Updating Probabilistic Seismic Intensity at Kathmandu after 2015 Gorkha Earthquake

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1 Journal of Cvl Engneerng and Archtecture 12 (2018) do: / / D DAVID PUBLISHING Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake Har Ram Paraul Department of Cvl Engneerng, Pulchowk Campus, Trbhuwan Unversty, Kathmandu, Nepal Abstract: Subducton of Indan plate beneath the Eurasan plate has formed three thrust faults along Hmalayas. Due to contnuous shortenng, many earthquakes have occurred n the past causng massve deaths and destructons showng that earthquakes are the greatest threat. Sesmc hazard of the central Hmalayan regon has been examned based upon kernel densty functon method. Faults are so nearer that t s dffcult to udge whch earthquake belongs to whch fault and even some parts of the faults do not hold earthquakes, and usual method of assgnng the earthquakes to the nearest fault developng magntude-frequency relatonshp s not applcable. Thus, sesmc hazard s estmated consderng area sources wth dfferent denstes at each locaton based upon hstorcal earthquakes usng kernel densty functons whch account both earthquake szes and numbers. Fault s consdered as one earthquake wth ts hghest magntude at centre when calculatng densty but does not ad n earthquake data base for recurrence relatonshp. Snce there are no specfc attenuaton laws developed for the Hmalayan regon, fve attenuaton laws developed for other subducton zones are selected and used gvng equal weght to all to mnmze the uncertantes. Then, probablstc spectra for varous natural perods at Kathmandu are calculated and plotted. Key words: Earthquakes, faults, Hmalayas, kernel densty, sesmc hazard, probablstc spectra, 2015 Gorkha earthquake. 1. Introducton Hmalayas, the youngest mountan range, approxmately 2,200 km n length, extends from north Inda through Nepal, Bhutan to eastern Inda. It was formed due to convergence of Indan plate and Eurasan plate mllons years ago. Mountan buldng process s stll ongong because Indan plate s movng towards Eurasan plate [1]. The slp rate s approxmately 2 cm per year. It means that n every 100 years Indan plate s plungng 200 cm beneath the Eurasa plate. Hgh level of tectonc actvty between the plates bult present geology of Hmalayas and three great faultng systems HFT (Hmalayan frontal thrust), MBT (man boundary thrust) and MCT (man central thrust) longtudnally through Nepal and STDT (South Tbetan detachment system) n the Tbetan regon. The colldng force bulds up pressure Correspondng author: Har Ram Paraul, Ph.D., assocate professor, research felds: earthquake engneerng, structural engneerng, lfelne rsk management. contnually for several years and ths pressure s released n the form of earthquakes. Due to ths process, the Hmalayan arc has experenced great earthquakes. Three maor earthquakes n 1505, 1833 and 1934 have been recorded n the Nepal Hmalayan regon n ts hstory. Recently n 2015 a maor quake M7.8 hts central Nepal clamng 8,900 peoples and damages one mllon houses. Damage dstrbuton s shown n Fg. 1. Another very bg earthquake has been revealed recently that s supposed to have occurred n the eastern Nepal though ts exact locaton s yet to verfy [2]. It shows that earthquakes are the greatest rsk to the Hmalayan regon. Of the total length, Nepal tself holds approxmately 1,000 km length of the central Hmalayas. The sesmc hazard assessment here s presented for ths regon. As mentoned above, there are three faults systems n Nepal and another faultng system s n Tbetan regons. The conventonal method used to estmate hazard s to develop recurrence relatonshp for each fault separately assgnng the past earthquakes to the

