفت مدلسازی انتشار و بالاروی سونامی و به خصوص گنجاندن دقیق‌تر اثر عواملی نظیر پاشش، اصطکاک بستر و ساحل و دینامیک موج در ساحل محسوس است اما ارزیابی مناسب خطر سونامی، هشدار سونامی و آمادگی در برابر آن همگی به مدلسازی چشمه سونامی وابسته می‌باشند که این مسئله تاکیدی بر نقش بسیار مهم آن می‌باشد.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Performance review of nonlinear shallow water equations in tsunami wave modeling

نویسندگان English

Amin Rashidi 1
Zaher Hossein Shomali 2
Ali Moradi 2
1 Assistant Professor, Department of Seismology, Institute of Geophysics, University of Tehran, Tehran, Iran
2 Associate Professor, Department of Seismology, Institute of Geophysics, University of Tehran, Tehran, Iran
چکیده English

This research examines and evaluates the nonlinear shallow water equations in the numerical modeling of tsunami waves. Tsunami modeling comprises three primary phases: the generation of tsunamis, their propagation across sea, and the final run-up upon reaching coastal regions. To evaluate the efficacy of the nonlinear shallow water model, an initial benchmark test was conducted. This test was pivotal in establishing the model's reliability, which then paved the way for simulating three significant historical tsunami events—the devastating 2004 Indian Ocean tsunami, the catastrophic 2011 tsunami in Japan, and the 1945 Makran tsunami. Laboratory data plays a crucial role in tuning and calibrating the numerical models, enabling them to better reflect real-world behaviors and outcomes. The results from these simulations showed a noteworthy alignment with actual historical data, showcasing an acceptable level of accuracy in the nonlinear shallow water numerical modeling approach. This compatibility was particularly pronounced for the 2011 Japan tsunami, where the availability of more contemporary and precise data supported more accurate modeling results. However, it is crucial to note that the observed discrepancies between the model outputs and the real-world scenarios cannot be entirely attributed to instrumental errors. Instead, a significant factor contributing to these discrepancies lies in the incomplete understanding of the underlying sources and mechanics of tsunami generation. Given this complexity, modeling tsunami generation carries a high level of uncertainty and represents a critical aspect of the modeling process. While the foundational equations governing water waves are well-established, there remains a pressing need for advancements in the modeling techniques utilized for tsunami propagation and run-up. Specifically, there is a strong imperative to refine the accuracy with which factors such as spray dynamics, friction with the seabed and coastal environments, and the multifaceted behavior of waves upon making landfall are incorporated into these models. These advancements have important effects beyond just research. They significantly impact tsunami risk assessment, early warning systems, and preparedness in coastal communities. Effective tsunami modeling not only enhances our understanding of these devastating natural phenomena but also fortifies our readiness to respond to future events. Given that tsunami modeling is a prerequisite for studying tsunami risk and developing warning systems in tsunami-prone areas, one essential requirement for accurate modeling is high-resolution bathymetric and topographic data. Furthermore, to better understand tsunamis, future studies must aim for a clearer picture of the geometry of tsunami sources, leading to more precise estimates of seabed deformation alongside conducting thorough geophysical, geological, remote sensing, and other field studies. The experiences from the 2004 Indian Ocean tsunami and the 2011 Japan tsunami demonstrate that utilizing tsunami early warning technology is crucial for providing timely alerts before the waves reach the shore, as there is no time to escape once the waves have arrived. In the two mentioned tsunamis, had a warning system been in place or functioning correctly, there would have been an appropriate opportunity to issue tsunami alerts from the source area to surrounding coastlines.

کلیدواژه‌ها English

Tsunami
numerical modeling
shallow water equations
benchmark test
tsunami warning
Barkan, R., & Brink, U.S. (2010). Tsunami simulations of the 1867 Virgin Islands earthquake: Constraints on epicenter location and fault parameters. Bull. Seism. Soc. Am., 100, 995-1009.
Becker, J.J., Sandwell, D.T., Smith, W.H.F. et al. (2009). Global bathymetry and elevation data at 30 arc seconds resolution: Srtm30_plus. Mar Geod, 32, 355-371.
Bilham, R. (2005). A flying start, then a slow slip. Science, 308, 1126-1127.
Bilham, R., Engdahl, E.R., Feldl, N. & Satyabala, S.P. (2005). Partial and complete rupture of the Indo-Andaman plate boundary 1847-2004. Seismol. Res. Lett., 76, 911-932.
Dalrymple, R.A., Grilli, S.T., & Kirby, J.T. (2006). Tsunamis and challenges for accurate modeling. Oceanography, 19, 142-151.
 
