Broadband Strong-Motion Prediction for Future Nankai-Trough Earthquakes Using Statistical Green’S Function Method and Subsequent Building Damage Evaluation

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Article Broadband Strong-Motion Prediction for Future Nankai-Trough Earthquakes Using Statistical Green’s Function Method and Subsequent Building Damage Evaluation

Baoyintu 1, Naren Mandula 2 and Hiroshi Kawase 3,*

1 Transportation Institute, Inner Mongolia University, Inner Mongolia 010070, China; [email protected] 2 College of Geographical Science, Inner Mongolia Normal University, Inner Mongolia 010022, China; [email protected] 3 DPRI, Kyoto University, Kyoto 606-0011, Japan * Correspondence: [email protected]; Tel.: +81-774-38-4052

Featured Application: The proposed method is applicable to the quantitative earthquake disaster impact evaluations in the areas of high seismic risk.

Abstract: We used the Green’s function summation method together with the randomly perturbed asperity sources to sum up broadband statistical Green’s functions of a moderate-size source and predict strong ground motions due to the expected M8.1 to 8.7 Nankai-Trough earthquakes along the southern coast of western Japan. We successfully simulated seismic intensity distributions similar to the past earthquakes and strong ground motions similar to the empirical attenuation relations of peak ground acceleration and velocity. Using these results, we predicted building damage by non-linear response analyses and find that at the regions close to the source, as well as regions with Citation: Baoyintu; Mandula, N.; relatively thick, soft sediments such as the shoreline and alluvium valleys along the rivers, there is a Kawase, H. Broadband possibility of severe damage regardless of the types of buildings. Moreover, the predicted damage Strong-Motion Prediction for Future ratios for buildings built before 1981 are much higher than those built after because of the significant Nankai-Trough Earthquakes Using code modifications in 1981. We also find that the damage ratio is highest for steel buildings, followed Statistical Green’s Function Method by wooden houses, and then reinforced concrete buildings. and Subsequent Building Damage Evaluation. Appl. Sci. 2021, 11, 7041. https://doi.org/10.3390/app11157041 Keywords: strong motion; Green’s function summation; asperity; ground motion modeling; damage prediction; subduction-zone earthquake; Nankai-Trough Academic Editor: Guido Ventura

Received: 29 June 2021 Accepted: 26 July 2021 1. Introduction Published: 30 July 2021 Off the Pacific coast of Tohoku, Japan, an earthquake of Mw 9.0 struck at 2:46 p.m., 11 March 2011, in the large regions of northeastern Japan. The ruptured area of this mega- Publisher’s Note: MDPI stays neutral thrust earthquake spanned a wide region from offshore Sanriku to offshore Ibaraki areas of with regard to jurisdictional claims in the Pacific coast of Japan. More than 22,000 people were killed or missing, primarily due to published maps and institutional affil- the tsunami, and devastating damage was incurred, particularly along the Pacific coast of iations. Tohoku. Although such massive M9-class earthquakes are expected to occur very infre- quently, typical M8-class subduction-zone earthquakes have a relatively high probability of happening and still, a wide region in the order of a few hundred kilometers will be affected. In addition to the direct damage, such as casualties and building damage from strong Copyright: © 2021 by the authors. ground motions, landslides, liquefaction, subsidence, and tsunami, there is secondary Licensee MDPI, Basel, Switzerland. damage including fires, damage to industrial facilities, and disruption of transportation. As This article is an open access article a result, the economy will be affected at the national level. The hypocenters are distributed distributed under the terms and along the Pacific coast of the Japanese islands, and taking earthquake disaster prevention conditions of the Creative Commons measures suitable for each region is considered an urgent task all over Japan. Attribution (CC BY) license (https:// The possibility that a mega-thrust earthquake of a separated segment at the Tokai, creativecommons.org/licenses/by/ Tonankai, or Nankai region along the Nankai Trough will happen within the next 30 years 4.0/).

Appl. Sci. 2021, 11, 7041. https://doi.org/10.3390/app11157041 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 7041 2 of 24

is estimated to be around 70~80% [1]. If one happens, severe damage by strong shaking and the subsequent tsunami is anticipated over a wide area, especially at the Pacific coast from the Tokai to Kyushu regions near the subducting Philippine Sea plate. To consider effective countermeasures, damage prediction that considers strong-motion characteristics and their building response is necessary to quantitatively evaluate the impact of the building damage from hypothesized earthquake scenarios that could happen in the future. There are still many old buildings that do not have sufficient earthquake resistance capacities in Japan. Grasping earthquake resistance performance of these actual buildings to predict damage is very important. Rigorous investigations after the 1995 Hyogo-ken Nanbu earthquake made damage prediction with considerable accuracy possible (e.g., Nagato and Kawase [2–4], Matsushima and Kawase [5,6]). However, several issues remain when predicting strong ground motions of subduction-zone earthquakes; for example, how to express the complex rupture process that can contribute various characteristics of strong ground motions in a wide frequency range. Moreover, the extremely important component to evaluate total damage using a quantitative damage prediction model of structures, rather than the conventional vulnerability function approach [7], and take damage mitigation measures based on the structural-type dependent evaluation is currently far from quantitative. For strong motion prediction, various methods have been developed toward a more quantitative prediction for a wider range of frequencies. As a gross categorization, we have theoretical methods, semi-empirical methods, and empirical methods. The accuracy of the theoretical methods depends on the accuracy of the velocity model used, which may need significant efforts to predict ground motions in a broadband frequency range [8,9]. The accuracy of the empirical method, such as the ground motion prediction equation (GMPE) [10,11], depends on the density of the observed data that constrain empirical relationships. Because of the infrequent occurrence of mega-thrust events, the density of observed data with large magnitude is far from ideal. In this regard, the semi-empirical method where moderate-sized earthquake ground motions are used as empirical Green’s functions and the summation with space and time are performed to predict strong motions from a mega-thrust event would be the best, for its broadband characteristics are based on the observed ground motions and the abundance of observed data to choose from [12–16]. Therefore, we follow them with different representations of the statistical Green’s function used. First, quantitative prediction of strong ground motions in a wide frequency range is provided based on the Green’s function summation technique using a statistical Green’s function valid from as low as 0.1 Hz up to 20 Hz derived from the observed strong motions in Japan [17]. Subduction-zone mega-thrust earthquakes along the Nankai Trough attract much concern and may lead to a chain rupture to adjacent fault segments (cascade model). Therefore, strong ground motions from hypothesized individual and chain ruptures of the Tokai, Tonankai, and Nankai segments in southwestern Japan are predicted in this paper. The predicted strong ground motions are compared with the seismic intensity distributions of past earthquakes. Their peak values in acceleration and velocity are also compared with empirical predictions from the well-calibrated GMPE [10]. Second, the predicted strong ground motions are used to estimate the damage of building structures using nonlinear response analysis models reflecting the characteristics of the seismic input and building types and their construction ages [2–4]. Finally, the merit of the proposed procedure for building damage prediction is discussed with special reference to the retrofitting policies for earthquake resistance performance of existing buildings based on the findings in this paper.

2. Development of a Statistical Green’s Function To predict strong ground motions over a wide frequency range, Ho and Kawase [17] developed a method to create a statistical Green’s function that is valid in the frequency range from 0.12 to 20 Hz based on the strong motion database in Japan. Their empirical modeling of the dataset based on the generalized inversion technique of Kawase and Matsuo [18] covered the entirety of Japan and investigated 110 earthquakes (with 25 inland Appl. Sci. 2021, 11, 7041 3 of 24

earthquakes, 34 subduction-zone intraplate earthquakes, and 51 subduction-zone interplate earthquakes) between August 1996 and March 2005, where the magnitude M ≥ 5.5, the hypocentral depth ≤ 60 km, the maximum acceleration ≤ 200 cm/s2, and the maximum distance to a hypocenter ≤ 400 km. Crustal earthquakes are defined by a hypocentral depth less than 25 km and an inland hypocenter location. Plate-boundary earthquakes have a hypocentral depth of more than 25 km, are low-angle reverse fault according to the fault mechanism solution by Harvard CMT [19] (before 1997) or F-net [20] (after 1997), and the slip direction is along the plate motion. The intraplate earthquakes have a hypocentral depth of more than 25 km and the fault mechanism solution is not a low angle reverse fault as in the interplate earthquakes. The K-NET, KiK-net [21], and Japan Meteorological Agency (JMA) network [22] data observed at 1684 sites for 110 earthquakes were used to separate source, path, and site terms in both spectral and envelope shapes first, and then the convolution scheme for a statistical Green’s function from a specific source valid up to a long period (<8 s) was derived. Using the estimated source, path, and site characteristics to evaluate strong ground motion over the entirety of Japan allows us to generate a quantitative input seismic motion for design or damage evaluation at any strong motion observation sites that considers the earthquake type and regional dependence in the source and path characteristics. Figure1 shows how the entirety of Japan is separated into six regions and where measurement points are located. Regions are determined based on the location distribution of crustal, intraplate, and interplate earthquakes, regional attenuation difference across the volcanic front, and the Itoigawa–Shizuoka Tectonic Line, as in Kawase and Matsuo [18]. Details of the Green’s function construction and its validation exercise, including modeling of time-varying characteristics, can be found in Ho and Kawase [17], so here we only briefly explain the scheme used. First, the logarithm of the observed Fourier spectra Fij as a function of frequency from an event i at a site j can be expressed as

logFij = logSi − nl(i)logXij + ∑ bl(i)kXijk + logGj (1) k

where Si is the source spectrum, nl(i) is the geometrical spreading factor, bl(i)k is the region- specific intrinsic and scattering attenuation, and Gj is the site factor. We use l(i) to describe earthquake types (C: crustal, I: intraplate, and B: plate boundary), while we use k to describe regions with different attenuations (Figure1d). X ij is the hypocentral distance, whereas Xijk is a part of the distance within the k-th region. The statistical characteristics of the Fourier spectra are extracted in the range of 0.12 to 20 Hz, in which the root mean square values of NS and EW components are used to reduce the influence of the radiation characteristics from the source. Fourier spectra were smoothed using a 0.05 Hz Parzen window. Because at least one constraint condition is required for the spectral inversion based on Equation (1), the site coded as YMGH01 of KiK-net is used as the reference observation site, and the amplification factor calculated by the 1D multiple-reflection theory [8] from the inverted ground structure at YMGH01 is given as a constraint. Therefore, the site characteristics of the other sites can be obtained as a ratio relative to this reference. Because we extracted the site amplification factor from the observed spectra at YMGH01 relative to the bottommost layer, whose S-wave velocity (Vs) is more than 3400 m/s, the obtained site characteristics of the other sites are considered to be absolute values from the seismological bedrock. A more complete picture of the delineated spectral characteristics with additional recent events can be found in Nakano et al. [23], where we obtained statistical properties to model the source, path, and site characteristics. In this study, however, we used directly a source spectrum separated from a selected moderate-sized event without using any moment-source spectra regressions in our statistical Green’s function method to predict strong ground motions for mega-thrust earthquakes. Appl. Sci. 2021, 11, 7041 4 of 24

