Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 10NCEE Anchorage, Alaska

AFTERSHOCK RISK IN JAPAN FOLLOWING TOHOKU EARTHQUAKE

Nilesh Shome1 and Chesley Williams2

ABSTRACT

The recent Tohoku Japan earthquake clearly demonstrated that aftershocks following large magnitude earthquakes can be a source of significant hazard. In this study, we have followed the Reasenberg and Jones (1989) approach to describe the aftershock activity based on: 1) Gutenberg-Richter model (GRM) specifying the relationship between the magnitude and total number of earthquakes in any region and time period, and 2) modified Omori model (MOM) defining the decay of the aftershock activity with time. The aftershock occurrence is represented by a non-stationary Poisson process whose rate varies with time after the main shock. Since the Tohoku earthquake occurred in a seismically active region, it is essentially impossible to differentiate aftershocks from background earthquakes in the catalog. Hence this study fitted the MOM and GRM to all the events in the catalog in order to estimate the post-Tohoku seismicity rates. We have used the JMA catalog with magnitude larger than or equal to M3.5 in order to estimate the seismicity that may cause damage to the built environment. The Method of Maximum Likelihood is used to estimate the parameters in MOM and GRM. The pre-Tohoku seismicity is calculated based on the observed seismicity since 1983 and that for post-Tohoku is based on the seismicity for one year following the Tohoku event. In this study, we consider only the change in the seismicity in the background sources. The change in seismicity rates in the shallow crustal faults, deep background sources, or the subduction sources are not considered in this study. In order to find out the change in the seismic risk in Japan after the Tohoku earthquake, we have estimated the average annual loss (AAL) for a well distributed building portfolio in Japan. We have calculated the AAL for each year from 2013 to 2017 in order to illustrate the evolution of risk with time following the Tohoku event. There is significant uncertainty in the estimation of the GRM and MOM parameters resulting in uncertainty in the estimation of risk and this is also addressed in this study. In addition, we investigate the suitability of MOM in forward prediction of post-event risks in a regional scale. The observed seismicity in the second year following the Tohoku earthquake is compared with those estimated based only on the first year post-event data.

1Senior Director, Model Development, Risk Management Solutions, Newark, CA 94560 2Senior Project Director, Model Development, Risk Management Solutions, Newark, CA 94560

Shome, N and Williams, C. Aftershock risk in Japan following Tohoku earthquake. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

DOI: 10.4231/D3GX44V5K

Aftershock Risk in Japan Following Tohoku Earthquake

Nilesh Shome1 and Chesley Williams2

ABSTRACT

The recent Tohoku Japan earthquake clearly demonstrated that aftershocks following large magnitude earthquakes can be a source of significant hazard. In this study, we have followed the Reasenberg and Jones (1989) approach to describe the aftershock activity based on: 1) Gutenberg- Richter model (GRM) specifying the relationship between the magnitude and total number of earthquakes in any region and time period, and 2) modified Omori model (MOM) defining the decay of the aftershock activity with time. The aftershock occurrence is represented by a non- stationary Poisson process whose rate varies with time after the main shock. Since the Tohoku earthquake occurred in a seismically active region, it is essentially impossible to differentiate aftershocks from background earthquakes in the catalog. Hence this study fitted the MOM and GRM to all the events in the catalog in order to estimate the post-Tohoku seismicity rates. We have used the JMA catalog with magnitude larger than or equal to M3.5 in order to estimate the seismicity that may cause damage to the built environment. The Method of Maximum Likelihood is used to estimate the parameters in MOM and GRM. The pre-Tohoku seismicity is calculated based on the observed seismicity since 1983 and that for post-Tohoku is based on the seismicity for one year following the Tohoku event. In this study, we consider only the change in the seismicity in the background sources. The change in seismicity rates in the shallow crustal faults, deep background sources, or the subduction sources are not considered in this study. In order to find out the change in the seismic risk in Japan after the Tohoku earthquake, we have estimated the average annual loss (AAL) for a well distributed building portfolio in Japan. We have calculated the AAL for each year from 2013 to 2017 in order to illustrate the evolution of risk with time following the Tohoku event. There is significant uncertainty in the estimation of the GRM and MOM parameters resulting in uncertainty in the estimation of risk and this is also addressed in this study. In addition, we investigate the suitability of MOM in forward prediction of post-event risks in a regional scale. The observed seismicity in the second year following the Tohoku earthquake is compared with those estimated based only on the first year post-event data.