2 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake 4555 Fg. 1 Damages n 2015 Gorkha earthquake. nearest faults. Here faults are so closed and t s very dffcult to know whch earthquake belongs to whch fault. So, n ths study, area sources are consdered. The area s further subdvded nto number of small areas call cells. All cells are taken as sources and separate recurrence relatonshp for all cells are developed consderng all the earthquakes around 300 km radus from the centre of the cells. But, due to ths assumpton, there s possblty of smearng out of earthquake denstes all over the areas. It over allocates earthquake denstes over the areas where earthquakes have rarely occurred and under allocates earthquakes over the areas where earthquakes have occurred frequently. To overcome ths dscrepancy, separate densty at each sub area s calculated based upon the numbers of earthquakes and ther szes at the cell and nearby cells by usng kernel densty method whch s explaned n the followng sectons. 2. Recurrence e Relatonshp Of the 2,200 km length of Hmalayas, 1,000 km length of the Nepal Hmalayas s dvded nto smalll grds at 0.5 and 1 degrees nterval n lattude and longtude respectvely. Then all the earthquakes wthn 3000 km radus of each grd ntersecton (ste) are collected. The earthquakes and the small dgtzedd faults of that earthquake catalogue was formed mergng the dataa from U.S. Geologcal Survey [4], Ambraseys and Jackson [5], Pant [6], BECA [7] and Ambraseys and Douglas [8]. The earthquakes data have been reported n dfferent magntudes and n ntensty scales. To make unformty, all data gven n McGure [10] and scalng relatonshp for Hmalayan regon [8]. regon are plotted n Fg. 2. The were converted to the moment magntude [9] usng varous relatonshpss

3 456 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake Fg. 2 Earthquakes n Hmalayan regon. Followng completeness method [11], magntude frequency relatonshp s developedd for each grd ntersecton separately. The coeffcents (a and b) ) for frequency magntude relaton are obtaned. The coeffcent a represents for numbers of earthquakes and b value represents for rate of occurrence of bgger earthquakes. a value s low for the southern stes and contnuously ncreasng towards north. In an average b value s 1 for the regon. Maxmum magntude (MM max ) reported n the data base s the hghest magntude of earthquake obtaned from the catalogue. 3. Attenuaton Laws Because of unavalablty of suffcent data, nstead of developng new equaton for the regon, attenuaton equatons among already developed equatons for subducton zone [12-20] whch support the tectoncs, geology and faultng system are studed. Out of them, consderng fve equatons [15-20], attenuaton laws that represent typcal sesmc envronment are selected. Among them, Atknson and Boore [17] predct the lowest values and Zhao et al. [20] the hghest values. There s no certanty that future earthquakes obey any partcular attenuaton law. Thus, sesmc hazard s estmated consderng all attenuaton gvng equal weght. 4. Probablst tc Spectra source and dvded nto smaller sub-areas (cells) of 10 km 10 km sze. Dstances between centre of cells and ste are calculated. Only the cells wthn 300 km radus are For each ste, 600 km 600 km areaa s taken as partcular value of acceleraton s calculated by summng up all the probabltes of occurrences of earthquakes gven magntudes and dstances. ν consdered to make the recurrence equaton applcable. The mean rate n Eq. (1) of exceedng N s * = y ν M mn =1 where, Ns s number of sources n the regon, = exp( α β s total rate of exceedances of ν M mn β m mn) * P[ Y > y m, r f ] ( m)f threshold magntude (M = 5.0 s taken n ths study), M R ()dmdr r (1)