Figure 1. Source locations and mechanisms of (a) crustal earthquakes, (b) plate-boundary earthquakes, and (c) intraplate earthquakes, and (d) positions of observed sites and regions of different attenuations referring to the volcanic front [18].

The time-varying characteristics of seismic motion are characterized by the envelope form and its duration or phase characteristics. In this study, the time-varying characteristics are modeled by the envelope function W(t) of Boore [12] and we identiﬁed its parameters. Boore’s model is speciﬁed by the duration Td, the time to the maximum amplitude Tr, ε the ratio of Tr to Td, and η the ratio of the amplitude at time Td relative to the maximum amplitude. The equation of W(t) is given below.

W(t) = a × tb × exp(−ct) × H(t) (2)

2.7182 b a = (3) ε × Td −ε × ln η b = (4) [1 + ε × (ln ε − 1)] b c = (5) ε × Td H(t) in Equation (2) represents the unit Heaviside step function, and a in Equation (3) is so specified that the maximum value of the function W(t) is 1. First, the observed waveform was selected for 120 s from the onset of S-wave, and a cosine taper of 2 s was applied before and after the extracted part. The maximum value of the observed waveform was normalized to 1, and the section-wise maximum of its absolute amplitude per 1 s was taken and used to fit the envelope to W(t) with the fixed η of 1/20. The fitting target was the entire observation waveform, and the optimal value was searched by varying ε in the 1

Appl. Sci. 2021, 11, 7041 5 of 24

range of 0.05 to 0.95 in every 0.02 increments. Next, the obtained Td and Tr were regressed on the magnitude M and the hypocentral distance X. In order to eliminate the possibility of a mutual trade-off between M and X, a two-step regression analysis method was used. As an example of the modeling of the time-varying characteristics, Figure2 shows the relationship between Tr (or Td) and magnitude M or the distance X, as well as an example of the statistical envelope identiﬁed for a speciﬁc observed record. The resultant Tr and Td are shown in Equations (6) and (7).

logTr = 0.0943 × M + 0.5109 × logX − 1.0396 (6) Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 27 logTd = 0.0884 × M + 0.6868 × logX − 0.7946 (7)

Figure 2. Statistical time-varying characteristics from observed data; (a) relationship between Tr versus magnitude, (b) Td Figure 2. Statistical time-varying characteristics from observed data; (a) relationship between Tr versus magnitude, (b) Td versus magnitude, (c) Tr versus hypocentral distance, and (d) Td versus hypocentral distance. We also show (e) an exam- versus magnitude, (c) Tr versus hypocentral distance, and (d) Td versus hypocentral distance. We also show (e) an ple of the comparison of the statistical envelope derived from the regression relationship and the observed acceleration exampleamplitude of characteristics the comparison normalized of the statistical by PGA. envelope derived from the regression relationship and the observed acceleration amplitude characteristics normalized by PGA. 3. Strong Ground Motion Prediction of the Nankai-Trough Earthquake 3. Strong Ground Motion Prediction of the Nankai-Trough Earthquake 3.1. Modeling of the Seismogenic Fault and Analyzed Points 3.1. Modeling of the Seismogenic Fault and Analyzed Points The source model of the hypothesized Tonankai earthquake that we used in this ar- The source model of the hypothesized Tonankai earthquake that we used in this ticle is a non-uniform kinematic source model consisting of three large asperities and a article is a non-uniform kinematic source model consisting of three large asperities and a background region. This This conforms with the mo modeldel proposed for the estimation of strong motions by the Headquarters Headquarters for Earthquake Earthquake Research Promotion (H (HERP)ERP) where Irikura’s recipe [[24]24] isis employed employed for for a standardized a standardiz settinged setting procedure procedure regarding regarding macroscopic macroscopic (outer) (outer)and microscopic and microscopic (inner) (inner) fault parameters. fault parameters. We also We refer also torefer the to model the model by Kawabe by Kawabe and

andKamae Kamae [25] for[25] thefor Nankaithe Nankai earthquake. earthquake. The so-calledThe so-called asperity asperity (or SMGA) (or SMGA) model model assumes as- sumesthat there that is there a non-uniform is a non-uniform slip distribution slip distribu ontion the on fault the fault surface, surface, where where the relative the relative slip slipamount amount is twice is twice as muchas much as theas the average average slip slip as as Somerville Somerville et et al. al. (1999) (1999) foundfound fromfrom the kinematic source inversions [26]. [26]. Here, Here, 22% 22% of of the the entire entire fault fault area area is considered to be asperities. As As shown shown in in Ho Ho and and Kawase [17], [17], however, we found that if we consider only a couple of smooth asperities for a mega-thrust event, their sizes seem to be too large to radiate sufficient sufﬁcient energy in the intermediate frequency range around 1 Hz. Therefore, we furtherfurther divide the asperities into small square sections where we assign slip ﬂuctuationsfluctuations with the amount of slip 1.5 times of the average asperity slip (parts denoted with ■ symbols) and the remaining areas should have slips less than the average. The earthquake moment is always conserved. The target analyzed points are K-NET, KiK-net, and JMA sites within 400 km of the assumed fault area of the Tonankai earthquake and are mostly in the Kinki and Chubu regions. Figure 3 shows the positions of asperities, together with the higher slip elements (■), in the three-segment seismogenic fault of the hypothesized Tonankai earthquake, the center of the background region (*), and the assumed rupture starting point (★). The target analyzed sites are shown as circles. Table 1 shows the major fault parameters of this Tonankai earthquake. The aforementioned statistical Green’s functions are used together with the waveform summation method by Irikura [13] to predict strong ground motions of the hypothesized Tonankai earthquake over a wide region in western Japan. As we show later, the estimated seismic intensity of the past earthquakes Appl. Sci. 2021, 11, 7041 6 of 24

with the amount of slip 1.5 times of the average asperity slip (parts denoted with symbols) and the remaining areas should have slips less than the average. The earthquake moment is always conserved. The target analyzed points are K-NET, KiK-net, and JMA sites within 400 km of the assumed fault area of the Tonankai earthquake and are mostly in the Kinki and Chubu regions. Figure3 shows the positions of asperities, together with the higher slip elements (), in the three-segment seismogenic fault of the hypothesized Tonankai earthquake, the center of the background region (*), and the assumed rupture starting point (F). The target analyzed sites are shown as circles. Table1 shows the major fault parameters of this Tonankai earthquake. The aforementioned statistical Green’s functions Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 27 are used together with the waveform summation method by Irikura [13] to predict strong ground motions of the hypothesized Tonankai earthquake over a wide region in western Japan. As we show later, the estimated seismic intensity of the past earthquakes that repeatedlythat repeatedly happen happen at the at Nankai the Nankai Trough Trough (e.g., 1854(e.g., Tokai1854 Tokai earthquake earthquake and 1944 and Tonankai 1944 To- earthquake)nankai earthquake) was reproduced. was reproduced. At the At same the time,same predictedtime, predicted waveforms waveforms correspond correspond well withwell thewith empirical the empirical attenuation attenuation function function [10] frequently [10] frequently referred referred to in Japan.to in Japan.

■ FigureFigure 3.3. LocationLocation of of asperities, asperities, with with higher higher slip slip elements elements ( ),( the), the center center of theof the background background region region (*), (*), and the rupture starting point (★ ) of the seismogenic fault of the hypothesized Tonankai earth- and the rupture starting point (F) of the seismogenic fault of the hypothesized Tonankai earthquake. quake.

Table 1. Major fault parameters of the hypothesized Tonankai earthquake. Table 1. Major fault parameters of the hypothesized Tonankai earthquake.

