This study aims to incorporate the effects of the spatial extent of the fault plane and the heterogeneous slip distributions in the probabilistic seismic hazard assessment (PSHA) of the Nankai Trough earthquakes. A method has been proposed to apply the characterized earthquake fault model (CEFM) developed for the probabilistic tsunami hazard assessment (PTHA) and the ground motion prediction equation employing the equivalent hypocentral distance (EHD) instead of conventional shortest fault distance (SFD). First, the PGV distributions were compared using the SFD and EHD with three different definitions of the weighting coefficients represented by the exponent (0, 1, and 2) of the slip amount. The results employing the EHD reflected the effect of the heterogeneous slip distributions, and the contrast became prominent with greater value of the exponent. Thereafter, in accordance with the scaling law of the fault parameters, the exponent was determined as 1 so that the contribution ratios of the large slip areas and the asperities in the characterized seismic source model are balanced in terms of seismic energy radiation. Analytical conditions for seismic and tsunami multi-hazard and risk assessment can be made consistent by employing the CEFM for both PSHA and PTHA.

1. [1] H. Park and D. T. Cox, “Probabilistic assessment of near-field tsunami hazards: Inundation depth, velocity, momentum flux, arrival time, and duration applied to Seaside, Oregon,” Coastal Engineering, pp. 79-96, 2016. http://doi.org/10.1016/j.coastaleng.2016.07.011
2. [2] H. Park, D. T. Cox, M. S. Alam, and A. R. Barbosa, “Probabilistic seismic and tsunami hazard analysis conditioned on a megathrust rupture of the Cascadia subduction zone,” Frontiers in Built Environment, Vol.3, Article No.32, 2017. http://doi.org/10.3389/fbuil.2017.00032
3. [3] E. L. Geist, “Complex earthquake rupture and local tsunamis,” J. of Geophysical Research: Solid Earth, Vol.107, Issue B5, pp. ESE 2-1-ESE 2-15, 2002. http://doi.org/10.1029/2000JB000139
4. [4] E. L. Geist and T. Parsons, “Probabilistic analysis of tsunami hazards,” Natural Hazards, Vol.37, pp. 277-314, 2006. http://doi.org/10.1007/s11069-005-4646-z
5. [5] R. D. Risi and K. Goda, “Probabilistic earthquake–tsunami multi-hazard analysis: Application to the Tohoku region, Japan,” Frontiers in Built Environment, Vol.2, Article No.25, 2016. http://doi.org/10.3389/fbuil.2016.00025
6. [6] K. Nakata, Y. Hayashi, H. Tsushima, K. Fujita, Y. Yoshida, and A. Katsumata, “Performance of uniform and heterogeneous slip distributions for the modeling of the November 2016 of Fukushima earthquake and tsunami, Japan,” Earth, Planets and Space, Vol.71, Article No.30, 2019. http://doi.org/10.1186/s40623-019-1010-1
7. [7] M. Nakano, S. Murphy, R. Agata, Y. Igarashi, M. Okada, and T. Hori, “Self-similar stochastic slip distributions on a non-planar fault for tsunami scenarios for megathrust earthquakes,” Progress in Earth and Planetary Science, Vol.7, Article No.45, 2020. http://doi.org/10.1186/s40645-020-00360-0
8. [8] D. Gopinathan, M. Heidarzadeh, and S. Guillasc, “Probabilistic quantification of tsunami current hazard using statistical emulation,” Proc. of the Royal Society A: Mathematical, Physical, and Engineering Sciences, Vol.477, Issue 2250, 2021. https://doi.org/10.1098/rspa.2021.0180
9. [9] A. Herrero and P. Bernard. “A kinematic self-similar rupture process for earthquakes,” Bulletin of the Seismological Society of America, Vol.84, No.4, pp. 1216-1228, 1994. http://doi.org/10.1785/BSSA0840041216
10. [10] P. Somerville, K. Irikura, R. Graves, S. Sawada, D. Wald, N. Abrahamson, Y. Iwasaki, T. Kagawa, N. Smith, and A. Kowada, “Characterizing crustal earthquake slip models for the prediction of strong motion,” Seismological Research Letters, Vol.70, No.1, pp. 59-80, 1999. http://doi.org/10.1785/gssrl.70.1.59
11. [11] P. M. Mai and G. C. Beroza, “A spatial random field model to characterize complexity in earthquake slip,” J. of Geophysical Research: Solid Earth, Vol.107, Issue B11, pp. ESE 10-1-ESE 10-21, 2002. http://doi.org/10.1029/2001JB000588
