vEGU21: Gather Online | 19 – 30 April 2021 EGU21-15824, Session SM7.1
Operational Aftershock Forecasting for 2017-2018 Seismic Sequence in Western Iran
Hossein Ebrahimian & Fatemeh Jalayer Department of Structures for Engineering and Architecture, University of Naples Federico II (UNINA), Italy Starting Point Methodology Application Conclusion
Conceptual framework for quasi real-time hazard and impact forecasting within an ongoing seismic sequence in terms of occurrence, ground-shaking, damage, and losses in a prescribed forecasting interval (in the order of hours to days)
Regional data, building inventory, population density, seismic micro-zonation, other required Quasi real-time earthquake catalog thematic maps related to the monitored area
ETAS: Epidemic Type Aftershock Aftershock Sequence-tuned updating of model Sequence model; spatio-temporal occurrence model(s) parameters occurrence; every earthquake within the sequence is a potential triggering event for subsequent earthquakes by generating its Operational forecasting of own Modified Omori aftershock decay. aftershock occurrence
Ground motion Forecasting of aftershock ground- prediction model(s) shaking
This study Empirical/Analytical Forecasting of aftershock damage Fragility model(s)
Retrospective early Loss model(s) Impact Forecasting forecasting of seismicity associated with the 2017- 2018 seismic sequence Expected Expected activities in western Iran Financial Losses Fatalities
EGU21-15824 Starting Point Methodology Application Conclusion
Fully simulation‐based framework for robust estimation of seismicity distribution in a prescribed forecasting time within an ongoing seismic sequence
A Bayesian updating approach A stochastic procedure is used in The procedure leads to the basedonanadaptiveMCMC order to generate plausible stochastic spatial distribution of simulation technique is used to sequences of events that are the forecasted events and learn the ETAS model parameters going to occur during the consequently to the uncertainty conditioned on the events that forecasting interval (the real in the estimated number of have already taken place in the sequence is unknown at the time events, corresponding to a ongoing seismic sequence before of forecasting). given forecasting interval the forecasting interval. (Robust seismicity forecasting)
STAGE 01 STAGE 02 STAGE 03 Learning ETAS model parameters Generating plausible sequences Estimating spatial distribution of events
Ebrahimian H, Jalayer F (2017) Robust seismicity forecasting based on Bayesian parameter estimation for epidemiological spatio-temporal aftershock clustering models. Sci Rep 7, 9803. https://doi.org/10.1038/s41598-017-09962-z. Ebrahimian H, Jalayer F, Maleki Asayesh B, Zafarani H (2021) Operational aftershock forecasting for 2017-2018 Kermanshah seismic sequence in Western Iran. Bull. Seismol Soc Am (in Preparation). EGU21-15824 Starting Point Methodology Application Conclusion
The conditional rate of occurrence of events (the seismicity rate)
based on ETAS model
mM mMl jl Kt Kr ETAS txym,,,θ ,seqtl , M e Ke pq 22 ttj tt c rd j j ETAStxy,,θ ,seqtl , M
The rate ETAS is at time t (with respect to a reference time), in the cell unit centered at the Cartesian coordinate (x, y)A (where A is the aftershock zone), with the magnitude M≥m, conditioned on: the vector of ETAS model parameters [, K, , c, p, d, q].