MagnitudeMagnitude M M 8.1 8.1 TotalTotal areaarea (km (km2)2) 14,04014,040 SeismicSeismic moment (N (N m) m) 2.119 2.119× ×10 102121 AverageAverage static stressstress drop drop (MPa) (MPa) 3.0 3.0 RuptureRupture speedspeed (km/s) (km/s) 2.7 2.7 Strike, dip, and rake (degree) 250.7/14.0/122.7 Strike, dip, and rake (degree) 250.7/14.0/122.7 Slip in asperities (left/center/right, cm) 601/850/601 Slip in asperities (left/center/right, cm) 601/850/601 Slip in background (cm) 299 Slip in background (cm) 299 3.2. Waveform Summation Scheme 3.2. WaveformThe strong Summation ground motion Scheme waveform of the hypothesized Tonankai earthquake was synthesizedThe strong using ground the motionestimated waveform subduction of the-zone hypothesized earthquake Tonankai elementary earthquake source wasand synthesizedpropagation using characteristics, the estimated site subduction-zone characteristics earthquakeof each target elementary site, and source the andempirical prop- agationGreen’s characteristics,function summation site characteristics method by ofIrik eachura target[13]. The site, empirica and thel empirical Green’s Green’sfunction functionmethod is summation a waveform method synthesis by Irikuramethod [ 13that]. Theconsiders empirical the difference Green’s function in the seismic method mo- is ament waveform and stress synthesis drop between method thatlarge considers and small the earthquakes difference inaccording the seismic to the moment ω−2 scaling and law, which is shown in Equation (8). () NN() ( ) U t = r rij× F(t)* C u ij (t) i=1 j=1 (N-1)n′ F() t =δ() t-t +() 1 n′′ δ{} t-t - ()() k-1 T N-1 n (8) ij  ij k=1

tij =() r ij -r oV+ξ s ij V r

stress drop between large and small earthquakes according to the ω−2 scaling law, which is shown in Equation (8).

N N ∗ U(t) = ∑ ∑ r/rij ×F(t) C uij(t) i=1 j=1 (N−1)n0 0 0 (8) F(t)= δ t − tij + (1/n ) ∑ δ t − tij − (k − 1)T/(N − 1)n = k 1 tij = rij−ro /Vs + ξij/Vr

Here, U(t) is the mainshock waveform, u(t) is the elementary source waveform with a small moment, N is the ratio of the fault plane dimension (i.e., the length and width) between large and small earthquakes, C is the stress drop ratio, and * indicates convolution. F(t) is a correction function expressing the difference in slip time function between large and small earthquakes, δ(t) is Dirac’s delta function, and T is the rise time of a large earthquake. Further, Vs is the S-wave velocity, Vr is the rupture velocity, r is the assumed hypocentral distance between the representative elementary source and the target site, r0 is the distance between the rupture initiation point and the site, rij is the distance between each elementary source at (i,j) on the fault plane of a large earthquake and the target site, and ξij is the distance between the rupture initiation point and the elementary source, n’ is an arbitrary integer to avoid effects of artifact frequency components from constant superposition. Regarding the correction function F(t), Miyake et al. [27] used a revised equation as Equation (9) to avoid the dip in the amplitude spectrum of the synthesized waveform, which is adopted here:

0 F(t) = δ t − tij + {1/n (1 − exp(−1))} (N−1)n0 0 0 (9) × ∑ exp{−(k − 1)/(N − 1)n }×δ t − tij − (k − 1)T/(N − 1)n k=1

The stress drop is estimated from the relation between the seismic moment M0 and corner frequency f0 as Equation (10), where β is the S-wave velocity of the seismogenic zone. The numbers of superposition of the elementary sources N and C are derived from Equations (11) and (12) as proposed in [13], where the subscript e refers to the values of the elementary sources. f 3 ∆σ = o M (10) 4.9 × 106β 0

M 1/3 N = 0 (11) C × Moe ∆σ C = o (12) ∆σoe

3.3. Waveform Synthesis and Its Validation A statistical Green’s function was generated using the source, path, and site characteristics for each target site, as estimated in Section2. Strong ground motion waveforms of the hypothesized Tonankai earthquake (Figure3), a hypothesized Tokai earthquake, and a hypothesized Nankai earthquake were generated by the summation method of Irikura [13]. Then, a hypothesized consecutive rupture scenario of all the three segments (Tokai, Tonankai, and Nankai) along the Nankai Trough were evaluated by adding these three earthquake waveforms with proper time differences. Figure4 shows a comparison between the peak ground acceleration (PGA) or peak ground velocity (PGV) calculated in this work for the hypothesized Tonankai earthquake and the attenuation relation (ground motion prediction equation, GMPE) by Si and Mi- dorikawa [10]. The synthetic PGAs from the Green’s function summation method agree quite well with the attenuation relation. The synthetic PGVs also correspond well to the Appl. Sci. 2021, 11, 7041 8 of 24

GMPE; however, we need to consider the difference in the assumed average velocity for site ampliﬁcation. When we plot the velocity GMPE by Si and Midorikawa [10], we assume that the average S-wave velocity in the top 30 m (Vs30) to be 600 m/s, whereas the overall average Vs30 of K-NET and KiK-net is around 400 m/s. A comparison of the PGV of the elementary source and the velocity GMPE for the same magnitude shows that the synthetic values are underestimated to the same extent as shown in Figure4, and thus the PGV of Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 27 the elementary source based on the assumed source spectrum is conﬁrmed to be slightly smaller than the average of previously observed events.

FigureFigure 4.4. PeakPeak groundground acceleration acceleration and and velocity velocity from from a hypothesizeda hypothesized Tonankai Tonankai earthquake earthquake by by the the statistical statistical Green’s Green’s function func- summationtion summation method method of this of this study study (symbols) (symbols) and and by theby the GMPE GMPE of of Si Si and and Midorikawa Midorikawa [10 [10]] as as a a function function of of the the shortestshortest distancedistance toto thethe fault.fault.

OneOne issueissue thatthat wewe shouldshould considerconsider isis thatthat thethe time-varyingtime-varying characteristics are deter- minedmined fromfrom thethe accelerationacceleration envelopeenvelope whenwhen generatinggenerating ourour statisticalstatistical Green’sGreen’s function,function, thusthus thethe envelopeenvelope isis mostlymostly governedgoverned byby short-periodshort-period componentscomponents soso thatthat PGVPGV wouldwould notnot bebe directlydirectly regulated.regulated. Therefore,Therefore, data data should should be be added added in in the the future future to to increase increase the the stability stabil- ofity separation of separation properties properties and and improve improve modeling modeling of long-period of long-period phase phase characteristics characteristics that maythat may govern govern PGV. PGV. Note Note that thethat maximum the maximum magnitude magnitude in the indatabase the database used used to derive to derive the empiricalthe empirical attenuation attenuation relation relation in Si andin Si Midorikawa and Midorikawa [10] was [10] 8.0, was and 8.0, thus and the thus comparison the com- shownparison here shown is a here small is extrapolation. a small extrapolation. FigureFigure5 5 shows shows a a comparison comparison of of seismic seismic intensity intensity scale scale according according to to the the converted converted seismicseismic intensityintensity fromfrom the the synthesized synthesized strong strong ground ground motions motions of of the the hypothesized hypothesized Tonankai Tonan- earthquakekai earthquake in this in studythis study and the and contour the contou map fromr map the from damage the damage survey of survey the 1944 of Tonankai the 1944 earthquakeTonankai earthquake according according to the publicly to the available publicly available information information from HERP from [28 HERP]. The [28]. seismic The intensityseismic intensity scale of scale VI lower of VI andlower VI and upper VI upper in red in circles red circles in this in study this study corresponds corresponds to the to maximumthe maximum rank rank of VIof lowerVI lower equivalent equivalent or or higher higher in in HERP, HERP, also also marked marked in in red. red. TheThe seismicseismic intensity scale of of V V in in orange orange circles circles also also corresponds corresponds to to the the same same class class marked marked in inyellow. yellow. The The strong strong ground ground motion motion of the of hypo the hypothesizedthesized Tonankai Tonankai earthquake earthquake in this in work this workdoes not does consider not consider a saturation a saturation phenomenon phenomenon near the near fault the and fault non-linearity and non-linearity of the under- of the undergroundground structure. structure. As described As described in the figures in the ﬁgures by HERP, by HERP,there is there uncertainty is uncertainty in the source in the sourcecharacteristics characteristics and some and somefluctuation ﬂuctuation of the of designated the designated underground underground structure structure within within the thesame same municipality municipality is inevitable. is inevitable. The The overall overall seismic seismic intensity intensity scale scale distributions distributions of thesethese twotwo resultsresults matchmatch well,well, asas seismicseismic intensityintensity maymay easilyeasily changechange byby oneone betweenbetween thesethese twotwo resultsresults forfor thethe reasonsreasons mentionedmentioned above.above. PleasePlease notenote thatthat thethe convertedconverted seismicseismic intensityintensity waswas calculated as as shown shown in in [22,29], [22,29 ],whereas whereas the the intensity intensity estimated estimated from from the thedamage damage sur- surveyvey was was based based on onthe the table table by byJMA JMA [30]. [30 ]. Appl. Sci. 2021, 11, 7041 9 of 24 Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 27