Dutykh. D. (2007). Mathematical modelling of tsunami waves, PhD thesis, Ecole Normale Sup´erieure de Cachan, France.
Dutykh, D., Poncet, R., & Dias, F. (2011). The VOLNA code for the numerical modeling of tsunami waves: generation, propagation and inundation. European Journal of Mechanics - B/Fluids, 30 (6), 598-615.
Dutykh, D., Mitsotakis, D., Chubarov, L.B. & Shokin, Y.I. (2012). On the contribution of the horizontal sea-bed displacements into the tsunami generation process. Ocean Modelling, 56, 43-56.
Dutykh, D. & Clamond, D. (2016). Modified shallow water equations for significantly varying seabeds. Applied Mathematical Modelling, 40(23–24), 9767-9787.
Etemadsaeed, L., Zafarani, H., & Saber, F. (2024). Sensitivity analysis of tsunami numerical modeling to bathymetric data resolution and finite difference grid spacing. 9th International Conference on Seismology and Earthquake Engineering, Tehran, Iran.
Fujiwara, T., Kodaira, S., No, T., Kaiho, Y., Takahashi, N., & Kaneda, Y. (2011). The 2011 Tohoku-Oki earthquake: Displacement reaching the trench axis. Science, 334, 6060, 1240-1240.
Geist, E.L., Titiov, V.V., Arcas, D., Pollitz, F.F., & Bilek, S.L. (2007). Implications of the 26 December 2004 Sumatra–Andaman Earthquake on Tsunami Forecast and Assessment Models for Great Subduction-Zone Earthquakes. Bull. Seism. Soc. Am., 97, 249-270.
Grilli, S.T., Ioualalen, M., Asavanant, J., Shi, F., Kirby, J., & Watts, P. (2007). Source constraints and model simulation of the December 26, 2004 Indian Ocean tsunami. J. Waterway Port Coast. Ocean Engineering, 133, 414-428.
Heidarzadeh M., & Satake, K. (2014). New Insights into the Source of the Makran Tsunami of 27 November 1945 from Tsunami Waveforms and Coastal Deformation Data. Pure Appl. Geophys., 172, 621-640.
Imamura, F., Shuto, N., & Goto, C. (1988). Numerical simulation of the transoceanic propagation of tsunamis. paper presented at the Sixth Congress of the Asian and Pacific Regional Division, Int. Assoc. Hydraul. Res., Kyoto, Japan.
Kanayama, H., & Dan, H. (2013). A tsunami simulation of Hakata Bay using the viscous shallow-water equations. Japan J. Indust. Appl. Math., 30, 605-624.
Karimpour A. (2018). Ocean Wave Data Analysis: Introduction to Time Series Analysis, Signal Processing, and Wave Prediction, KDP.
Lay, T., et al. (2005), The great Sumatra-Andaman earthquake of 26 December 2004. Science, 308(5725), 1127-1133.
Liu, P.L.F., Synolakis, C.E., & Yeh, H. (1991). Impressions from the First International Workshop on Long Wave Runup. J. Fluid Mech., 229, 675-688.
Liu, P.L.F., Yeh, H., & Synolakis, C.E. (2008). Advanced Numerical Models for Simulating Tsunami Waves and Runup. Advances in Coastal and Ocean Engineering, 10, 250pp.
Mansinha, L., & Smylie, D.E. (1971). The Displacement Field of Inclined Faults. Bull. Seism. Soc. Am., 61, 1433-1440.
NOAA NGDC (NOAA's National Geophysical Data Center), https://www.ngdc.noaa.gov/
Neetu, S., Suresh, I., Shankar, R., Nagarajan, B., Sharma, R., Shenoi, S.S.C., Unnikrishnan, A.S., & Sundar, D. (2011). Trapped waves of the 27 November 1945 Makran tsunami: Observations and numerical modeling. Natural Hazards, 59, 1609-1618.
Okada, Y. (1985). Surface deformatipon due to shear and tensile faults in a half-space. Bull. seism. Soc. Am., 75, 1135-1154.
Page, W.D., Alt, J.N., Cluff, L.S., & Plafker, G. (1979). Evidence for recurrence of large-magnitude earthquakes along the Makran coast of Iran and Pakistan. Tectonophysics, 52, 533-547.