4 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake 457 * wth α = 2.303a, β = 2.303b. P [ Y y m, r ] > s condtonal probablty that s chosen acceleraton exceeded for a gven magntude (M) and dstance (R), and f M ( m ) and f R () r are probablty densty functons for magntude and dstance respectvely. Here, M and m are used as random varable and specfc value for magntude respectvely. The probablty densty functon for Gunterberg-Rchter law wth lower and upper bound magntudes s expressed n Eq. (2). [ β( m mmn )] [ β( m m )] β exp f M ( m) = (2) 1 exp max mn Earthquake densty s smply number of earthquakes per unt area. However, sze of earthquake makes maor nfluence n terms of effects. Effect of a sngle bg event would be far greater than thousands of smaller events. Thus, actvty rate based upon sze of earthquake s calculated usng kernel estmaton method [21]. Consderng total rate around the partcular ste s unty, fracton of actvty rate whch called earthquake densty here, for all the sources around the ste s calculated dependng upon the numbers and sze of the earthquakes avalable n and nearby cells. The mean actvty rate λ ( m, x), at a cell s taken as a kernel estmaton sum consderng the contrbuton of N events nversely weghted by ts effectve return perod whch satsfes the condton (Eq. (3)) that can be obtaned from Eqs. (4)-(7). K ( ) r h m (3) = N = 1 ( m, r ) T ( r ) K λ ( m, x) (4) ( m, r ) h = 2π D h ( m ) h r ( m ) ( m ) H exp( ) Cm 2 D (5) = (6) λ( m, x) ρ = N s λ( m, x) = 1 where, K ( m, x) s kernel functon, () r perod of the event located at dstance from r, ( m) (7) T s return h s kernel band wdth scalng parameter shorter for smaller magntude and vce vce-versa, whch may be regarded as a fault length [22] and D s fractal dmenson whch s taken as 1.7. H and C are constants equal to 1.45 and Magntude s dvded nto 0.1M and dstance nto 10 km ntervals. N m and N r are the total numbers of magntude and dstance bns. There are many small faults around the bg faults systems (Fg. 3a). Earthquakes have occurred n or near some of the faults but many of them are empty. Even f the faults have earthquakes, they are not suffcent to develop magntude frequency relatonshp. Thus, areal sources have been taken as explaned above. However, these faults are also real evdences of hstorcal sesmcty, even though there mght not be any earthquakes wth n the short tme span. So, one equvalent earthquake wth ts maxmum magntude [23] was assgned at each fault. Then earthquake denstes by usng kernel method are calculated and plotted for hstorcal earthquakes (Fg. 3b) and faults (Fg. 3c). Hgher denstes can be seen where greater earthquakes and bg faults exst. Future earthquake may occur near the fault or near the locaton of past earthquakes, outsde also. There s no certanty where future quakes occur. Thus, to account ths uncertanty, average of both s taken and multpled to Eq. (1) yelds Eq. (8) whch gves mean rate of occurrences at a partcular ste. ν Ns Nr Nm * = y ν ρ M mn = 1 = 1 k = 1 m * [ > y m, r] P[M P Y ][ P R r] ΔmΔr = = (8) Mean rate of exceedances for peak ground acceleratons and varous spectral acceleratons are calculated from fve attenuaton laws. Consderng earthquake occurrences follow Posson s process, acceleratons for three probabltes of exceedances n 50 years were calculated from all attenuaton laws at each ste, and combned together gvng equal weghts. PGA (peak ground acceleraton) and SA (spectral acceleratons) at varous natural perods for 10%

5 458 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake (a) (b) (c) (d) Fg. 3 (a) Hstorcal earthquakes and faults; (b) Denstes from hstorcal earthquakes; (c) Denstes from faults; (d) Combned densty from earthquakes and faults.

6 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake Spectral acceleraton (gal) RT 100 years RT 500 years RT 1000 years Perod (secs) Fg. 4 Probablstc spectra at Kathmandu (rock) Spectral acceleraton (gal) RT 100 years RT 500 years RT 1000 years Perod (secs) Fg. 5 Probablstc spectra at Kathmandu (sol). Table 1 Return perod Acceleraton at rock and sol condton. Rock Peak ground acceleraton (gal) at Average Sol Amplfcaton factor