Introduction

The Tohoku-oki (henceforth “Tohoku”) earthquake (Mw 9.0) of March 11, 2011, was the largest event in the recent history of Japan. Like any other large magnitude events, large number of aftershocks followed the Tohoku earthquake around the rupture zone. The number of aftershocks, however, has become fewer over the time. This spatial and temporal clustering of earthquakes is an important aspect of aftershocks and is a source of significant increase in hazard in short term (e.g., InsuranceInsight [4] reported up to 50% increase in reported earthquake insurance following the Tohoku event). Temporal clustering, as commonly observed during

1Senior Director, Model Development, Risk Management Solutions, Newark, CA 94560 2Senior Project Director, Model Development, Risk Management Solutions, Newark, CA 94560

Shome, N and Williams, C. Aftershock risk in Japan following Tohoku earthquake. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014. aftershock sequences, constitutes strong evidence for time-dependent behavior of the seismic process. This is a departure from a simple spatially-variable, time-independent Poisson process, which is commonly assumed to model seismicity in earthquake risk calculations. In this paper, we represent the aftershock hazard by looking into increased recurrence rate over the long-term rate.

Fusakichi Omori [6], a pioneer Japanese seismologist, based on the observed frequency of felt earthquakes per day, following the 1891 Nobi earthquake (M8) in central Japan, theorized that aftershocks decrease regularly with time and this is known as Omori’s law. Utsu [7] later on updated the law, known as modified Omori Model (MOM) based on observation of additional aftershocks. Lately, Reasenberg and Jones [8] proposed a simple comprehensive model (referred here as RJM) where the productivity is modeled by Gutenberg and Richter model (GRM) for magnitude-frequency relationship of earthquakes and the aftershock rate decay with time by MOM. In this study, we use this model to predict the Tohoku aftershock seismicity rate. A similar model is used by USGS in the Short-Term Earthquake Probability (STEP) model [9] to calculate time-dependent earthquake hazard for clustering of earthquakes. This model is no longer in use because of difficulty in prediction of spatial decay of aftershock seismicity rates, particularly for main shocks on faults. This is, however, not an issue in this study since we are estimating the spatial decay based on the observation of earthquakes during the first year after the Tohoku earthquake.

There are other approaches for predicting aftershock seismicity rates, which are the stochastic Epidemic Type Aftershock Sequence model (ETAS) [10] and a physical approach proposed by Dieterich[11] based on the rate- and state-model of fault friction. Researchers also explored static stress change to provide explanation for seismicity rate increase in the aftershock zone. It is found [12] that about 60% of earthquakes following large magnitude earthquakes (M>7) within the zone of positive stress change follow MOM and the rest are associated with stress decrease decaying much faster than those predicted by MOM. All these approaches are expected to predict the seismicity rate, which is different from the approach presented here. Recently Risk Management Solutions (RMS) researched to find out the change in earthquake occurrence rates in the Tohoku region due to static stress changes [2]. In this study, RMS chose 13 well accepted finite fault slip models and the rate change is calculated based on the static stress changes on the receiver sources for each of those models. It is found that the model-to- model variability in stress change is high (coefficient of variation > 1) and the mean recurrence rate change of earthquakes is expected to be even higher. The approach presented in this paper is followed for updating the Japan Earthquake Model of Risk Management Solutions (RMS) to take into account the increased seismicity from the Tohoku earthquake [13].