Rashidi, A., Shomali, Z.H., & Keshavarz, N. (2018). Tsunami simulations in the western Makran using hypothetical heterogeneous source models from world's great earthquakes. Pure and Applied Geophysics, 175(4), 1325-1340.
Rashidi, A., Shomali, Z.H., Dutykh, D., & Keshavarz, N. (2018). Evaluation of tsunami wave energy generated by earthquakes in the Makran subduction zone. Ocean Engineering, 165, 131-139.
Rashidi, A., Dutykh, D., Shomali, Z.H., Keshavarz, N., & Nouri, M. (2020). A Review of Tsunami Hazards in the Makran Subduction Zone. Geosciences, 10(9), 372.
Rashidi, A., Shomali, Z.H., Dutykh, D., & Keshavarz, N. (2020). Tsunami hazard assessment in the Makran subduction zone. Natural Hazards, 100, 861-875.
Rashidi, A., Dutykh, D., Keshavarz, N., & Audin L. (2022). Regional tsunami hazard from splay faults in the gulf of Oman. Ocean Engineering, 243, 110169.
Rashidi, A., Dutykh, D., & Beck, C. (2023). Modeling the potential genesis of tsunamis from below an accretionary prism and their potential impact: a case study along the eastern boundary of the Caribbean Plate. Natural Hazards, 118, 307-329.
USGS (United States Geological Survey); http://www.usgs.gov/
Satake, K., Fujii, Y., Harada, T., & Namegaya, Y. (2013). Time and space distribution of coseismic slip of the 2011 Tohoku earthquake as inferred from tsunami waveform data. Bull. Seism. Soc. Am., 103(2B), 1473-1492.
Shao, G., Li, X., Ji, C., & Maeda, T. (2011). Focal mechanism and slip history of the 2011 Mw 9.1 off the pacific coast of tohoku earthquake, constrained with teleseismic body and surface waves. Earth, Planets and Space, 63(7), 559-564.
Smith, W.H.F., & Sandwell, D.T. (1997). Global sea floor topography from satellite altimetry and ship depth soundings. Science, 277(5334), 1956-1962.
Wang, X. (2008). Numerical modelling of surface and internal waves over shallow and intermediate water, PhD thesis, Cornell University, USA.
Wang, X., & Liu, P.L-F. (2006(. An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian Ocean tsunami. J. Hydraul. Res, 44(2), 147-154.
Wei, S., Graves, R., Helmberger, D., Avouac, J.P., & Jiang, J. (2012). Sources of shaking and flooding during the Tohoku-Oki earthquake: A mixture of rupture styles. Earth and Planetary Science Letters, 333-334, 91-100.
Woods, M., & Okal, E. (1987). Effect of variable bathymetry on the amplitude of teleseismic tsunamis: A ray–tracing experiment. Geophysical Research Letters, 14(7), 765-768.
Yalciner, A.C., Ghazali, N.H., & Wahab, A.K.A. (2005a). December 26, 2004 Indian Ocean tsunami field survey July. 09-10, 2005 at North west peninsular Malaysia Coast, Penang and Langkawi Islands. http://yalciner.ce.metu.edu.tr/malaysia-survey.
Yalciner, A.C., Perincek, D., Ersoy, S., Presateya, G., Hidayat, R., & McAdoo, B. (2005b). Report on December 26, 2004, Indian Ocean tsunami, field survey on Jan 21–31 at north of Sumatra. ITST of UNESCO IOC, http://yalciner.ce.metu.edu.tr/sumatra/survey.
Yamada, F., Fernandez, H., Goff, J., Higman, B., & Jaffe, B. (2005). An overview of the ITST expedition to Sri Lanka. Proc. 5th Int. Conf. on Ocean Wave Measurement and Analysis, WAVES 2005, Madrid, Spain, Paper No. 217.
Yoon, S.B. (2002). Propagation of distant tsunamis over slowly varying topography. J. Geophys. Res., 101(C10), 3140.
Zafarani, H., Etemadsaeed, L., Rahimi, M., Kheirdast, N., Rashidi, A., Ansari, A., Mokhtari, M., & Eskandari-Ghadi, M. (2023). Probabilistic tsunami hazard analysis for western Makran coasts, south-east Iran. Natural Hazards, 115, 1275-1311.