12. [12] R. W. Graves and A. Pitarka, “Broadband ground-motion simulation using a hybrid approach,” Bulletin of the Seismological Society of America, Vol.100, No.5A, pp. 2095-2123, 2010. https://doi.org/10.1785/0120100057
13. [13] J. Douglas, “Earthquake ground motion estimation using strong-motion records: A review of equations for the estimation of peak ground acceleration and response spectral ordinates,” Earth-Science Reviews, Vol.61, Issues 1-2, pp. 43-104, 2003. http://doi.org/10.1016/S0012-8252(02)00112-5
14. [14] W. B. Joyner and D. M. Boore, “Peak horizontal acceleration and velocity from strong motion records including records from the 1979 Imperial Valley, California, earthquake,” Bulletin of the Seismological Society of America, Vol.71, No.6, pp. 2011-2038, 1981. https://doi.org/10.1785/BSSA0710062011
15. [15] N. Abrahamson, N. Gregor, and K. Addo, “BC Hydro ground motion prediction equations for subduction earthquakes,” Earthquake Spectra, Vol.32, Issue 1, pp. 23-44, 2016. http://doi.org/10.1193/051712EQS188MR
16. [16] N. Morikawa and H. Fujiwara, “A new ground motion prediction equation for Japan applicable up to M9 mega-earthquake,” J. Disaster Res., Vol.8, No.5, pp. 878-888, 2013. http://doi.org/10.20965/jdr.2013.p0878
17. [17] K. Goda and R. D. Risi, “Multi-hazard loss estimation for shaking and tsunami using stochastic rupture sources,” Int. J. of Disaster Risk Reduction, Vol.28, pp. 539-554, 2018. http://doi.org/10.1016/j.ijdrr.2018.01.002
18. [18] H. Park, M. S. Alam, D. T. Cox, A. R. Barbosa, and J. W. van de Lindt, “Probabilistic seismic and tsunami damage analysis (PSTDA) of the Cascadia Subduction Zone applied to Seaside, Oregon,” Int. J. of Disaster Risk Reduction, Vol.35, Article No.101076, 2019. http://doi.org/10.1016/j.ijdrr.2019.101076
19. [19] H. Sugino, Y. Iwabuchi, and F. Imamaura, “Scenario tsunami source modeling and probabilistic tsunami hazard assessment method,” Proc. of 16th World Conf. on Earthquake Engineering, Paper No.1556, 2017.
20. [20] T. Kito, K. Hirata, T, Maeda, Y. Dohi, H. Fujiwara, and H. Matsuyama, “Characterized fault models for the reproduction of the tsunami traces by the great earthquakes along the Nankai Trough – Towards probabilistic tsunami hazard assessment –,” J. of Japan Association for Earthquake Engineering, Vol.21, No.1, pp. 82-105, 2021 (in Japanese). http://doi.org/10.5610/jaee.21.1_82
21. [21] Earthquake Research Committee, The Headquarters for Earthquake Research Promotion, “Tsunami prediction method for earthquakes with characterized source faults (tsunami recipe),” 2022.
22. [22] Earthquake Research Committee, The Headquarters for Earthquake Research Promotion, “Probabilistic hazard assessment of tsunami due to large earthquakes along the Nankai Trough,” 2020 (in Japanese).
23. [23] National Research Institute for Earth Science and Disaster Resilience, “Japan Tsunami Hazard Information Station (J-THIS), 2020. http://doi.org/10.17598/nied.0016
24. [24] H. Miyake, T. Iwata, and K. Irikura, “Source characterization for broadband ground-motion simulation: Kinematic heterogeneous source model and strong motion generation area,” Bulletin of the Seismological Society of America, Vol.93, No.6, pp. 2531-2545, 2003. https://doi.org/10.1785/0120020183
25. [25] S. Murotani, H. Miyake, and K. Koketsu, “Scaling of characterized slip models for plate-boundary earthquakes,” Earth, Planets and Space, Vol.60, pp. 987-991, 2008. http://doi.org/10.1186/BF03352855
26. [26] K. Irikura and H. Miyake, “Recipe for predicting strong ground motion from crustal earthquake scenarios,” Pure and Applied Geophysics, Vol.168, pp. 85-104, 2011. http://doi.org/10.1007/s00024-010-0150-9
27. [27] Earthquake Research Committee, The Headquarters for Earthquake Research Promotion, “Strong ground motion prediction method for earthquakes with specified source faults (recipe),” 2017 (in Japanese).