Seismologists have traditionally labeled earthquakes as ‘‘foreshocks’’, ‘‘main shocks’’ or ‘‘aftershocks’’, where only the main shocks can be considered to be a time-independent stationary process. The direct aftershocks are dependent events of the main shocks and those aftershocks typically generate the secondary aftershocks thus producing many different overlapping aftershock sequences. Since Japan is seismically active region, it would be impossible to separate the stationary background earthquakes, which are significant in number, and the aftershocks only from the Tohoku main shock. So we calculate the increase in the rate of earthquakes following the Tohoku event based on all the events in the catalog following the main shock and apply MOM to those events which are combination of direct and secondary aftershocks, and background earthquakes to predict number of earthquakes following the Tohoku event.

Seismicity Following Tohoku

The Tohoku earthquake was the fourth-largest recorded earthquake and generated a widespread aftershock activity (aftershock-zone length extended about 500 km along strike of the subduction zone) in the eastern half of Honshu. The event changed the inland region from a zone of East–West (EW) contraction to a zone of significant EW stretching causing some unexpected activity in some areas, such as the border between Fukushima and Ibaraki prefectures. This region had previously a low level of background seismicity, but experienced a swarm of shallow normal faulting earthquakes following the Tohoku event. Fig.1 illustrates the seismicity of Mw3.5 earthquakes in Japan 1 year before and after the Tohoku earthquake, clearly

(a) Over one year before Tohoku (b) First year after Tohoku Figure 1. Comparison of seismicity and distribution of depth of earthquakes in Japan before and after the Tohoku earthquake. The regions around Tokyo and Iwaki (150km around the city) are shown by the blue and purple box respectively. demonstrating significant increase in seismicity following the Tohoku earthquake. The plot of distribution of depth earthquake during those time periods shows that there is practically no change in the distribution of depth of earthquakes due to the increase in seismicity. Fig. 2 shows the magnitude-frequency relationship of earthquakes within ± 150km around Iwaki and Tokyo city (shown by the boxes in Fig. 1), where we observe significant and slight increase in seismicity rates respectively. Since the earthquake catalog of Mw3 is complete since 1982[3], we are using the 28 years of earthquake data since 1982 in order to estimate the average annual rate of earthquakes before the Tohoku event. The annual rate of MW4 earthquake increased approximately 9 and 21 times around Tokyo and Iwaki respectively. Note that the hazard calculations in California considered minimum M4 earthquake in UCERF2 model [5] for calculating rates for background events. The results in Fig. 2 for MW4 are used for calculating the GR parameters. A similar exercise is carried out at all the grid locations to estimate the increased seismicity for background events following the Tohoku earthquake. In this study, we will use the catalog of Earthquakes exceeding MW3.5 for estimating the parameters of MOM since the model requires large number of events to reduce the uncertainty in the estimation of those parameters. Fig. 3 shows the decay in the number of daily earthquakes with time in the first year in the 150km box around Iwaki and Tokyo. These figures illustrate that the seismicity in Tokyo region as defined by the box was about 25 times higher after a month and 3 times higher after 1 year compared to the 28-year daily average seismicity (versus about 52 and 7 times higher respectively for Iwaki region). The temporary increase in rate will reach the pre-Tohoku rate over the years and the figure indicates that Tokyo will reach that rate sooner than Iwaki.

(a) Iwaki (b) Tokyo Figure 2. Comparison of magnitude-frequency relationship of earthquakes during different time periods before and after Tohoku.

Prediction of Post-Tohoku Seismicity

As discussed before, we will follow the modified-Omori model (MOM) [7] to predict the seismicity rates in Japan following the Tohoku earthquake as given in the first part of the following equation: ( ) ( ) (1) ⏟( ) ⏟ ( )

where: N(t,M) = Number of aftershocks per unit time, at time t of magnitude M following the main shock Mm. K = Productivity of the aftershock sequence. c = Small time shift (usually <1 day) that controls the sequence behavior in the early period following the main shock. p = Factor determines the speed of decay of aftershock rate with time (in general between 0.8- 1.2). The variability in p-value is expected to be related to the structural heterogeneity, stress and temperature of the crust. a and b = Gutenberg and Richter (GR) constants.

