Tsunami Waveform Inversion based on Oceanographic Radar Data

Transcription

1 Research Institute for Applied Mechanics Workshop of Oceanographic Radar December Tsunami Waveform Inversion based on Oceanographic Radar Data Ryotaro Fuji 1), Hirofumi Hinata 1), Tomoyuki Takahashi 2) 1) National Institute for Land and Infrastructure Management 2) Faculty of Safety Science, Kansai University

2 Today s Topic 2 Tsunami Waveform Inversion Which is to guess Tsunami Initial Sea Surface Elevation (SSE) by using Oceanographic Radar Data >>>Background We had 2 problems on 2011 Japan Tsunami 1 Delay of resident s evacuation 2 Delay of rescue activities by governments Causes 1 First guess of Tsunami warning was underestimated 2 Government offices of themselves were largely damaged, took much time to identify extremely damaged area

3 Aim of Research 3 Time duration Earthquake happens Tsunami attack to coast 24 hours time (For evacuation) 1Tsunami detection (For rescue activities) 2Identification of extremely damaged area Estimation of Tsunami Initial SSE We start research from second problem We try to identify extremely damaged area within 24 hours just after earthquake happens For that reason We aim to get Tsunami source information (initial SSE) much accurately by inversion technique

4 Current Tsunami Warning System in Japan 4 Estimate initial SSE (Sea Surface Elevation) from seismic wave information, not observed Tsunami wave itself Seismometer Predict (Tsunami propagation cal) Tsunami source (initial SSE) Sea Surface Elevation Estimate 3 Estimate 1 Sea bottom movement Estimate 2 Dislocation movement >>> Technical Issues <<< It is well known that Tsunami prediction may be underestimated especially for huge earthquake, Tsunami earthquake in case Tsunami initial SSE is disproportioned

5 Previous Studies 5 Tsunami Inversion (with GPS or Coastal wave gauge data) (e.g. Yasuda et al. (JSCE, 2006, 2007), Tatsumi et al. (JSCE, 2008, 2009)) We use time series of wave height data observed by GPS wave gauge or Coastal wave gauge Applying linear long wave theory to Tsunami 1Calculate unit Tsunami 2Calculate unit fault amplitude by least-squares method (minimize error between observed and unit Tsunami) 3 Tsunami Initial SSE is given as Sum of unit fault amplitude Disadvantage of GPS or CGW Installed number is not enough to conduct for Tsunami inversion As for GPS wave gauge, initial and running costs are much higher than those for radar 0km Pacific Ocean GPS wave gauge Coastal wave gauge 500km

6 Our Research 6 Tsunami Inversion (with observed Radar radial velocity) Tsunami current velocities induced by the 2011 Japan Tsunami have been successfully observed by Radars (e.g. Hinata et al. (ECSS, 2011), Lipa et al. (Remote Sensing, 2011), Helzel ( Spatial resolution of Oceanographic Radar is much better compared to those of GPS wave gauge or CWG great advantage for Tsunami Inversion We are trying to develop Tsunami Inversion method using Radar radial velocity 2011/3/11 18:13 50 (cm/s) Inversion by using Radar Tsunami Initial SSE Tsunami source area

7 Procedure of Inversion 7 Applying linear long wave theory to Tsunami motion Calculate unit fault amplitude by least squares method Tsunami Initial SSE is given as Sum of unit fault amplitude *In case, unit response function is water surface p1 1: 2: time, fault unit No. time (1) Divide entire Tsunami source area into some unit fault pieces Land (3) Carry out unit Tsunami calculation (Get time series of water surface at observation sites, p1, p2 pn) Tsunami source area (2) Give 1m water surface rise to each unit faults Shore line pn (4) Carry out Inversion (least-squares method) Inversion analysis (least-squares method) Coefficient a (Amplitude) (5) Finally, get Tsunami initial SSE a gives Tsunami initial SSE

8 8 Numerical Experiment (2011 Japan Tsunami)

9 Numerical Experiment, Tohoku Area Japan 9 We carried out 2 cases of inversion, using data are as follows: Case1 : Radar 2sites, radial velocity, sampling interval : 10sec Case2 : Radar 2sites, radial velocity, 2min average, sampling interval : 1min corresponding to practical Radar observation Tsunami Calculation area 500 km Unit faults:760 (15 km 15 km) STEP 1 Calculation of unit Tsunami (760 unit faults) Output data (stocked) at Radar site :Radial velocity Government equation:linear long wave equation Tsunami initial SSE GPS1 from Fujii Satake ver 4.2 fault model GPS2 STEP 2 STEP 3 STEP 4 Spatial resolution:1 km Calculation time step:2 sec Unit fault size:15 km 15km Tsunami source area:300 km 600 km (760 unit faults) Making of observation data (Velocity) Calculate Tsunami initial SSE applying Fujii Satake ver4.2 fault model Calculate Tsunami propagation applying estimated Tsunami initial SSE Calculation conditions and output data are the same as STEP 1 Tsunami wave form inversion Calculate Tsunami initial SSE by least-squares method Data sampling interval : 2 hour (for identify extremely damaged area) Validation (Error estimation) Calculate Tsunami propagation for 6 hours applying estimated Tsunami initial SSE in STEP 3 Compare calculated SSE (STEP3 result and STEP 2 result) at the sites ( ) 900 km Tokyo Sendai GPS6 GPS3 GPS4 GPS5 Spatial resolution in radial direction is 1.5km Pacific Ocean 300 km GPS wave gauge (actual site) Radar (virtual site):2 sites, 576 data sites for verification about SSE 600 km Tsunami source area