28. [28] A. Pitarka, R. W. Graves, K. Irikura, K. Miyakoshi, and A. Rodgers, “Kinematic rupture modeling of ground motion from the M7 Kumamoto, Japan Earthquake,” Pure and Applied Geophysics, Vol.177, pp. 2199-2221, 2020. http://doi.org/10.1007/s00024-019-02220-5
29. [29] Earthquake Research Committee, The Headquarters for Earthquake Research Promotion, “National seismic hazard maps for Japan 2020 edition,” 2020 (in Japanese).
30. [30] National Research Institute for Earth Science and Disaster Resilience, “Japan Seismic Hazard Information Station (J-SHIS),” 2019. http://doi.org/10.17598/nied.0010
31. [31] H. Si and S. Midorikawa, “New attenuation relationships for peak ground acceleration and velocity considering effects of fault type and site condition,” J. of Structural and Construction Engineering (Trans. of AIJ), Vol.64, No.523, pp. 63-70, 1999 (in Japanese). http://doi.org/10.3130/aijs.64.63_2
32. [32] H. Si and S. Midorikawa, “New attenuation relationships for peak ground acceleration and velocity considering effects of fault type and site condition,” Proc. of the 12th World Conf. on Earthquake Engineering, Article No.0532, 2000.
33. [33] National Research Institute for Earth Science and Disaster Resilience, “Probabilistic tsunami hazard assessment for earthquakes occurring along the Nankai Trough Volume 1 Part II,” Research Material No.439, April 2020 (in Japanese). http://doi.org/10.24732/nied.00002258
34. [34] S. Ohno, T. Ohta, T. Ikeura, and M. Takeumura, “Revision of attenuation formula considering the effect of fault size to evaluate strong motion spectra in near field,” Tectonophysics, Vol.218, Issues 1-3, pp. 69-81, 1993. http://doi.org/10.1016/0040-1951(93)90260-Q
35. [35] S. Ohno, M. Takemura, M. Niwa, and K. Takahashi, “Intensity of strong ground motion on pre-quaternary stratum and surface soil amplifications during the 1995 Hyogo-ken Nanbu earthquake, Japan,” J. of Physics of the Earth, Vol.44, No.5, pp. 623-648, 1996. http://doi.org/10.4294/jpe1952.44.623
36. [36] C. B. Crouse, “Ground-motion attenuation equations for earthquakes on the Cascadia subduction zones,” Earthquake Spectra, Vol.7, No.2, pp. 201-236, 1991. https://doi.org/10.1193/1.1585626
37. [37] C. B. Crouse, Y. K. Vyas, and B. A. Schell, “Ground motion from subduction-zone earthquakes,” Bulletin of the Seismological Society of America, Vol.78, No.1, pp. 1-25, 1988.
38. [38] K. Goda and G. M. Atkinson, “Variation of source-to-site distance for megathrust subduction earthquakes: effects on ground motion prediction equations,” Earthquake Spectra, Vol.30, No.2, pp. 845-866, 2014. https://doi.org/10.1193/080512EQS254M
39. [39] Y. Jiao and N. Nojima, “A method to apply equivalent hypocentral distance for probabilistic seismic hazard assessment of the Nankai Trough Earthquakes,” The 78th Annual Conf. of JSCE, Paper No.CS10-46, 2 pp., 2023 (in Japanese).
40. [40] Y. Jiao and N. Nojima, “Probabilistic tsunami hazard assessment considering the sequence of the first and second earthquakes along the Nankai Trough,” J. Disaster Res., Vol.18, No.8, pp. 839-851, 2023. http://doi.org/10.20965/jdr.2023.p0839
41. [41] Y. Dohi, H. Nakamura, and H. Fujiwara, “Development of the japan tsunami hazard information station (J-THIS),” J. Disaster Res., Vol.17, No.6, pp. 934-943, 2022. http://doi.org/10.20965/jdr.2022.p0934
42. [42] K. Fujimoto and S. Midorikawa, “Relationship between average shear-wave velocity and site amplification inferred from strong motion records at nearby station pairs,” J. of Japan Association for Earthquake Engineering, Vol.6, No.1, pp. 11-22, 2006 (in Japanese). http://doi.org/10.5610/jaee.6.11
43. [43] S. Ohno, “Ground motion prediction equation applicable to mega earthquakes considering strong-motion generation areas,” Proc. of 16th World Conf. on Earthquake Engineering,” Paper No.2685, 2017.
