Abstract
The aim of this study is to demonstrate the bias created in the seismic hazard studies due to the choice of magnitude scaling equations without any statistical basis. The earthquake catalogue of Tripura, India, has been used for the purpose of this study. The catalogue was homogenized using the various scaling equations suitable for the region. Then, the bias created on parameters, like the magnitude of completeness (Mc), a and b values of the Gutenberg–Richter recurrence relation, maximum magnitude (Mmax), and peak ground acceleration, was demonstrated. The standard deviations of Mc, a, and b parameters were observed to be 0.23, 0.27, and 0.037 respectively. The maximum variations in the Mmax and ground motion estimates were found to be 0.7 magnitude units and 0.2 g respectively. Then, the robustness of the regional rupture characters in overcoming the observed variations has been demonstrated. The trend of the rupture behavior of the seismic sources seems to be unaffected by the change in the magnitude scaling equations. The Mmax calculated from the rupture-based procedure was observed to be higher than that calculated from the probabilistic method. This variation in Mmax estimation has been utilized to critically assess the suitability of the magnitude scaling equations for the particular study area.
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References
Abramowitz M, Stegun IA (1972) Handbook of mathematical functions: with formulas, graphs, and mathematical tables, vol 55. Dover publications, New York, p 886
Anbazhagan P, Bajaj K, Patel S (2015a) Seismic hazard maps and spectrum for Patna considering region-specific seismotectonic parameters. Nat Hazards 78(2):1163–1195
Anbazhagan P, Bajaj K, Moustafa SS, Al-Arifi NS (2015b) Maximum magnitude estimation considering the regional rupture character. J Seismol 19(3):695–719
Anderson JG, Wesnousky SG, Stirling MW (1996) Earthquake size as a function of fault slip rate. Bull Seismol Soc Am 86(3):683–690
Baruah S, Baruah S, Bora PK, Duarah R, Kalita A, Biswas R, Gogoi N, Kayal JR (2012) Moment magnitude (MW) and local magnitude (ML) relationship for earthquakes in Northeast India. Pure Appl Geophys 169(11):1977–1988
Bender B (1983) Maximum likelihood estimation of b values for magnitude grouped data. Bull Seismol Soc Am 73(3):831–851
Bora DK (2016) Scaling relations of moment magnitude, local magnitude, and duration magnitude for earthquakes originated in northeast India. Earthq Sci 29(3):153–164
Castellaro S, Mulargia F, Kagan YY (2006) Regression problems for magnitudes. Geophys J Int 165(3):913–930
Das R, Wason HR, Sharma ML (2011) Global regression relations for conversion of surface wave and body wave magnitudes to moment magnitude. Nat Hazards 59(2):801–810
Das R, Wason HR, Sharma ML (2012a) Homogenization of earthquake catalog for northeast India and adjoining region. Pure Appl Geophys 169(4):725–731
Das R, Wason HR, Sharma ML (2012b) Temporal and spatial variations in the magnitude of completeness for homogenized moment magnitude catalogue for northeast India. J Earth Syst Sci 121(1):19–28
Das R, Sharma ML, Wason HR (2016) Probabilistic seismic hazard assessment for northeast India region. Pure Appl Geophys 173(8):2653–2670
Dasgupta S, Narula PL, Acharyya SK, Banerjee J (2000) Seismotectonic atlas of India and its environs. Geol Surv India
Gardner JK, Knopoff L (1974) Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian? Bull Seismol Soc Am 64(5):1363–1367
Gasperini P, Lolli B, Vannucci G, Boschi E (2012) A comparison of moment magnitude estimates for the European—Mediterranean and Italian regions. Geophys J Int 190(3):1733–1745
Grünthal G, Wahlström R (2003) An M w based earthquake catalogue for central, northern and northwestern Europe using a hierarchy of magnitude conversions. J Seismol 7(4):507–531
Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seismol Soc Am 34(4):185–188
Hanks TC, Kanamori H (1979) A moment magnitude scale. J Geophys Res Solid Earth 84(B5):2348–2350
Hurukawa N, Maung Maung P (2011) Two seismic gaps on the Sagaing Fault, Myanmar, derived from relocation of historical earthquakes since 1918. Geophys Res Lett 38(1)
IS 1893-Part 1 (2016) Criteria for earthquake resistant design of structures: general provisions and buildings. Bureau of Indian Standards, New Delhi
Jin A, Aki K (1988) Spatial and temporal correlation between coda Q and seismicity in China. Bull Seismol Soc Am 78(2):741–769