The parameters of the model are calculated here by following maximum likelihood method, which maximizes the likelihood function, ( ), for the observed aftershock data [10] as shown below:

( ) ( ) ∑( ) ∫ ( ) ( ) where ti is the time of an aftershock since the main shock. The fitted model is compared with the observed seismicity around Tokyo and Iwaki city and the results are shown in Fig. 3. There is, however, significant uncertainty in the estimation of the parameters and this can be estimated by assuming asymptotic normality of the likelihood function. The variance and covariance of the estimated parameters is estimated based on the following:

( ) ( ̂) [ ( ̂)] { } (3)

where I() is the Fisher Information matrix and  is the parameter of MOM. The uncertainty in the prediction of the daily rate of earthquakes exceeding M3.5 around Tokyo and Iwaki based on the events in the first year is shown in Fig. 3 by the red dotted lines. The results show that uncertainty is significantly lower around Iwaki because of relatively higher number of events observed during the first year. The daily rate of events as observed in the second year is also compared in the figure with those predicted by the model.

The annual rate of different magnitude of events is predicted based on RJM [8]. The model is shown in part 2 of the Eq. 1. In this study, we have fitted GRM separately to the data to estimate the productivity of MOM. Weichert approach [15] is followed in order to estimate the parameters of GRM. The result of the fit is shown in Fig. 3. Although the standard MOM does not give the rate of different magnitude events, the RJM provides an estimate of those, which are

(a) Iwaki (b) Tokyo Figure 3. Comparison of decay of number of earthquakes within two years after the Tohoku event. essential for earthquake risk assessment of buildings. The annual rate of different magnitude of events in the 2nd to 6th year following the Tohoku earthquake around Tokyo and Iwaki is shown in Fig. 4. Since there is significant uncertainty in estimating the risk due to aftershocks, the RMS model uses the 5-year average rate for medium-term risk assessment of building portfolios. The uncertainty in the 5-year average rate around Tokyo is shown in Fig. 5(a) and it is found that the co-efficient variation of the rate is 0.3 (vs. 0.1 in Iwaki because of observation of higher number of events). In order to validate the approach followed in this study, we have compared in Fig. 5(b) the prediction of annual rate of MW4 earthquakes around Tokyo in the second year after the Tohoku event with those observed. It is found that the observed rate in the second year around is higher than the rate predicted here, but the observed rate is well within the 90%-confidence band of that predicted.

Estimation of Post-Tohoku Risk

The approach shown in the previous paragraphs for the estimation of parameters for MOM and GRM are followed to calculate the increase in background seismicity rates in order to estimate the post-Tohoku seismic risk. The standard seismic risk calculations, however, considers only the independent main shocks by removing all the dependent aftershock events. We will follow the approach developed by ERC [3] in order to remove the aftershock events from the catalog. Since MOM provides an estimate of the rate of all the events (including aftershocks), we will first estimate the rate of those events and then adjust those rates based on the observation of fraction of those events being the main shock. Recently Uniform California Earthquake Forecast (UCERF3) model [16] also followed a similar approach in order to estimate the rate of main shocks from the predicted “total rates”. In addition, since MOM is applied to all the events at all depths, we will calculate the rates for shallow crustal events (25km) and deep events (60- 80km) based on the fraction of total events in each zone falls into these depth categories based on the depth distribution shown in Fig. 1.

(a) Iwaki (b) Tokyo Figure 4. Comparison of annual rate of different magnitude of earthquakes at different years following the Tohoku event. The rate of earthquakes exceeding Mw4 after the Tohoku event is compared with those for the pre-Tohoku events as well as with the post-Tohoku 5-year average rates.