Figure 5. A comparison of the seismic intensity scale distribution of strong ground motions calcu- Figurelated from 5. A comparisonthe hypothesized of the Tonankai seismic intensity earthquake scale in distributionthis study (top) of strong and that ground of the motions estimated calculated ones fromfrom the the hypothesized damage survey Tonankai of the 1944 earthquake Tonankai in earthquake this study according (top) and to that HERP of the (bottom). estimated ones from the damage survey of the 1944 Tonankai earthquake according to HERP (bottom). Although it is difficult to consider nowadays to have an independent rupture at the TokaiAlthough segment itbefore is difficult the Tonankai to consider and Nankai nowadays earthquakes, to have the an Tokai independent segment had rupture been at theconsidered Tokai segment to rupture before as an the independent Tonankai and Toka Nankaii earthquake earthquakes, within the the foreseeable Tokai segment future had beenin the considered 1970s based to on rupture the slip as deficit an independent in the segment Tokai (e.g., earthquake Ishibashi, 1981 within [31]). the Therefore, foreseeable futurethe Central in the Disaster 1970s based Management on the slipCouncil deficit (CDMC), in the Cabinet segment Office (e.g., of Ishibashi, Japan, had 1981 been [31 ]). Therefore,evaluating the strong Central ground Disaster motions Management based on the Council hypothesized (CDMC), Tokai Cabinet earthquake Office as ofan Japan,in- haddependent been evaluating event until strong recently. ground We motions adopted based the onfault the rupture hypothesized scenario Tokai proposed earthquake by asCDMC an independent [32] and used event the until same recently. method Weas th adoptede Tonankai the earthquake fault rupture described scenario above proposed to bycalculate CDMC strong-motion [32] and used waveforms. the same method Figure 6 as shows the Tonankai a comparison earthquake of the synthetic described PGAs above toor calculate PGVs calculated strong-motion for the hypothesized waveforms. Toka Figurei earthquake6 shows awith comparison GMPE by of Si and the Midori- synthetic PGAskawa or[10] PGVs as in calculatedFigure 4. Furthermore, for the hypothesized Figure 7 shows Tokai a earthquake comparison withof seismic GMPE intensity by Si and Midorikawascales estimated [10] from as in the Figure synthetic4. Furthermore, strong ground Figure motions7 shows of the a comparisonTokai earthquake of seismic and intensitythe estimated scales seismic estimated intensity from thescale synthetic of the 18 strong54 Tokai ground earthquake motions (stars), of the which Tokai ruptured earthquake andmuch the larger estimated areas including seismic intensity (but not limited scale of to) the the 1854 Tokai Tokai segment. earthquake Again, correspond- (stars), which rupturedence of the much synthetic larger strong areas motions including with (butthe empirical not limited prediction to) the by Tokai GMPE segment. as well as Again,the correspondenceintensity estimated of the for synthetic the previous strong earthquake motions is with fairly the good. empirical prediction by GMPE as well as the intensity estimated for the previous earthquake is fairly good. Appl. Sci. 2021, 11, 7041 10 of 24 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 27

Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 27

Figure 6. Peak ground acceleration and velocity from a hypothesized Tokai earthquake by the statistical Green’s function Figure 6. Peak ground acceleration and velocity from a hypothesized Tokai earthquake by the statistical Green’s function summation method of this study (symbols)(symbols) and by the GMPE of Si and Midorikawa [[10]10] as aa functionfunction ofof thethe shortestshortest distancesummation to the method fault. of this study (symbols) and by the GMPE of Si and Midorikawa [10] as a function of the shortest distancedistance to theto the fault. fault.

Figure 7. A comparison of the seismic intensity scale distribution of strong ground motions calcu- Figure 7. A comparison of the seismic intensity scale distribution of strong ground motions calculated Figurelated from7. A thecomparison hypothesized of the Tokai seismic earthquake intensity in thscaleis study distribution (top) and of that strong of the ground estimated motions ones ( calcu-★) from the hypothesized Tokai earthquake in this study (top) and that of the estimated ones ( ) from the latedfrom from the damage the hypothesized survey of the Tokai 1854 earthquake Ansei Tokai in earthquake this study (bottom).(top) and Squares that of thein the estimated bottomF panelones ( ★) fromdamageindicate thesurvey damagethe same of survey theresults 1854 asof Ansei inthe Figure 1854 Tokai 5Ansei (bottom), earthquake Tokai based earthquake (bottom). on the numerical Squares (bottom). in calculation theSquares bottom in for panelthe the bottom Tonankai indicate panel the indicatesameearthquake results the same asaccording in results Figure to 5as HERP (bottom), in Figure and basedso 5 (bottom),we onshould the based numericalnot refer on the to calculation themnumerical for the for calculation Tokai the Tonankai earthquake for the earthquake Tonankai simu- earthquakeaccordinglation. Please to according HERP note that and to the soHERP wemap should andscales so are not we different. refershould to themnot refer for theto them Tokai for earthquake the Tokai simulation.earthquake Pleasesimu- lation.note that Please the mapnote scalesthat the are map different. scales are different. Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 27

Appl. Sci. 2021, 11, 7041 11 of 24

The strong ground motions of the hypothesized Nankai earthquakes had been pre- Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 27 dicted by Ho and Kawase [17] in which they used the same statistical Green’s function and summationThe strong method ground shown motions in of the the previous hypothesized section. Nankai Figure earthquakes8 shows the fault had beenmodel pre- of Hodicted and by Kawase Ho and [17] Kawase and Figure [17] in 9 whichshows theythe comparison used the same of the statistical synthetic Green’s PGAs functionor PGVs and summationThe strong ground method motions shown of the in hypoth the previousesized Nankai section. earthquakes Figure had8 shows been pre- the fault model of calculateddicted by Ho for and the Kawase hypothesized [17] in which Nankai they used eart thehquake same statistical with GMPEGreen’s functionby Si and Midorikawa Ho and Kawase [17] and Figure9 shows the comparison of the synthetic PGAs or PGVs [10]and reproduced summation method from shown Ho and in the Kawase previous [17]. section. Figure 8 shows the fault model of calculatedHo and Kawase for the[17] hypothesizedand Figure 9 shows Nankai the comparison earthquake of the with synthetic GMPE PGAs by or Si PGVs and Midorikawa [10] reproducedcalculated for fromthe hypothesized Ho and Kawase Nankai [earthquake17]. with GMPE by Si and Midorikawa [10] reproduced from Ho and Kawase [17].

Figure 8. Location of asperities, large slip segments (■ ), and the rupture starting point (★ ) of the Figure 8. Location of asperities, large slip segments ( ), and the rupture starting point ( ) of the Figureseismogenic 8. Location fault of the of hypothesized asperities, Nankailarge slipearthquake segments used by(■ Ho), and Kawase the rupture [17]. starting point (★F) of the seismogenicseismogenic fault fault of of the hypothesized Nankai earthquake used by Ho and Kawase [[17].17].

Figure 9. Peak ground acceleration and velocity from a hypothesized Nankai earthquake by the statistical Green’s function summation method of Ho and Kawase [17] (symbols) and by the GMPE of Si and Midorikawa [10] as a function of the shortest distance to the fault.

Finally, we considered here a consecutive rupture scenario of all the three segments Figure 9. PeakPeak ground ground acceleration accelerationalong theand and Nankai velocity velocity Trough, from from namea a hypothesized hypothesizedly, Tokai, Tonankai, Nankai Nankai and earthquake Nankai segments, by the statistical statistical as a hypothe- Green’s function sized worst-case scenario. Here, the calculated strong ground motions from each earth- summation method of Ho and Kawase [17] [17] (symbols) and by th thee GMPE of Si and Midorikawa [10] [10] as a function of the shortest distance to the fault. quake were superimposed along with the time history, while considering the delay in the shortest distance to the fault.rupture start time of each segment by assuming the constant rupture velocity of 2.7 km/s between the next rupture initiation point and the closest point of the adjacent segment alreadyFinally,Finally, ruptured. we Figure considered 10 shows here a comparison a consecutive between rupture PGA or PGV scenario calculated of allfor the three segments alongalongwhole theearthquake NankaiNankai scenario Trough,Trough, along namely, name the Nankaily, Tokai, Tokai, Trough Tonankai, Tonankai, and the and GMPEand Nankai Nankai by Si segments, and segments, Midori- as a as hypothesized a hypothe- sizedworst-casekawa worst-case[10]. Figure scenario. 11 scenario. compares Here, the Here, the seismic calculated the in tensitycalculat scales stronged convertedstrong ground ground from motions the synthesizedmotions from from each earthquakeeach earth- waveforms of this study and the seismic intensity distribution from the similar whole quake were superimposed along with the time history, while considering the delay in the wereearthquake superimposed scenario calculated along withby thethe Centra timel Disaster history, Management while considering Council [7]. theThe delaydis- in the rupture rupturestarttribution time start of of the eachtime sites segment estimatedof each segmentto by result assuming in bya seismic assuming the intensity constant the scale constant rupture of VI upper velocity rupture or higher of velocity 2.7 km/s of 2.7 between km/s betweenthein this next study the rupture is next concentrated initiationrupture in initiation coastal point areas and point of the Shikoku, closestand the Kii point Peninsula,closest of point the and adjacent around of the Ise adjacent segment segment already alreadyruptured.Bay, as well ruptured. Figureas the areas 10Figure showswith relatively 10 ashows comparison soft asediments comparison between such asbetween areas PGA with or PGA PGVan alluvial or calculated PGV plain calculated for the for whole the or basin. The results in this study slightly underestimate the CDMC’s estimated seismic wholeearthquake earthquake scenario scenario along thealong Nankai the Nankai Trough Trough and the and GMPE the by GMPE Si and by Midorikawa Si and Midori- [10]. kawaFigure [10]. 11 compares Figure 11 thecompares seismic the intensity seismic scales intensity converted scales from converted the synthesized from the synthesized waveforms waveformsof this study of andthis thestudy seismic and the intensity seismic distribution intensity distribution from the similar from wholethe similar earthquake whole earthquakescenario calculated scenario bycalculated the Central by the Disaster Centra Managementl Disaster Management Council [7]. Council The distribution [7]. The dis- of tributionthe sites estimated of the sites to estimated result in a to seismic result intensity in a seismic scale intensity of VI upper scale or of higher VI upper in this or study higher is inconcentrated this study inis concentrated coastal areas ofin Shikoku,coastal areas Kii Peninsula, of Shikoku, and Kii around Peninsula, Ise Bay, and as around well as theIse Bay,areas as with well relatively as the areas soft with sediments relatively such soft as areas sediments with an such alluvial as areas plain with or basin. an alluvial The results plain orin thisbasin. study The slightly results underestimatein this study slightly the CDMC’s underestimate estimated the seismic CDMC’s intensity estimated distribution seismic in the east coast of Miyazaki Prefecture and slightly overestimate in the Izu Peninsula, but Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 27 Appl. Sci. 2021, 11, 7041 12 of 24

intensity distribution in the east coast of Miyazaki Prefecture and slightly overestimate in the Izu predicted Peninsula, results but almost the predicted match those results of al CDMCmost match at coastal those areas of CDMC near Shikoku at coastal and areas Kii nearPeninsula. Shikoku Please and noteKii Peninsula. that PGAs Please and PGVs note calculated that PGAs by and our PGVs method calculated are slightly by lessour methodthan those are from slightly GMPE less as than shown those in Figurefrom GMPE10. This as is shown because in there Figure would 10. This be only is because a small therecontribution would frombe only different a small segments contribution arriving from at different the same segments instance so arriving that our at PGAs the same and instancePGVs are so very that closeour PGAs to the and highest PGVs values are very among close theto the independent highest values waveforms among the from inde- the pendentthree segments. waveforms On thefrom other the three hand, segments. the assumed On the magnitude, other hand, which the assumed is much larger magnitude, in the whichwhole ruptureis much scenariolarger in than the whole the individual rupture earthquakes,scenario than will the actindividual to increase earthquakes, predicted PGA will actor PGVto increase by GMPE predicted proportionally. PGA or PGV Thus, by the GM differencePE proportionally. in Figure 10 Thus, shows the that difference PGAs and in FigurePGVs based 10 shows on GMPE that PGAs could and be PGVs overestimated based on ifGMPE the whole could rupture be overestimated scenario is if a cascadingthe whole rupture scenario asis a assumed cascading here. rupture scenario as assumed here.