7 460 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake probabltes of exceedances n 50 years (475 years return perod) for hard sol condton for 5% dampng are calculated and plotted (Fg. 3). Obtaned probablstc spectra for Kathmandu, the cty of Hmalayan regon are shown n Fg Concluson Mean rate of exceedances for peak ground acceleratons and varous spectral acceleratons are calculated from seven attenuaton laws. Consderng earthquake occurrences follow Posson s process, acceleratons for three probabltes of exceedances n 50 years were calculated from all attenuaton laws at each ste, and combned together gvng equal weghts. Peak ground acceleraton for 100, 475 and 975 years are found 298, 554 and 714 gals respectvely. Other values n varous natural perods are plotted as shown n Fgs. 4 and 5. It s the case for hard sol. Kathmandu has very soft sol and ground moton can be easly amplfed reachng hgher values approxmately (Table 1). Thus, for partcularly at Kathmandu, spectra have been plotted n Fgs. 4 and 5. The values are qute hgh and hgher than prevous estmate [7] also. Thus, the prevous estmate should be revsed to better estmate the sesmc hazard for the purpose of buldng code. References [1] Molnar, P Structures and Tectoncs of Hmalaya: Constrants and Implcaton of Geophyscal Data. Ann. Rev. Earth Planet Sc. I2: [2] Blham, R., and Ambraseys, N. N Apparent Hmlayan Slp Defct from the Summaton of Sesmc Moments for Hmalayan Earthquakes. Current Scence 88 (10): [3] Blham, R., Gaur, V. K., and Molnar, P Hmalayan Sesmc Hazard. Scence 293: [4] USGS. /epc/epc_rect. [5] Ambraseys, N. N., and Jackson, D A Note on Early Earthquakes n Northern Inda and Southern Tbet. Current Scence 84 (4): [6] Pant, M. R A Step towards Hstorcal Sesmcty of Nepal. Fransco-Nepal Conference on People, Envronment and Landscape of Hmalayas, Nepal. [7] BECA World Internatonal (New Zealand) n assocaton wth SILT Consultants (P.) Ltd. (Nepal), TAEC Consult (P.) Ltd. (Nepal), Golder Assocates (Canada) and Urban Regonal Research (USA) Sesmc Hazard Mappng and Rsk Assessment for Nepal. [8] Ambraseys, N. N., and Douglas, J Magntude Calbraton of North Indan Earthquakes. Geophyscs. J. Int. 159: [9] Hank, T. C., and Kanamor, H A Moment Magntude Scale. Journal of Geophyscs Res. 84: [10] McGure, R. K Sesmc Hazard and Rsk Analyss. Earthquake Engneerng Research Insttute, MNO-10. [11] Stepp, J Analyss of Completeness of the Earthquake Sample n the Pudet Sound Area and Its Effect on Statstcal Estmates of Earthquake Hazard. Proceedngs of the Frst Mcrozonaton Conference, [12] Crouse, C. B Ground-Moton Attenuaton Equatons for Earthquakes on the Cascada Subducton Zone. Earthquake Spectra 7 (2): [13] Fukushma, Y., and Tanaka, T A New Attenuaton Relaton for Peak Horzontal Acceleraton of Strong Earthquake Ground Moton n Japan. Bulletn of Sesmologcal Socety of Amerca 80 (4): [14] Molas, G. L., and Yamazak, F Attenuaton of Earthquake Ground Moton n Japan Includng Deep Focus Events. Bull. Sesmol. Soc. Am. 85: [15] Youngs, R. R., Chou, S. J., Slva, W. J., and Humhrey, J. R Strong Ground Moton Attenuaton Relatonshps for Subducton Zone Earthquakes. Sesmologcal Research Letters 68 (1): [16] Gregor, N. J., Slva, W. J., Wong, I. G., and Youngs, R. R Ground-Moton Attenuaton Relatonshps for Cascada Subducton Zone. Bull. Sesmol. Soc. Am. 92 (5): [17] Atknson, G. M., and Boore, D. M Emprcal Ground-Moton Relatons for Subducton-Zone Earthquakes and Ther Applcaton to Cascada and Other Regons. Bull. Sesmol. Soc. Am. 93 (4): [18] Atknson, G. M., and Boore, D. M Erratum to Emprcal Ground-Moton Relatons for Subducton-Zone Earthquakes and Ther Applcaton to Cascada and Other Regons. Bull. Sesmol. Soc. Am. 98 (5): [19] Kanno, T., Narta, A., Morkawa, N., Fuwara H., and Fukushma, Y A New Attenuaton Relaton for Strong Ground Moton n Japan Based on Recorded Data. Bull. Sesmol. Soc. Am. 96 (3): [20] Zhao, J. X., Zhang, J., Asano, A., Ohno, Y., Oouch, Y., Takahash, T., Ogawa, H., Irkura, K., Thno, H. K.,

8 Updatng Probablstc Sesmc Intensty at Kathmandu after 2015 Gorkha Earthquake 461 Somervlle, P. G., Fukushma, Y., and Fukushma, Y Attenuaton Relatons of Strong Ground Motons n Japan Usng Ste Classfcaton Based upon Predomnant Perod. Bull. Sesmol. Soc. Am. 96 (3): [21] Woo, W Kernel Estmaton Methods for Sesmc Hazard Area Source Modelng. Bull. Sesmol. Soc. Am. 86 (2): [22] Chen, Y., Lu, J., Chen, L., Chen, Q., and Chan, L. S Global Sesmc Hazard Assessment Based on Area Source Model and Sesmcty Data. Natural Hazards, Kluwer Academc Publshers 17: [23] Wells, D. L., and Copersmth, K. J New Emprcal Relatonshps among Magntude, Rupture Length, Rupture Wdth, Rupture Area, and Surface Dsplacement. Bull. Sesmol. Soc. Am. 84 (4):