10 Distribution of Tsunami Initial SSE True initial SSE (Fujii Satake ver4.2 fault model) 1Radar Radial Velocity (sampling interval : 10 sec) 2Radar Radial Velocity (2 min average, sampling interval : 1 min) 10 RMS error 1 2 RMSE (m) RMSE/maximum wave height (True value) (%)

11 Time Series of Wave Height 11 Data sampling 120 min (for inversion) GPS1 Prediction 360 min Tsunami Calculation area 500 km Unit faults:760 (15 km 15 km) GPS2 GPS1 GPS2 GPS3 GPS3 GPS4 GPS5 900 km Sendai GPS4 GPS5 600 km Tsunami source area GPS6 GPS6 120min 240min 360min Radar Radial Velocity (sampling interval : 10 sec) Radar Radial Velocity (2 min average, sampling interval : 1 min) True Wave Height Tokyo Pacific Ocean 300 km GPS wave gauge (actual site) Radar (virtual site):2 sites, 576 data sites for verification about SSE

12 Time Series of Wave Height 12 Variance Reduction* This value shows agreement (concordance rate) of wave height between observation and prediction Variance Reduction (%) Tsunami Calculation area 500 km GPS1 Unit faults:760 (15 km 15 km) st1 GPS2 *NIED (2008) : As for seismic wave, this value is used to assess quality of seismic moment tensor solution GPS1 Radar Radial Velocity st8 (sampling interval : 10 sec) st9 Radar Radial Velocity (2 min average, sampling interval : 1 min) st2 GPS2 st3 GPS3 st4 GPS4 st5 GPS5 st6 st7 GPS6 (VR for 6 hours) 900 km Tokyo Sendai GPS6 GPS3 GPS4 GPS5 Pacific Ocean 300 km GPS wave gauge (actual site) Radar (virtual site):2 sites, 576 data sites for verification about SSE 600 km Tsunami source area

13 Questions? 13 We would like to know How we decide optimum number and location of Oceanographic Radar for estimation of Tsunami initial SSE What is the required specification of Radar for Tsunami inversion? Now we are trying on to answer these questions thorough idealized experiments

14 Aim of Experiment 14 We would like to know about Effect of these conditions on Tsunami Inversion (1) Location of Radar site (2) Spatial resolution of Radar velocity (3) Temporal average and data sampling interval No Average Spatial Average North Middle Tsunami calculation mesh Tsunami calculation mesh Geographical mean Fault Region Tsunami source area points for Inversion No Average --- Sampling interval 10 sec points for Inversion Temporary Average 2 min moving average Sampling interval 1 min Shore Line Corresponding to practical Radar

15 Experiment Conditions 15 Geometry : 1/100 bottom slope Fault Model rise : 3 m, 2 m, 1 m Tsunami calculation spatial resolution : 1 km time step : 2 sec unit fault size : 10 km 10 km calculation period : 2 hour Radar location : North, Middle, Inversion conditions data sampling period : 40min, 60min using data : Radar radial velocity North Middle Rise : 1m Unit faults:360 (10 km 10 km) 120km Fault region Rise : 2m 300km Tsunami source area 540km Rise : 3m shore line 350km

16 16 Inversion Result influences of Radar Location

17 st8 Inversion Result 1 (Radar Location) (1) Radar location : (2) Spatial average : No (3) Sampling interval : 10 sec Estimated Initial SSE Data sampling period : 40min Time first wave reach coast RMSE (m) st7 st6 st5 st4 st3 st2 3m 0m -1m Variance Reduction (%) St St St St St St St St St (6 hours)

18 North Middle Inversion Result 2 (Radar Location) (1) Radar location : Middle, North (2) Spatial average : No (3) Sampling interval : 10 sec st8 st7 st6 st5 st4 st3 st2 st8 st7 st6 st5 st4 st3 st2 40min 3m 0m -1m 60min Data sampling period : 40min, 60min 60min RMSE (m) Variance Reduction (%) St St8 good 98.7 St St St5worse26.1 St St St good St min RMSE (m) Variance Reduction (%) St St St St St St4 0.0 St St St (6 hours) North (6 hours) 18 Middle

19 Inversion Result 3 (Radar Location) Variance Reduction Variance (%) st9 St9 st8 St8 M2 North (60min) M2 (60min) st7 St7 st6 St6 M2 M1 Middle (60min) M1 (60min) st5 St5 st4 St4 M1 (40min) st3 St3 st2 St2 st1 St1