Figure 10. Peak groundground accelerationacceleration andand velocity velocity from from a a hypothesized hypothesized whole whole rupture ruptur scenarioe scenario along along the the Nankai Nankai Trough Trough by superimposingby superimposing three three individual individual earthquakes earthquakes (symbols) (symbols) and and by theby the GMPE GMPE ofSi of and Si and Midorikawa Midorikawa [10 ][10] as a as function a function of the of the shortestAppl. Sci. 2021 distance, 11, x FOR PEERto the REVIEW fault. 14 of 27 shortest distance to the fault.

Figure 11. A comparison of the seismic intensity scale distribution of strong ground motions calcu- Figurelated from 11. the Ahypothesized comparison whole ofrupture the seismicscenario along intensity the Nankai scale Trough distribution in this study (top) of strong ground motions calcu- latedand the from distribution the hypothesizedof the estimated seismic whole intensity rupture by the Cent scenarioral Disaster along Management the Nankai Council Trough in this study (top) and [7] for a similar three-segment model (bottom). the distribution of the estimated seismic intensity by the Central Disaster Management Council [7] for4. Building a similar Damage three-segment Prediction Based model on the (bottom). Calculated Ground Motions 4.1. Motivation The earthquake off the Pacific coast of Tohoku, Japan (Tohoku) of 11 March 2011, of Mw9.0 forced a radical revision of previously hypothesized source characteristics for subduction zone earthquakes along the Pacific coast of Japan. The CDMC doubled or tripled the hypocentral areas and its magnitude of a hypothesized whole rupture scenario along the Nankai Trough in March 2012 and simultaneously made public the estimated seismic intensity distributions and tsunami heights of various sites. Then, in August 2012, the CDMC revised the tsunami height prediction and estimated structural damage and subsequent human casualties [32]. Their estimation suggested a maximum of 320,000 casualties, half of which would be associated with structural damage and subsequent fire. How- ever, this estimation uses an empirical building damage prediction formula (i.e., the so- called vulnerability function) derived primarily from the field survey data during the 1995 Hyogo-ken Nanbu earthquake, which may be leading to an overestimation for the subduction zone earthquake because of the large difference of their frequency content, as evidenced by the observed damage during the 2011 Tohoku earthquake [33]. Therefore, structural damage prediction with much higher precision is necessary which employs a method of using dynamic nonlinear response analysis for the calculated seismic waveform. Such a method can reflect the difference in the input ground motion characteristics Appl. Sci. 2021, 11, 7041 13 of 24

4. Building Damage Prediction Based on the Calculated Ground Motions 4.1. Motivation The earthquake off the Pacific coast of Tohoku, Japan (Tohoku) of 11 March 2011, of Mw9.0 forced a radical revision of previously hypothesized source characteristics for subduction zone earthquakes along the Pacific coast of Japan. The CDMC doubled or tripled the hypocentral areas and its magnitude of a hypothesized whole rupture scenario along the Nankai Trough in March 2012 and simultaneously made public the estimated seismic intensity distributions and tsunami heights of various sites. Then, in August 2012, the CDMC revised the tsunami height prediction and estimated structural damage and subsequent human casualties [32]. Their estimation suggested a maximum of 320,000 casualties, half of which would be associated with structural damage and subsequent fire. However, this estimation uses an empirical building damage prediction formula (i.e., the so-called vulnerability function) derived primarily from the field survey data during the 1995 Hyogo- ken Nanbu earthquake, which may be leading to an overestimation for the subduction zone earthquake because of the large difference of their frequency content, as evidenced by the observed damage during the 2011 Tohoku earthquake [33]. Therefore, structural damage prediction with much higher precision is necessary which employs a method of using dynamic nonlinear response analysis for the calculated seismic waveform. Such a method can reflect the difference in the input ground motion characteristics between crustal and subduction-zone earthquakes. In this section, we used the calculated strong ground motions of the hypothesized (independent) Tonankai earthquake and the whole rupture scenario obtained in the previous section. Nonlinear response analyses based on nonlinear building properties with statistical variabilities [2–4] were carried out to calculate damage ratio distributions that consider characteristics such as the building structure type, height, and the construction age in the epicentral regions of these two large earthquake scenarios along the Nankai Trough in southwestern Japan.

4.2. Method of Damage Prediction The damage prediction method for realistic damage prediction should reflect both the difference of the input motion characteristics and the difference in the seismic capacity of the target category of buildings. Empirical methods represented by the conventional vulnerability function use a strength index for the former and the building types for the latter based on the statistical properties of the observed damage during the past devastating earthquakes [34,35]. The former, such as PGA or PGV, is a crude index to represent the real damaging demand of the input. The latter, such as wooden houses or reinforced concrete (RC) buildings, is also a crude category to differentiate their seismic capacity. The method proposed by Nagato and Kawase [2–4], hereafter referred to as the Nagato–Kawase model, uses multiple structural models in their nonlinear response analyses with the input acceleration waveforms calculated at a target site. By comparing the observed damage ratios from the 1995 Hyogo-ken Nanbu earthquake and the results of the earthquake response analyses from the reproduced strong ground motions in Kobe by Matsushima and Kawase [5], Nagato and Kawase [2–4] successfully constructed a total of 15 nonlinear response models for different structural categories and construction ages, namely, for a two-storied wooden house without age differences, three-, six-, nine-, and twelve-storied RC buildings, as well as three-, four-, and five-storied steel buildings with the construction age considered (before 1981 large code modification and after 1981). The criterion for a wooden house is considered to suffer heavy damage or collapse when the maximum inter-story deformation angle exceeds 1/10 rad, whereas those for RC and steel structures are defined as the maximum inter-story deformation angle being more than 1/30 rad. In the actual calculation of the damage ratio from a single waveform at a site, we utilized 12 sub-models for each category to represent the statistical variation of the building capacities in Japan, without which we cannot reproduce statistical properties of the observed damage distribution. Figure 12 shows an example of the log-normal distribution for RC buildings. Figure 13 shows an example of the comparison of the reproduced and Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 27

between crustal and subduction-zone earthquakes. In this section, we used the calculated strong ground motions of the hypothesized (independent) Tonankai earthquake and the whole rupture scenario obtained in the previous section. Nonlinear response analyses based on nonlinear building properties with statistical variabilities [2–4] were carried out to calculate damage ratio distributions that consider characteristics such as the building structure type, height, and the construction age in the epicentral regions of these two large earthquake scenarios along the Nankai Trough in southwestern Japan.

4.2. Method of Damage Prediction The damage prediction method for realistic damage prediction should reflect both the difference of the input motion characteristics and the difference in the seismic capacity of the target category of buildings. Empirical methods represented by the conventional vulnerability function use a strength index for the former and the building types for the latter based on the statistical properties of the observed damage during the past devastating earthquakes [34,35]. The former, such as PGA or PGV, is a crude index to represent the real damaging demand of the input. The latter, such as wooden houses or reinforced concrete (RC) buildings, is also a crude category to differentiate their seismic capacity. The method proposed by Nagato and Kawase [2–4], hereafter referred to as the Nagato–Ka- wase model, uses multiple structural models in their nonlinear response analyses with the input acceleration waveforms calculated at a target site. By comparing the observed damage ratios from the 1995 Hyogo-ken Nanbu earthquake and the results of the earthquake response analyses from the reproduced strong ground motions in Kobe by Matsushima and Kawase [5], Nagato and Kawase [2–4] successfully constructed a total of 15 nonlinear response models for different structural categories and construction ages, namely, for a two-storied wooden house without age differences, three-, six-, nine-, and twelve-storied RC buildings, as well as three-, four-, and five-storied steel buildings with the construction age considered (before 1981 large code modification and after 1981). The criterion for a wooden house is considered to suffer heavy damage or collapse when the maximum inter- story deformation angle exceeds 1/10 rad, whereas those for RC and steel structures are defined as the maximum inter-story deformation angle being more than 1/30 rad. In the actual calculation of the damage ratio from a single waveform at a site, we utilized 12 sub- models for each category to represent the statistical variation of the building capacities in Appl. Sci. 2021, 11, 7041 14 of 24 Japan, without which we cannot reproduce statistical properties of the observed damage distribution. Figure 12 shows an example of the log-normal distribution for RC buildings. Figure 13 shows an example of the comparison of the reproduced and observed damage ratioobserved distributions damage ratiofor wooden distributions houses for in wooden the Higashinada houses in Ward the Higashinada during the Ward1995 Hyogo- during kenthe 1995Nanbu Hyogo-ken earthquake, Nanbu calculated earthquake, by Nagato calculated and Kawase by Nagato [4]. and Kawase [4].