44. [44] H. Si, K. Koketsu, and H. Miyake, “Attenuation characteristics of strong ground motion from megathrust earthquakes in subduction zone – On the pass effects –,” J. of Japan Association for Earthquake Engineering, Vol.16, No.1, pp. 96-105, 2016 (in Japanese). http://doi.org/10.5610/jaee.16.1_96
45. [45] S. Ohno, “Strong motion attenuation characteristics and applicability of ground-motion prediction equations for the 2011 Tohoku earthquake,” J. of Japan Association for Earthquake Engineering, Vol.16, No.4, pp. 2-11, 2016 (in Japanese). http://doi.org/10.5610/jaee.16.4_2
46. [46] K. Dan, “Technical terminology of asperity used in the strong motion prediction,” J. of Structural and Construction Engineering (Trans. of AIJ), Vol.88, No.788, pp. 1533-1543, 2020 (in Japanese). http://doi.org/10.3130/aijs.85.1533
47. [47] Y. Shiba, “Broadband source characteristics of recent in-slab earthquakes off the Pacific Coast of Tohoku,” Proc. of the 17th Annual Meeting of Japan Association for Earthquake Engineering, Paper No.TS_20220053, December 2022 (in Japanese).
48. [48] Y. Yokota, K. Koketsu, Y. Fujii, K. Satake, S. Sakai, M. Shinohara, and T. Kanazawa, “Joint inversion of strong motion, teleseismic, geodetic, and tsunami datasets for the rupture process of the 2011 Tohoku earthquake,” Geophysical Research Letters, Vol.38, Issue 7, Article No.L00G21, 2011. http://doi.org/10.1029/2011GL050098
49. [49] T. Ishii, T. Sato, and P. G. Somerville, “Identification of main rupture areas of heterogeneous fault models for dtrong-motion estimation,” J. of Structural and Construction Engineering (Trans. of AIJ), Vol.65, No.527, pp. 61-70, 2000 (in Japanese). http://doi.org/10.3130/aijs.65.61_1
50. [50] Cabinet Office, “Nankai Trough mega earthquake modeling group (second report) Seismic fault model – On seismic fault model and seismic intensity distribution –,” 2012 (in Japanese). https://www.bousai.go.jp/jishin/nankai/model/pdf/20120829_2nd_report05.pdf [Accessed December 27, 2023]
51. [51] H. Fujiwara, N. Morikawa, S. Aoi, T. Maeda, and A. Iwaki, “3.3 Source modeling method for the Nankai Trough earthquakes,” FY2012 Report of Support Project for Developing Seismic Hazard Map for Long-period Ground Motion, pp. 68-99, 2013 (in Japanese). https://jishin.go.jp/main/chousakenkyuu/choshuki_shien/h24/index.htm
52. [52] K. Dan, Y. Ishii, J. Miyakoshi, H. Takahashi, M. Mori, and N. Fukuwa, “Modeling of fault rupturing of subduction plate-boundary earthquakes with magnitude 9 for predictiong strong motions – Application to the Nankai trough and examples of strong motions predicted in Tokai region –,” J. of Structural and Construction Engineering (Trans. of AIJ), Vol.78, No.692, pp. 1685-1694, 2013 (in Japanese). http://doi.org/10.3130/aijs.78.1685
53. [53] M. Matsu’ura, “Reconsideration of the energy balance in earthquake faulting,” Progress in Earth and Planetary Science, Vol.11, No.2, Article No.2, 2024. https://doi.org/10.1186/s40645-023-00602-x
54. [54] K. Dan, M. Watanabe, T. Sato, and T. Ishii, “Short-period source spectra inferred from variable-slip rupture models and modeling of earthquake faults for strong motion prediction by semi-empirical method,” J. of Structural and Construction Engineering (Trans. of AIJ), Vol.66, No.545, pp. 51-62, 2001 (in Japanese). http://doi.org/10.3130/aijs.66.51_4