the observation history up to the time t denoted as seqt={(tj, xj , yj, mj), tj Sequence of events (seq) To ≤ ti EGU21-15824 Starting Point Methodology Application Conclusion Robust seismicity forecasting E,,,Nxymseq M N xymM ,, lb l Tend txym,,,θ ,seq , M d t pθ | seq,d M θ ETAS ll θ Tstart A robust estimate of the average number of events (E[·]) in the spatial cell unit centered at (x, y) with M≥m in the The conditional probability forecasting interval [Tstart, Tend], which is calculated over density function (PDF) for the domain of the model parameters . given the seq and Ml. Nb(x, y, m|Ml): average number of events occurred due to the background seismicity with magnitude M ≥m in the forecasting interval [Tstart, Tend]. Forecasting interval IAT1 IAT2 IAT3 IATi Mainshock T t t t ti o 1 2 3 Tstart Tend Time (t) Sequence of events (seq) To ≤ ti EGU21-15824 Starting Point Methodology Application Conclusion Robust seismicity forecasting E,,,Nxymseq M N xymM ,, lb l Tend ETAS txym,,,seqg ,,θ seq , Mlll d t p seqg|θ,,seq M d seqg pθ|seq,d M θ θ seqg Tstart The robust estimate for the average number of aftershock events should also consider all the plausible sequences of events seqg (i.e., the domain seqg)that can happen during the forecasting time interval. A plausible seqg is defined as the events within the forecasting interval defined as seqg={(IATi =ti-ti-1, xi, yi, mi), Tstart≤ ti ≤Tend, mi ≥Ml}. Theuseoftheterm“robust” here implies that a set of possible model parameters is used to estimate the conditional number of events N(x, y, m|seq, Ml) rather than a single nominal model parameter. EGU21-15824 Starting Point Methodology Application Conclusion Robust seismicity forecasting E,,,Nxymseq M N xymM ,, lb l Tend ETAS txym,,,seqg ,,θ seq , Mlll d t p seqg|θ,,seq M d seqg pθ|seq,d M θ θ seqg Tstart This Equation can be solved via a fully simulation‐based framework: • Vector of model parameters are sampled from p(|seq, Ml) using an adaptive Markov Chain Monte Carlo (MCMC) simulation technique. (1) The samples are used to generate plausible sequences seqg taking place within the forecasting interval [Tstart, Tend] according to p(seqg| seq, Ml). Note: The sequence of events that precede Tend is {seq, seqg}, where seq remains unchanged (observed data) among plausible samples; Thus, a robust estimate for the average number of events can be obtained based on the plausible model parameters. EGU21-15824 Starting Point Methodology Application Conclusion About the model parameter K mM mMl jl Kt Kr ETAS txym,,,θ ,seqtl , M e Ke pq 22 ttj tt c rd j j [, K, , c, p, d, q] ETAStxy,,θ ,seqtl , M Method (a) Calculate K: Considering that K is directly affected by No (i.e., the number of events taken place before the forecasting interval [Tstart, Tend]), it has an analytical closed‐form expression, and its distribution can be derived based on other ETAS parameters. Thus, the vector of model parameters has six parameters =[, , c, p, d, q]. Tstart Forecasting interval IAT1 IAT2 IAT3 IATi Mainshock txy,,θ ,seq , Ml ddd x y t No T t t t ti Txy, A o 1 2 3 Tstart Tend Time (t) o Total conditional intensity including also background seismicity rate Sequence of events (seq) To ≤ ti Method (b) Learn K through the Bayesian Updating framework: The parameter K is drawn from the conditional distribution p(|seq, Ml),where=[, K, , c, p, d, q] has seven parameters. EGU21-15824 Starting Point Methodology Application Conclusion Kermanshah 2017‐2018 Seismic Sequence Seismic Sequence from 11/01/2017 up to 01/12/2019 36 Kurdistan 35.5 M7.3 Sanandaj 35 12/11/2017 Ezgele M5.9 25/8/2018 34.5 Kermanshah Sarpol-e Zahab Kermanshah M6.3 34 25/11/2018 Latitude 33.5 Ilam Map of active faults of Iran (prepared by: B. Maleki Asayesh, IIEES, Iran) 2.5 M < 3 Ilam 33 3 M < 4 4 M < 5 32.5 5 M < 6 6 M < 7 M 7 32 44.5 45 45.5 46 46.5 47 47.5 Longitude EGU21-15824 Starting Point Methodology Application Conclusion Kermanshah 2017‐2018 Seismic Sequence Ezgeleh MS Tazehabad event Mw7.3 Mw5.9 12/11/2017 25/08/2018 To=01/11/2017 06:00 UTC 630 casualties, immense Sarpol‐e Zahab event Mw6.3 buildings’ damages and 25/11/2018 economic losses From 12/11/2017 up to 18/04/2020 (i.e., in the time interval of around 2.5 years after the Ezgeleh MS), about 9000 seismic events were