Figure 12. An example of the degrading trilinear models used for RC buildings based on the current building standard in Appl. Sci.JapanJapan 2021 ((left,left 11,) )x and andFOR the thePEER log-normal log-normal REVIEW distribution distribution of of existing existing ratios ratios with with different different yield yield capacity capacity ratios ratios for for RC RC buildings buildings based based on16 of 27

theon the ﬁeld field survey survey by Shibataby Shibata [36 ]([36]right (right). ).

Figure 13. AA comparison comparison of of the the reproduced reproduced ( leftleft)) and and observed observed ( (rightright)) damage damage ratio ratio (heavy (heavy or or hi higher)gher) distributions distributions during the Hyogo-ken Nanbu earthquake of wooden houses [[4].4].

4.3.4.3. Results Results of of Building Building Damage Damage Predictions Predictions WhenWhen we predicted building damage dist distributionsributions based on the synthetic ground motionsmotions in in the the previous section, we restricted the calculation of the damage ratios to the K-NET,K-NET, KiK-net, and JMA strong motion networ networkk sites within 400 km of the assumed fault surfacesurface with the PGA higher than 200200 cm/scm/s22. .The The threshold threshold in in PGA PGA was was primarily primarily based onon our our experience that that showed that heavy damage or higher does not occur in almost all buildingsbuildings when the maximum acceleration isis 200200 cm/scm/s22 oror less. less. The The damage distribution figuresfigures in thisthis sectionsection onward onward distinguish distinguish sites sites where where no no calculation calculation was was conducted conducted because be- causethe input the seismicinput seismic motion motion is less thanis less 200 than cm/s 2002 usingcm/s2 using black (solid)black (solid) circles circles and sites and where sites wherethe damage the damage calculation calculation was conducted was conducted but no but damage no damage was estimated was estimated using whiteusing (open)white (open)circles. circles. Hereafter, Hereafter, we show we the show building the build damageing estimationdamage estimation of the hypothesized of the hypothesized Tonankai Tonankaiearthquake earthquake and the whole and th rupturee whole scenario rupture along scenario the Nankaialong the Trough. Nankai Trough. FiguresFigures 14–1714–17 show the damage ratio distributions based on the Nagato–Kawase modelmodel from from the the strong strong ground ground motion motion of of a a hy hypothesizedpothesized Tonankai Tonankai earthquake for wooden houseshouses W02 W02 (Figure (Figure 14,14, together together with with the the esti estimatedmated seismic seismic intensity intensity distribution), distribution), three- three- andand five-storied five-storied steel steel structures, structures, S03 S03 and and S05 S05 (Figure (Figure 15),15), three- three- and and six-storied six-storied RC RC struc- struc- tures,tures, R03 R03 and and R06 R06 (Figure (Figure 16),16), and nine- and twelve-storied RC structures, R09 and R12 (Figure(Figure 17).17). The The old old (pre-1981) (pre-1981) and and new new (post-1981) (post-1981) building building standard standard for for seismic seismic perfor- perfor- mancemance is distinguished exceptexcept forfor wooden wooden houses. houses. Figure Figure 18 18 shows shows simple simple average average damage dam- ageratios ratios at all at the all sitesthe sites where where the damage the damage ratios ra aretios calculated are calculated for different for different structural structural types, types,the number the number of stories, of stories, and construction and construction ages. ages. From From these these figures figures it is it apparent is apparent that that the theold old buildings buildings built built before before 1981 1981 have have higher higher damage damage ratios ratios than than new new buildings buildings built built after after 1981, low-rise steel structures have the highest damage ratios in lower stories, and old nine-storied RC buildings have highest damage ratio among RC structures. Based on the structural type, the damage ratio is highest in steel structures, followed by wooden houses, and then RC structures.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 27

Figure 13. A comparison of the reproduced (left) and observed (right) damage ratio (heavy or higher) distributions during the Hyogo-ken Nanbu earthquake of wooden houses [4].

4.3. Results of Building Damage Predictions When we predicted building damage distributions based on the synthetic ground motions in the previous section, we restricted the calculation of the damage ratios to the K-NET, KiK-net, and JMA strong motion network sites within 400 km of the assumed fault surface with the PGA higher than 200 cm/s2. The threshold in PGA was primarily based on our experience that showed that heavy damage or higher does not occur in almost all buildings when the maximum acceleration is 200 cm/s2 or less. The damage distribution figures in this section onward distinguish sites where no calculation was conducted because the input seismic motion is less than 200 cm/s2 using black (solid) circles and sites where the damage calculation was conducted but no damage was estimated using white (open) circles. Hereafter, we show the building damage estimation of the hypothesized Tonankai earthquake and the whole rupture scenario along the Nankai Trough. Figures 14–17 show the damage ratio distributions based on the Nagato–Kawase model from the strong ground motion of a hypothesized Tonankai earthquake for wooden houses W02 (Figure 14, together with the estimated seismic intensity distribution), three- and five-storied steel structures, S03 and S05 (Figure 15), three- and six-storied RC structures, R03 and R06 (Figure 16), and nine- and twelve-storied RC structures, R09 and R12 (Figure 17). The old (pre-1981) and new (post-1981) building standard for seismic performance is distinguished except for wooden houses. Figure 18 shows simple average dam- Appl. Sci. 2021, 11, 7041 15 of 24 age ratios at all the sites where the damage ratios are calculated for different structural types, the number of stories, and construction ages. From these figures it is apparent that the old buildings built before 1981 have higher damage ratios than new buildings built after1981, 1981, low-rise low-rise steel steel structures structures have have the highestthe highest damage damage ratios ratios in lower in lower stories, stories, and and old oldnine-storied nine-storied RC buildingsRC buildings have have highest highest damage damage ratio ratio among among RC structures.RC structures. Based Based on theon thestructural structural type, type, the damagethe damage ratio ratio is highest is highest in steel in structures, steel structures, followed followed by wooden by wooden houses, houses,and then and RC then structures. RC structures.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 17 of 27

Figure 14. The seismic intensity scale distribution of strong ground motions calculated from the hypothesized Tonankai Figure 14. The seismic intensity scale distribution of strong ground motions calculated from the hypothesized Tonankai earthquake in this study (left) and the damage ratio distribution for wooden houses calculated from strong ground motions earthquake in this study (left) and the damage ratio distribution for wooden houses calculated from strong ground mo- tionsfor the for hypothesized the hypothesized Tonankai Tonankai earthquake earthquake and the and Nagato–Kawase the Nagato–Kawase model model [4](right [4] ().right).

FigureFigure 15. Damage ratio distributiondistribution fromfrom the the hypothesized hypothesized Tonankai Tonankai earthquake earthquake for for steel steel structures structures by theby the Nagato–Kawase Nagato–Ka- wasemodel. model. Top Top row: row: three-storied three-storied structures structures (S03), (S03), bottom bottom row: row: ﬁve-storied five-storied structures structures (S05); (S05); left left column:column: old structures (pre-1981),(pre-1981), right column: new new structures structures (post-1981). Appl. Sci. 2021, 11, 7041 16 of 24 Appl. Sci. 2021, 11, x FOR PEER REVIEW 18 of 27

Figure 16.FigureDamage 16. Damage ratio distribution ratio distribution from from the hypothesizedthe hypothesized Tonankai Tonankai earthquake earthquake for for RC RC structures structures by bythe the Nagato–Ka- Nagato–Kawase wase model. Top row: three-storied structures (R03), bottom row: six-storied structures (R06); left column: old structures model.Appl. Sci. Top(pre-1981), 2021 row:, 11, rightx three-storied FOR column: PEER REVIEW new structures structures (R03),(post-1981). bottom row: six-storied structures (R06); left column: old structures19 of 27

(pre-1981), right column: new structures (post-1981).

Figure 17.FigureDamage 17. Damage ratio distribution ratio distribution from from the hypothesizedthe hypothesized Tonankai Tonankai earthquake earthquake for RC RC structures structures by bythe the Nagato–Ka- Nagato–Kawase wase model. Top row: nine-storied structures (R09), bottom row: twelve-storied structures (R12); left column: old struc- model. Toptures row: (pre-1981), nine-storied right column: structures new structures (R09),bottom (post-1981). row: twelve-storied structures (R12); left column: old structures (pre-1981), right column: new structures (post-1981).

Figure 18. Average damage ratios for different structural types (W: wooden, S: steel, R: reinforced concrete), the number of stories (nn = 02, 03, 04, 05, 06, 09, 12), and construction ages (OLD: before 1981, NEW: after 1981).

Similarly, Figures 19–22 compare damage ratio distributions from the hypothesized whole rupture scenario along the Nankai Trough for wooden houses (W02), three- and five-storied steel structures (S03, S05), three- and six-storied RC structures (R03, R06), and nine- and twelve-storied RC structures (R09, R12). The corresponding average damage ratios at all the sites with non-zero damage ratios are shown in Figure 23. When we compare these overall damage ratios for the whole rupture scenario with those for the Tonan- kai earthquake shown in Figure 18, we found that the percentage of increase is only 10 to 20% from the damage ratios of the Tonankai earthquake and the increased ratios are only a few percent at most. A comparison of the damage ratio distributions presented here against the distribution of the numbers of damaged buildings per unit area from the Appl. Sci. 2021, 11, x FOR PEER REVIEW 19 of 27

Appl. Sci.Figure2021, 17.11, 7041Damage ratio distribution from the hypothesized Tonankai earthquake for RC structures by the Nagato–Ka-17 of 24 wase model. Top row: nine-storied structures (R09), bottom row: twelve-storied structures (R12); left column: old structures (pre-1981), right column: new structures (post-1981).