(a) 5-Year average (2012-16) (b) Second year

Figure 5. Uncertainty in the estimation of annual rate of Mw4 earthquakes around Tokyo.

The background seismicity rates in Japan is updated in this study only for the following zones (shown in Fig. 6): 1) Northeast Honshu Arc zone (green), 2) Interface background zone (blue) and 3) Chokkagata interface and intraplate zone (red). We have first estimated the variation of annual rates of all earthquakes in different years following the Tohoku earthquake as shown in Fig. 4 for all these zones since we need large number of observed events in order to estimate the parameters of MOM and GRM accurately. We have adjusted these rates based on the fraction of total earthquakes at all depths falls within the depth of these zones (e.g., earthquakes in Northeast Honshu Arc zone should have depth less than 25km and 31% of total earthquakes around Iwaki belongs to the zone). Next, we adjust the total rates by finding out the fraction of total rates in these zones is main shock. For example, we have calculated the magnitude-frequency distribution (MFD) of the observed total earthquakes before and after the Tohoku event within 100km boundary of Northeast Honshu Arc zone and compared those with the MFD only for the main shocks by removing the aftershocks following ERC [3]. The results are shown in Fig. 7. It is found that 84% of total events of MW  5 are main shocks before vs. 22% in the first year after the Tohoku event. The annual rates calculated for each of the zones as shown in Fig. 4 are not uniformly distributed within the zone as observed in

Fig. Figure 6: Different background zones 1. In order to distribute the seismicity considered in this study for updating the within these zones, we will first calculate the seismicity. observed seismicity at 1010km grids and then apply Gaussian-Kernel smoothing for 50km correlated distance in order to estimate the seismicity at a specific grid. Note that ERC [3] and UCERF2 [5] followed the same approach to distribute the background seismicity. The estimated average increase in seismicity during 2012- 16 in Honshu Arc zone for shallow crustal earthquakes is shown in Fig. 8. The figure shows that the increase in seismicity is significantly higher in the east as observed in Fig. 1.

Note that the calculation of time-dependent probability of earthquake shows that the probability of large magnitude subduction earthquakes in Japan Trench zone after the Tohoku event is very low and so the seismic hazard due to those events reduces to the East of Honshu. So it is found that if the background seismicity has not increased significantly in the East of Japan where Japan Trench source contributes significantly to the hazard, the near- term seismic risk actually reduces significantly. A detailed discussion on time-dependent probability calculations in Japan this can be Figure 7. Annual rate of events before and after the Tohoku event for all the events and for only found in the ERC report [3]. main shocks in Northeast Honshu Arc zone.

Loss Results

The procedure described in the previous paragraphs is used for updating the RMS Japan earthquake model [13] in order to estimate the post-Tohoku risk in Japan. In addition, the model also updated the time-dependent probability calculations for earthquakes in Japan Trench. This is not discussed here for brevity, but we have included those calculations in order to improve the accuracy of the loss results presented here. We consider here a well distributed portfolio in Japan for estimating the change in the losses for the change in seismicity rates after the Tohoku event. The change in average annual loss (AAL), which is the sum of expected loss for all the possible future events in a year, is shown in Fig. 9, which shows significant increase in loss in Fukushima prefecture near the coast and a smaller increase as we move away from the coast. This increase in loss, however, is in line with the seismicity as observed in Fig. 1. The dramatic increase in loss is partly due to the increase in seismicity from recent rupturing of two faults near Southern Fukushima [14]. These faults were not active during the last hundreds of years and so seismicity was relatively low in Fukushima. The figure also shows that the AAL decreases in the north of Fukushima prefecture due to the reduction in the recurrence rate of the subduction earthquakes in Japan Trench based on time-dependent probability calculations.