20 20 Inversion Result influences of Spatial and Temporal Averaging

21 st8 Inversion Result 4 (Spatial Averaging) (1) Radar location : (2) Spatial average : Yes (3) Sampling interval : 10 sec Estimated Initial SSE Data sampling period : 40min RMSE (m) (0.069) 21 st7 Variance Reduction (%) (6 hours) st6 st5 Still good compared to no spatial averaging results St (81.1) St (83.4) St (90.8) St (98.9) st4 3m St (99.9) St (99.0) st3 0m St (91.8) St (83.8) st2-1m St (81.8) ( ) :, No Spatial Average

22 Inversion Result 5 (Spatial and Temporal Averaging) 22 st8 (1) Radar location : Data sampling period : 40min (2) Spatial average : Yes (3) 2min Temporal average, Sampling interval : 1 min Estimated Initial SSE RMSE (m) (0.069) st7 Variance Reduction (%) (6 hours) st6 st5 Become worse compared to previous result (spatial average) St (30.6) St (67.9) St (87.9) St (95.4) st4 3m St (99.8) St (96.0) st3 0m St (86.9) St (69.2) st2-1m St (31.3)

23 Inversion Result 9 (Spatial and Temporal Averaging) Influences of Influences of Spatial Average Radar Combination Temporal Average st9 St9 st8 St8 Variance Variance Reduction (%) No Spatial Average Sampling Interval : 10sec () significantly recovered around the Middle-North Spatial Average Sampling Interval : 10sec () Spatial Average 2min Temporal Average, Sampling interval : 1min () Spatial Average 2min Temporal Average, Sampling interval : 1min ( + Middle) Spatial Average 2min Temporal Average, Sampling interval : 1min ( + North) Spatial Average 2min Temporal Average, Sampling interval : 1min ( + Middle + North) st7 St7 st6 St6 st5 St5 st4 St4 st3 St3 st2 St2 st1 St1

24 Conclusion and Future Study 24 Through this study... Temporal averaging process largely affects inversion results compared to spatial averaging process Although Variance Reductions decrease due to temporal averaging process, maximum wave heights and their appearance time seem to agree well (As for Radar, it seems necessary to get high resolution data for Tsunami waveform inversion) We would like to evaluate these influences quantitatively We are trying to reveal the mechanism of these influences in terms of Energy Flux and Wave Ray Also we are considering to estimate influences of red / white noise etc.

25 Backup Slides 25

26 Application of Oceanographic Radar 26 Oceanographic Radar Practical Radial velocity Wide area Verification Observe (Radial velocity) GPS wave gauge In operation SSE Point data Propagating Tsunami Continental shelf Guess (inverse technique) Tsunami source (initial SSE)

27 st8 Inversion Result 6 (Spatial and Temporal Averaging) (1) Radar location : + Middle Data sampling period : 40min (2) Spatial average : Yes (3) 2min Temporal average, Sampling interval : 1 min Estimated Initial SSE RMSE (m) (0.069) 27 st7 Middle st6 st5 Variance Reductions are recovered around the Middle Variance Reduction (%) St (0.00) St (0.00) St (0.00) St (73.8) (6 hours) Middle st4 3m St (97.6) St (68.5) st3 0m St (0.00) St (0.00) st2-1m St (0.00) ( ) : Spatial & Temporal Average

28 North st8 Inversion Result 7 (Spatial and Temporal Averaging) (1) Radar location : + North Data sampling period : 40min (2) Spatial average : Yes (3) 2min Temporal average, Sampling interval : 1 min Estimated Initial SSE RMSE (m) (0.069) 28 st7 Variance Reduction (%) (6 hours) st6 st5 Variance Reductions are recovered around the North St9 2.4 (0.00) St (0.00) St7 4.8 (0.00) St (73.8) North st4 3m St (97.6) St (68.5) st3 0m St (0.00) St (0.00) st2-1m St (0.00) ( ) : Spatial & Temporal Average

29 North st8 Inversion Result 8 (Spatial and Temporal Averaging) (1) Radar location : + Middle + North Data sampling period : 40min (2) Spatial average : Yes (3) 2min Temporal average, Sampling interval : 1 min Estimated Initial SSE RMSE (m) (0.069) 29 st7 Middle st6 st5 st4 3m Variance Reductions are significantly recovered around the Middle - North Variance Reduction (%) St (0.00) St (0.00) St (0.00) St (73.8) St (97.6) St (68.5) (6 hours) North Middle st3 0m St (0.00) St (0.00) st2-1m St (0.00) ( ) : Spatial & Temporal Average

30 Wave Ray Calculation 30 Method : applying ray equation Ray emission : from 50 grids in fault region Ray emission angle : every 5 Total number of Ray : 3600 (50 grids 72 angles) Arrival time of the first wave : 40min Distribution of wave ray within 40min after ray emission North Middle 40min (Fastest) Fault Region Ray Emission : 3600 (50 72) 50km 100km Tsunami source area

31 Wave Ray Calculation 31 Number of ray reach Rader observation area (at a range of 50km from shoreline) North North North Middle Fault region Tsunami source area Middle Fault region Tsunami source area Middle Fault region Tsunami source area : 336 Middle : 254 North : 107 : Emission source of ray reached Radar area within 40 min