FigureFigure 18.18. AverageAverage damagedamage ratiosratios forfor differentdifferent structuralstructural typestypes (W:(W: wooden,wooden, S:S: steel,steel, R:R: reinforcedreinforced concrete),concrete), thethe numbernumber ofof storiesstories (nn(nn == 02,02, 03,03, 04,04, 05,05, 06,06, 09,09, 12),12), andand constructionconstruction agesages (OLD:(OLD: beforebefore 1981,1981, NEW:NEW: afterafter 1981).1981).

Similarly,Similarly, FiguresFigures 1919–22–22 comparecompare damagedamage ratioratio distributionsdistributions fromfrom thethe hypothesizedhypothesized wholewhole rupturerupture scenario scenario along along the the Nankai Nankai Trough Trough for for wooden wooden houses houses (W02), (W02), three- three- and ﬁve-and storiedfive-storied steel steel structures structures (S03, (S03, S05), S05), three- three- and six-storied and six-storied RC structures RC structures (R03, R06),(R03, andR06), nine- and andnine- twelve-storied and twelve-storied RC structures RC structures (R09, R12).(R09, TheR12). corresponding The corresponding average average damage damage ratios atratios all the at all sites the with sites non-zero with non-zero damage damage ratios ratios are shown are shown in Figure in Figure 23. When 23. When we compare we com- thesepare these overall overall damage damage ratios ratios for the for wholethe whol rupturee rupture scenario scenario with with those those for for the the Tonankai Tonan- earthquakekai earthquake shown shown in Figure in Figure 18, we 18, found we found that thethat percentage the percentage of increase of increase is only is only 10 to 10 20% to Appl. Sci. 2021, 11, x FOR PEER REVIEW 20 of 27 from20% from the damage the damage ratios ratios of the of Tonankai the Tonankai earthquake earthquake and the and increased the increased ratios areratios only are a only few percenta few percent at most. at A most. comparison A comparison of the damage of the ratio damage distributions ratio distributions presented herepresented against here the distributionagainst the ofdistribution the numbers of ofthe damaged numbers buildings of damaged per unit buildings area from per the unit CDMC area report from [ 32the], whichCDMC is report reproduced [32], which in Figure is reproduced 24, shows in that Figure the calculated 24, shows damagethat the ratioscalculated in this damage study ratiosare high in this at places study where are high not at a places large populationwhere not a exists large and population so the resultant exists and numbers so the re- of sultantbuildings numbers could notof buildings be so high could at these not placesbe so high as in at the these CDMC places map. as in On the the CDMC other hand,map. Onthe overallthe other estimate hand, the of the overall numbers estimate of damaged of the numbers buildings of perdamaged unit area buildings (i.e., density) per unit in areathe urbanized (i.e., density) districts in the such urbanized as Osaka district City ands such Nagoya as Osaka City City seems and too Nagoya high in City the CDMC seems predictiontoo high in consideringthe CDMC prediction the not-so-high considering damage the ratios not-so-high predicted damage in this ratios study. predicted There are in thisseveral study. reasons There to are which several we reasons can attribute to which the we source can ofattribute this signiﬁcant the source discrepancy, of this significant which willdiscrepancy, be discussed which later. will be discussed later.

Figure 19. TheThe seismic seismic intensity intensity scale scale distribution distribution of ofstrong strong grou groundnd motions motions calculated calculated from from the hypothesized the hypothesized whole whole rup- ruptureture scenario scenario in this in this study study (left (left) and) and the the damage damage ratio ratio distribution distribution for for wood woodenen houses houses calculated calculated from from strong ground motions for the hypothesized wholewhole rupturerupture scenarioscenario andand thethe Nagato–KawaseNagato–Kawase modelmodel [[4]4]( (rightright).).

Appl. Sci. 2021, 11, x FOR PEER REVIEW 20 of 27

CDMC report [32], which is reproduced in Figure 24, shows that the calculated damage ratios in this study are high at places where not a large population exists and so the resultant numbers of buildings could not be so high at these places as in the CDMC map. On the other hand, the overall estimate of the numbers of damaged buildings per unit area (i.e., density) in the urbanized districts such as Osaka City and Nagoya City seems too high in the CDMC prediction considering the not-so-high damage ratios predicted in this study. There are several reasons to which we can attribute the source of this significant discrepancy, which will be discussed later.

Appl. Sci. 2021, 11, 7041 18 of 24 Figure 19. The seismic intensity scale distribution of strong ground motions calculated from the hypothesized whole rupture scenario in this study (left) and the damage ratio distribution for wooden houses calculated from strong ground motions for the hypothesized whole rupture scenario and the Nagato–Kawase model [4] (right).

Appl. Sci. 2021, 11, x FOR PEER REVIEW 21 of 27

Figure 20. Damage ratio distribution from the hypothesized whole rupture scenario for steel structures by the Nagato– Kawase model.Figure Top 20. Damage row: three-storied ratio distribution structures from the (S03), hypothesized bottom whole row: ﬁve-storiedrupture scenario structures for steel structures (S05); left by column: the Nagato– old structures Kawase model. Top row: three-storied structures (S03), bottom row: five-storied structures (S05); left column: old struc- (pre-1981), right column: new structures (post-1981). tures (pre-1981), right column: new structures (post-1981).

Figure 21. FigureDamage 21. Damage ratio distribution ratio distribution from from the the hypothesized hypothesized whole whole rupture rupture scenario scenario for RC for structures RC structures by the Nagato– by the Nagato– Kawase model. Top row: three-storied structures (R03), bottom row: six-storied structures (R06); left column: old struc- Kawase model.tures (pre-1981), Top row: right three-storied column: new structures structures(R03), (post-1981). bottom row: six-storied structures (R06); left column: old structures (pre-1981), right column: new structures (post-1981). Appl. Sci. 2021, 11, 7041 19 of 24 Appl. Sci. 2021, 11, x FOR PEER REVIEW 22 of 27

Appl. Sci. 2021, 11, x FOR PEER REVIEW 22 of 27

Figure 22. Damage ratio distribution from the hypothesized whole rupture scenario for RC structures by the Nagato– Figure 22. Damage ratio distribution from the hypothesized whole rupture scenario for RC structures by the Nagato– KawaseFigure 22.model. Damage Top row:ratio nine-storied distribution stru fromctures the (R09),hypothesized bottom row:whole twelve-storied rupture scenario structures for RC (R12); structures left column: by the old Nagato– struc- Kawase model. Top row: nine-storied structures (R09), bottom row: twelve-storied structures (R12); left column: old turesKawase (pre-1981), model. Top right row: column: nine-storied new structures structures (post-1981). (R09), bottom row: twelve-storied structures (R12); left column: old struc- structures (pre-1981), right column: new structures (post-1981). tures (pre-1981), right column: new structures (post-1981).

Figure 23. Average damage ratios for different structural types (W: wooden, S: steel, R: reinforced concrete),FigureFigure 23.23. the AverageAverage number damagedamage of stories ratiosratios (nn forfor = 02, differentdifferent 03, 04, structural structural05, 06, 09, types types12), and (W:(W: construction wooden,wooden, S:S:steel, steel,ages R:(OLD:R:reinforced reinforced before 1981,concrete),concrete), NEW: thethe after numbernumber 1981). ofof storiesstories (nn(nn == 02,02, 03,03, 04,04, 05,05, 06,06, 09,09, 12),12), andand constructionconstruction agesages (OLD:(OLD: beforebefore 1981,1981, NEW:NEW: afterafter 1981).1981). Appl. Sci. 2021, 11, 7041 20 of 24 Appl. Sci. 2021, 11, x FOR PEER REVIEW 23 of 27

Figure 24. The distribution of the numbers of damaged buildings per unit area byby CDMCCDMC [[32].32].