There is, however, significant uncertainty in the results due to the uncertainty in the prediction of future aftershocks as shown in Fig. 4. We have estimated the uncertainty in the 5-year average post-Tohoku annual rate in shallow and deep background zones during the period of 2012-2016. This gives us the uncertainty in the amplification of rates at different locations in those zones. The change in AAL in entire Japan as well as in four different prefectures due to 10th-and 90th- percentile rate amplifications is shown in Fig. 10. It is observed that there is significant uncertainty in the estimation of AAL and this issue needs to be considered for assessing post-Tohoku seismicity rates. The biggest swing in Ibaraki prefecture is due the difference in the distribution of buildings compared to the other regions – more high valued industrial buildings in the west of Ibaraki whereas the other prefecture has nearly uniform distribution of buildings. Figure 8. Ratio of seismicity in Honshu Arc zone for shallow

crustal earthquakes before and The loss results presented in Fig. 9 are based on 5-year after the Tohoku event. average post-Tohoku rate. It is, however, observed in Fig. 4 that the annual rate decreases exponentially with time. Hence, annual rate in 2012 will be significantly higher than the 5-year average. In order to understand the variation of risk with time after the Tohoku event, we have estimated the AAL in each year during 2012-16. The ratio of AAL during those years and the 5-year average rate is shown in Fig. 11. The figure illustrates that the aftershock seismicity in Fukushima decreases rapidly reaching close to the background rate in 6th year following the Tohoku earthquake when we see slight reduction in AAL due to the reduction in rate of the subduction earthquakes in Japan Trench due to the time-dependent probability calculations. The AAL in Tokyo, however, remains high due to some change in the calculation of annual probability of earthquakes in Nankai Subduction zone [3]. The result in the figure shows that the post-Tohoku seismicity reaches the background state in the 3rd year.

Conclusion

We have estimated the change in seismic risk in Japan following the Tohoku earthquake over the period of 2012-2016 based on building loss results. The Reasenberg and Jones methodology [8] is followed here for estimating post-Tohoku hazard. The average annual loss for entire Japan is estimated and the results show that there is significant increase in seismicity vis-à-vis risk in some regions (e.g., eastern Fukushima Prefecture). The increase in seismicity over 5 years is estimated based on the events in the first year after the Tohoku earthquake. Since there is significant uncertainty in the estimation of post-Tohoku seismicity rates and it is changing rapidly with time, we have used 5-year average rate in order to calculate the average annual loss (AAL) for post-Tohoku risk estimation. Since the number of events is limited in the first year after the Tohoku earthquake within the mainland, the uncertainty is significant in the inland areas where only a small number of events has occurred leading to significant uncertainty in the estimation of post-Tohoku rate. Hence, we have estimated the uncertainty in the calculations of AAL to provide some guidance on the uncertainty in the estimation of post-Tohoku risk.

We have followed the Reasenberg-Jones approach [8] in order to estimate the post-Tohoku hazard in Japan. There are many other approaches that can be used for predicting aftershock hazard, but most of these studies do not match the observations well (e.g., see the RMS [2] study on the use coulomb stress to predict the frequency and location of future events). On the other hand, a comparison of the observation of the number of events in 2012-13 with those predicted here shows that the observation is within the uncertainty bound of the predictions. So the approach followed in this study can be applied with high confidence to manage the risk due to aftershocks. The uncertainty, in general, is quite narrow where there is significant number of aftershocks and so where the increase in hazard is higher. In addition, it is observed that although the seismicity rate is increased significantly, the increase in risk is quite modest. In general, the uncertainty in Figure 9. Ratio of 5-year average annual seismicity as well as in loss estimation is significant and loss (AAL) pre- and post-Tohoku. this should be considered for assessing and managing aftershock risk. Although we have showed the loss results based on the 5-year average rate of earthquakes following the Tohoku event, we have also shown the change in the seismicity as well as risk with time following the Tohoku earthquake. The results show that the increase in seismicity due to aftershocks is insignificant by the 6th year in Fukushima Prefecture versus by the 3rd year in Tokyo Prefecture.

Acknowledgments

Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect those of Risk Management Solutions, Inc.

References

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