Kijko A, Sellevoll MA (1989) Estimation of earthquake hazard parameters from incomplete data files. Part I. Utilization of extreme and complete catalogs with different threshold magnitudes. Bull Seismol Soc Am 79(3):645–654
Kijko A, Singh M (2011) Statistical tool for maximum possible earthquake magnitude estimation. Acta Geophys 59:674–700
Kolathayar S, Sitharam TG, Vipin KS (2012) Spatial variation of seismicity parameters across India and adjoining areas. Nat Hazards 60(3):1365–1379
Kramer SL (1996) Geotechnical earthquake engineering. Prentice–Hall international series in civil engineering and engineering mechanics. Prentice-Hall, New Jersey
Last M, Rabinowitz N, Leonard G (2016) Predicting the maximum earthquake magnitude from seismic data in Israel and its neighboring countries. PloS One 11(1):e0146101
Lolli B, Gasperini P, Vannucci G (2014) Empirical conversion between teleseismic magnitudes (mb and Ms) and moment magnitude (M w) at the Global, Euro-Mediterranean and Italian scale. Geophys J Int 199(2):805–828
Nath SK, Vyas M, Pal I, Sengupta P (2005) A seismic hazard scenario in the Sikkim Himalaya from seismotectonics, spectral amplification, source parameterization, and spectral attenuation laws using strong motion seismometry. J Geophys Res Solid Earth 110(B1)
NDMA (2010) Development of probabilistic seismic hazard map of India; technical report by National Disaster Management Authority, Government of India
Omori F (1894) On the after-shocks of earthquakes. J Coll Sci Imp Univ Tokyo 7:111–200
Osher B (1996) Statistical estimation of the maximum magnitude and its uncertainty from a catalogue including magnitude errors. In: Earthquake hazard and risk. Springer, Dordrecht, pp. 25-37
Pandey AK, Chingtham P, Roy PNS (2017) Homogeneous earthquake catalogue for northeast region of India using robust statistical approaches. Geomat Nat Haz Risk 8(2):1477–1491
Reasenberg P (1985) Second-order moment of central California seismicity, 1969–1982. J Geophys Res Solid Earth 90(B7):5479–5495
Rhoades DA (1996) Estimation of the Gutenberg-Richter relation allowing for individual earthquake magnitude uncertainties. Tectonophysics 258(1–4):71–83
Richter CF (1935) An instrumental earthquake magnitude scale. Bull Seismol Soc Am 25(1):1–32
Scordilis EM (2006) Empirical global relations converting M S and m b to moment magnitude. J Seismol 10(2):225–236
Sil A, Sitharam TG, Kolathayar S (2013) Probabilistic seismic hazard analysis of Tripura and Mizoram states. Nat Hazards 68(2):1089–1108
Sitharam TG, Sil A (2014) Comprehensive seismic hazard assessment of Tripura and Mizoram states. J Earth Syst Sci 123(4):837–857
Stromeyer D, Grünthal G, Wahlström R (2004) Chi-square regression for seismic strength parameter relations, and their uncertainties, with applications to an M w based earthquake catalogue for central, northern and northwestern Europe. J Seismol 8(1):143–153
Thingbaijam KKS, Nath SK, Yadav A, Raj A, Walling MY, Mohanty WK (2008) Recent seismicity in northeast India and its adjoining region. J Seismol 12(1):107–123
Tinti S, Mulargia F (1985) Effects of magnitude uncertainties on estimating the parameters in the Gutenberg-Richter frequency-magnitude law. Bull Seismol Soc Am 75(6):1681–1697
Uhrhammer RA (1986) Characteristics of northern and central California seismicity. Earthq Notes 57(1):21
Wason HR, Das R, Sharma ML (2012) Magnitude conversion problem using general orthogonal regression. Geophys J Int 190(2):1091–1096
Wells DL, Coppersmith KJ (1994) New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull Seismol Soc Am 84(4):974–1002
Woessner J, Wiemer S (2005) Assessing the quality of earthquake catalogues: estimating the magnitude of completeness and its uncertainty. Bull Seismol Soc Am 95(2):684–698
Yin A, Harrison TM (2000) Geologic evolution of the Himalayan-Tibetan orogen. Annu Rev Earth Planet Sci 28(1):211–280
Funding
The “Board of Research in Nuclear Sciences (BRNS),” Department of Atomic Energy (DAE), Government of India funded the project titled “Probabilistic seismic hazard analysis of Vizag and Tarapur considering regional uncertainties & Studies of Tripura Earthquake and Liquefied Soil” (Ref No. Sanction No. 36(2)/14/16/2016-BRNS-36016 dated July 1st, 2016 ).
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Anbazhagan, P., Balakumar, A. Seismic magnitude conversion and its effect on seismic hazard analysis. J Seismol 23, 623–647 (2019). https://doi.org/10.1007/s10950-019-09826-1
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DOI: https://doi.org/10.1007/s10950-019-09826-1