5. Discussion In this paper, we calculated calculated the the strong strong ground ground motions motions in in southwestern southwestern Japan Japan for for a ahypothesized hypothesized Tonankai Tonankai earthq earthquakeuake and and the the whole whole rupture rupture scenario along the NankaiNankai Trough usingusing aa non-uniformnon-uniform slipslip modelmodel andand aa statisticalstatistical Green’sGreen’s functionfunction derivedderived fromfrom observed ground motions. The resultant syntheticssynthetics were compared with well-established GMPE predictions and seismic intensity estimatesestimates from the historicalhistorical damagedamage recordsrecords asas well as thethe predictedpredicted mapsmaps mademade byby CDMCCDMC forfor disasterdisaster preparationpreparation activitiesactivities insideinside thethe Japanese government. As long as the stochastic nature ofof the source, path,path, andand sitesite effectseffects is properlyproperly representedrepresented inin thethe elementaryelementary sourcesource andand thethe scalingscaling relationshipsrelationships fromfrom thethe elementary source to the hypothesized mega-thrust events are properly expressed, the elementary source to the hypothesized mega-thrust events are properly expressed, the resultant synthetics would be quantitatively predicted. The major drawback of the current resultant synthetics would be quantitatively predicted. The major drawback of the current approach, which is based on the observed strong motions, is its inability of prediction at an approach, which is based on the observed strong motions, is its inability of prediction at arbitrary point; we need to deploy a seismic station at a target site if it is not close to any of an arbitrary point; we need to deploy a seismic station at a target site if it is not close to the stations that we used. any of the stations that we used. There are several ways to skip that kind of time-consuming effort in order to obtain a There are several ways to skip that kind of time-consuming effort in order to obtain site-specific site amplification factor. One way is to use observed microtremors at the site a site-specific site amplification factor. One way is to use observed microtremors at the and apply the recently proposed double correction method on the horizontal-to-vertical site and apply the recently proposed double correction method on the horizontal-to-ver- spectral ratio (HVSR) of microtremors [37]. In the double correction method, first, the HVSR tical spectral ratio (HVSR) of microtremors [37]. In the double correction method, first, the of microtremors should be converted to the HVSR of earthquakes using an empirically determinedHVSR of microtremors spectral ratio. should Then, be theconverted transformed to the HVSR HVSR of of earthquakes earthquakes using should an beempir- con- vertedically determined to the horizontal spectral site ratio. amplification Then, the factor transformed using an HVSR empirically of earthquakes determined should average be verticalconverted amplification to the horizontal correction site amplification factor. The validity factor of using thelatter an empirically has also been determined reported av- by Itoerage et al.vertical [38]. amplification correction factor. The validity of the latter has also been re- portedAnother by Ito et viable al. [38]. way is to use ground response analysis (GRA) to calculate the site- specificAnother site amplification viable way is factor to use through ground 1D/2D/3D response analysis numerical (GRA) modeling to calculate of the the under- site- groundspecific structuresite amplification around thefactor site. through However, 1D/2D/3D we need numerical to have a modeling good velocity of the structure under- fromground the structure surface down around to thethe seismologicalsite. However, bedrock we need where to have we needa good not velocity consider structure any site effects,from the which surface means down the to layerthe seismological whose S-wave bedrock velocity where should we need be 3 km/snot consider or higher. any Itsite is noteffects, easy which to delineate means athe reliable layer velocitywhose S-wave structure velo ofcity that should scale at be an 3 km/s arbitrary or higher. point withoutIt is not aeasy significant to delineate investment. a reliable Recently, velocity westructure have proposedof that scale an at innovative an arbitrary way point to interpolate without a sitesignificant amplification investment. factors Recently, in between we have the strong proposed motion an innovative stations using way 1D to GRAinterpolate based site on theamplification detailed velocity factors profilesin between with the the strong spatial motion resolution stations of 250 using m in 1D the GRA Kanto based and on Tokai the regionsdetailed [ 39velocity]. profiles with the spatial resolution of 250 m in the Kanto and Tokai re- gionsAfter [39]. synthetic ground motions were obtained, we performed the damage prediction of woodenAfter synthetic houses, steel ground structures, motions and were RC structuresobtained, we using performed the building the damage prediction modelof wooden that houses, relies on steel the struct nonlinearures, structuraland RC structures responses using with the multiple building sub-models damage predic- with tion model that relies on the nonlinear structural responses with multiple sub-models Appl. Sci. 2021, 11, 7041 21 of 24

different yield capacities. As a result, the possibility of heavy building damage or collapse was identified in the coastal regions close to the fault and regions with relatively thick, soft sediments, such as areas inside alluvial plains. These dangerous cities are found mainly around near-fault regions such as Kochi, Tokushima, and Wakayama Prefecture, and areas around the Ise Bay. The damage ratio by structure type is highest in steel structures, followed by wooden houses, and then RC structures. The overall geographical pictures of our damage prediction are similar to the previous simulations by the government; however, we found that the prediction by CDMC [32] for the whole rupture scenario (Figure 24) seems to be overestimated by several reasons, although we have not translated yet our damage ratio prediction into the number of damaged buildings per unit area as conducted by CDMC. What are the possible sources of the difference between our prediction and theirs? The most influential problem of overestimation in CDMC prediction would be the use of the empirical vulnerability function based on the estimated PGVs and the damage ratios from the field survey during the past devastating earthquakes. In Japan, the majority of such data are coming from the 1995 Kobe earthquake [34,35], which is a typical crustal earthquake. The observed high PGVs in the epicentral areas of this earthquake were primarily controlled by the asperity pulses with a coherent nature in the intermediate period range around 1 s [5,6]. On the other hand, the high PGVs would be obtained inside a deep basin structure with thick and soft sediments during the mega-thrust events away from the shore, as is the case for the 2011 Tohoku earthquake. As mentioned before, we did not see any emergence of the high PGV regions in the intermediate period range and, subsequently, we did not see any significant structural damage during the Tohoku earthquake [33]. In our prediction of building damage, the Nagato–Kawase model also relies on the strong ground motions and the damage statistics during the 1995 Kobe earthquake; however, Nagato and Kawase utilized them to construct the nonlinear response models that consider basic dynamic structural behavior from the current building standard and to optimize the realistic yield capacities in order to reproduce observed damage ratios. Thus, the model can be used to predict damage for synthetic ground motions from not only crustal earthquakes but also mega-thrust events. We also need to point out the potential problem of the strength index of the ground motion to be used in the damage prediction. As mentioned above, no matter what we use as the representative strength index of the ground motion at a site, they would be a kind of extracted value from the whole ground motion time history. This means that we cannot have a perfect strength index to be used for damage prediction. By any operation to the time history in order to obtain the strength index, we are losing some valuable information from the whole time history of ground motion. It is not so meaningful to find a better strength index among so many possibilities because of the fundamental nature of the extraction. It would be better to use the whole time history of ground motion when we predict structural damage because the structural damage is a direct consequence of the input ground motion, not the direct consequence of the strength index extracted from the ground motion. For example, among the strength index based on the peak value of the ground motion, PGV would be the best index for damage prediction (e.g., [34,35]). However, a ground motion with high PGV in a long-period (>2 s) range could not cause any heavy structural damage because ordinary low- and middle-rise buildings would not respond to such a long-period input. As an advantage of using the Nagato–Kawase model, we can evaluate the effectiveness of countermeasures such as seismic retrofitting and increase of seismic demand in the regulations for new construction. Although we would like to report separately, we have conducted two case studies by introducing the policy to retrofit all the buildings to have 1.25 or 1.5 times the current yield capacity. We found that, roughly speaking, we can reduce damage ratios by about 20% for a 1.25 times increased case and by 30% for a 1.5 times increased case with respect to the average damage ratios shown in Figure 18 or Figure 23. It is a kind of significant number, however, if we consider the necessary cost as a whole Appl. Sci. 2021, 11, 7041 22 of 24

and the benefit of this retrofitting when the event occurs; it turns out that this kind of countermeasure for all the buildings in the area does not make sense. This means that when we consider countermeasures using earthquake resistance reinforcement against a coming mega-thrust earthquake along the Nankai Trough, such efforts should be focused only on the regions and structures with high damage potential as delineated by our prediction maps (Figures 14–17 and 19–22). Although it may not be easy to implement such a selective strategy as a public policy, it is not rational to reinforce all the buildings in the whole target area, most of which will survive without reinforcement. It is still early to practically implement the earthquake prediction and subsequent broadcast of the warning message for the expected Nankai Trough mega-thrust events; the emerging discovery reported recently by Sarlis et al. [40] could make it possible for such an earthquake prediction a few months before the mainshock in future. Once it becomes possible, we can better prepare for such an event by using the damage prediction shown in this paper for the specific location and size of the predicted event. Our damage prediction shows that the structural damage would be concentrated in several areas and cities with strong dependence on the type of the building and number of stories and therefore, the effective countermeasures should be made by reflecting these differences in the predicted structural damage. Our damage prediction here is much more modest than those worst- case scenarios of CDMC (e.g., Figure 24), and each local government could make a concrete plan for the immediate actions toward the potential disaster in such a short time. As a necessary process for more quantitative prediction of building damage, we need to carry out earthquake response analysis using building models in the historical events during these last several hundreds of years along the Nankai Trough [31] to calibrate both our modeling technique for the rupture complexity on the fault and the proper representation of the source, path, and site effects during these events in the past.

6. Conclusions We calculated the strong ground motions in southwestern Japan from a hypothesized Tonankai earthquake and a hypothesized whole rupture scenario along the Nankai Trough using a seismogenic fault model with a kinematic representation of heterogeneous slip distribution and a statistical Green’s function based on the observed ground motions by the nationwide strong-motion networks. Then, we performed the damage prediction of wooden houses, RC structures, and steel structures using the synthetic strong ground motions from these two types of events as input to building damage prediction models that utilize statistical properties of the nonlinear behavior of buildings with different types, stories, and construction ages. As a result, the possibility of serious building damage was identiﬁed in the coastal regions and regions with relatively soft sediments where we have stronger ground motions. We found that spatial irregularities of the predicted damage level are quite strong and different from structural types, stories, and construction ages. The damage ratio by structure type is highest in steel structures, followed by wooden houses and RC structures. When we consider countermeasures including earthquake resistance reinforcement against a mega-thrust event along the Nankai Trough, we need to reﬂect the strong spatial dependence of the higher damage potential for cost-effective implementation of such countermeasures.

Author Contributions: Conceptualization, H.K.; methodology, H.K. and N.M.; software, N.M.; validation, B. and N.M.; formal analysis, B.; investigation, B.; resources, B. and H.K.; data curation, B.; writing—original draft preparation, B.; writing—review and editing, H.K.; visualization, B.; supervision, H.K.; project administration, H.K.; funding acquisition, H.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was partially funded by Hanshin Consultants Co., Ltd (2-4-25 Ohmiyacho, Nara 630-8115, JAPAN), as a donation for the chair of Sophisticated Earthquake Risk Evaluation, Disaster Prevention Research Institute, Kyoto University. Institutional Review Board Statement: Not applicable. Appl. Sci. 2021, 11, 7041 23 of 24

Informed Consent Statement: Not applicable. Data Availability Statement: Strong motion data used in this paper are available at https://www. kyoshin.bosai.go.jp/ (accessed on 28 April 2021) for K-NET and KiK-net, whereas at https://www. data.jma.go.jp/svd/eqev/data/kyoshin/jishin/index.html (accessed on 28 April 2021) for JMA seismic intensity meters. Acknowledgments: We would like to express our acknowledgment to NIED and JMA who offered observed strong ground motions and related metadata. The comments from anonymous reviewers contributed to improve the quality of the manuscript. Conﬂicts of Interest: There is no conﬂict of interest as far as the authors are concerned.

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