recorded by Iranian Seismological Center, IRSC, in the area shown in Figure. From this pool of seismicity, 2318 events have Mw≥2.5. In addition to the Ezgeleh MS, 19 events with Mw≥5.0, and more than 125 events with magnitude larger than 4 and less than 5 (4≤Mw<5) were recorded within this sequence. EGU21-15824 Starting Point Methodology Application Conclusion Kermanshah 2017‐2018 Seismic Sequence Ezgeleh MS Tazehabad event Sarpol‐e Zahab event Mw7.3 Mw5.9 Mw6.3 12/11/2017 25/08/2018 25/11/2018 To=01/11/2017 06:00 UTC Daily observed number of events (starting from 6:00 UTC each day) 100 M7.3 at 12/11/2017 - 18:18:16UTC M5.0 at 20/11/2017 - 15:23:39UTC 80 M5.5 at 11/12/2017 - 14:09:57UTC 60 M 2.5 40 M 3.0 Number of events 20 0 7 7 -17 17 v-17 c-17 ec-17 c- c-1 ec-17 De -No -Nov -Nov-1 2-Nov-17 02-Nov-17 07 12 17 2 27-Nov-17 02- 07-D 12-Dec-17 17-De 22-De 27-D EGU21-15824 Starting Point Methodology Application Conclusion Distribution of the ETAS model parameters (marginal PDF’s of posterior and prior) with their statistics (mean and COV) after Mw 7.3 at 12‐November 2017 [Tstart, Tend] (dd/mm‐hour) c [day] pd [km] qK sample mean=0.39 mean=0.04 mean=1.12 mean=1.36 mean=1.04 mean=208.40 [12/11‐21:00, prior COV=0.43 COV=0.29 COV=0.09 COV=0.19 COV=0.03 COV=0.34 13/11‐06:00]; ML=1.12 mean=0.99 Ml =2.5 COV=0.16 1 2 3 4 1 2 3 4 0.05 0.1 0.15 1 2 3 1 2 3 4 1 2 3 500 1000 1500 sample mean=0.64 mean=0.04 mean=1.11 mean=1.40 mean=1.05 mean=73.31 [13/11‐00:00, prior COV=0.24 COV=0.27 COV=0.08 COV=0.17 COV=0.03 COV=0.41 13/11‐06:00]; ML=1.21 M =2.5 mean=1.12 l COV=0.12 1 2 3 4 1 2 3 4 0.05 0.1 0.15 1 2 3 1 2 3 4 1 2 3 200 400 600 sample mean=0.72 mean=0.04 mean=1.20 mean=1.46 mean=1.05 mean=31.41 [13/11‐06:00, prior COV=0.20 COV=0.30 COV=0.12 COV=0.18 COV=0.03 COV=0.33 =1.54 14/11‐06:00]; ML mean=1.50 Ml =3.0 COV=0.12 1 2 3 4 1 2 3 4 0.05 0.1 0.15 1 2 3 1 2 3 4 1 2 3 50 100 150 mean= mean=2.00 mean=0.03 mean=1.10 mean=1.00 mean=1.50 Prior MLE – COV=0.30 COV=0.30 COV=0.50 COV=0.30 COV=0.30 COV=0.30 Note: To provide the forecast for each time window, the observation history, seq,comprisesallthe events form To up to Tstart with M≥Ml. For the first forecasting interval (Tstart=12/11/2017‐21:00, i.e., 2 hours and 42 minutes after the main event) , the seq includes exactly 28 events with M≥2.5. EGU21-15824 Starting Point Methodology Application Conclusion Seismicity forecasting The forecasted seismicity maps (98% confidence interval) for the number of events with M≥Ml; the earthquakes within the corresponding forecasting interval are illustrated as coloured dots (distinguished by their magnitudes) + main event of Mw7.3. 103 Theobserved(greenstar)vs.forecasted 92 number of events (error‐bar format) with 79 71 th 64 M≥Ml: the median value (the 50 percentile) th 50 marked with a gray‐filled square; the 16 and 84th percentiles (marked with blue numbers); the 2nd and 98th percentiles (marked with red numbers). PM m1exp E Nxym ,,seq , M dd xy l xy, A The first seismicity forecasting map shows 9 hours forecasting starting 2 hours and 42 minutes after the main event. EGU21-15824 Starting Point Methodology Application Conclusion Seismicity forecasting 61 73 55 61 49 53 43 41 50 34 39 32 The second seismicity forecasting map shows 6 The third seismicity forecasting map shows 24 hours forecasting starting 5 hours and 42 minutes hours forecasting starting around 12 hours after after the main event. the main event. EGU21-15824 Starting Point Methodology Application Conclusion Simplifications within the robust seismicity forecasting framework ETAS model parameter K is estimated by a closed‐form expression in method a, where the restricted condition that No events took place in the aftershock zone at the time of starting the forecast is satisfied for individual generated samples I is solved Proposed r Calculate K (method a) numerically Method Integral over the whole aftershock zone A: Semi-Fast Calculate K (method a) Method ddx y r Approximated with I that 22q xy, A rd is over infinite space; thus, I 1 Learn K through the Fast Bayesian Updating Method (method b) Relaxing the calculation of the spatial contribution of ETAS model over the whole aftershock zone I (i.e., assuming I 1), which manifests itself both in the likelihood estimation for drawing the samples as well as generating the sequence seqg. EGU21-15824 Starting Point Methodology Application Conclusion Simplifications within the robust seismicity forecasting framework EGU21-15824 Starting Point Methodology Application Conclusion Discussion on the effect of considering the integration over the whole aftershock zone (1) The first forecast, which might be the most important one (while less observed data is available at the time of forecasting), has higher dispersion and lower median by relaxing the estimation of I . This increase can mainly be attributed to the increase to some extent in the rate of rejection of samples through MCMC procedure. This is a key issue as there might be particular cases (not observed here in this case study), where this approximation results in biased estimates. (2) As the sequence evolves, the difference between to two methods becomes negligible. This observation has been also made in Schoenberg (2013), where the assumption of an infinite spatial domain was shown to have negligible effect on likelihood. (3) As a general observation within the five forecasting intervals in Table 3, the time of conducting the Semi‐Fast method is around 75% of the required time for performing Proposed method. Thus, Semi‐Fast method can be used to reduce the computational cost of calculating I , knowing that it may not be reliable for early forecasts after the occurrence of a main event. EGU21-15824 Starting Point Methodology Application Conclusion Discussion on the effect of calculating K (1) For the first and foremost forecasting interval, Fast method did not properly manage to capture the number of events. This is mainly due to the lack of observed data used for learning parameter K through MCMC procedure within the Fast method (note that ETAS model parameters has 7 variables in this method). Thus, K becomes quite sensitive to the choice of the prior (i.e., non‐informative prior does not work properly and the informative prior forces the posterior distribution of K to follow similar trend to prior). This is by no means a trivial problem and may cause significant underestimation in the early forecasts (as can be seen in the first column of Fast method in Table 3). (2) As the sequence evolves, the forecasts issued by the Fast method become more similar to those obtained by Semi‐Fast method (and consequently the Proposed method). This is an interesting observation showing that Fast method is reliable as the sequence evolves. (3) Similar to Semi‐Fast method, this method is also exposed to high rate of sample rejections through MCMC procedure which may lead to biased estimates. (4) The time of conducting the Fast method is less than 50% of the required time for performing Semi‐Fast method, making the procedure appealing (not reliable for early forecasts after the occurrence of a main event). EGU21-15824 Starting Point Methodology Application Conclusion Final Remarks It is recommended to do the Proposed method at least for early forecasts. As the sequence evolves, it is possible to do the Fast (or even the Semi‐Fast) methods. We observe that after an initial transition time (in the order of few hours to accumulate enough events for updating the model parameters), the model quickly and automatically tunes into the sequence and provides forecasts that are reliable in most cases (the observed number of events are within plus/minus one standard deviation of the distribution provided by the robust framework). The Proposed method is quite efficient, and the most challenging first forecast (2 hours and 42 minutes after the main event) is performed around 40 minutes on a normal PC. Moreover, the model updating and forecasting procedure is carried on without human interference and use of expert judgement. We have proposed a fully simulation‐based procedure for both Bayesian updating of ETAS model parameters and robust operational forecasting of the number of events of interest expected to happen in each forecasting time frame. The robust seismicity forecasting framework herein is conditioned on the available catalogue of events and the epidemiological model adopted for capturing the spatio‐temporal aftershock clustering. EGU21-15824 Thank you for your attention! vEGU21: Gather Online | 19 – 30 April 2021