1. Participants of Nurmerical Benchmark Test and Misfit Criteria for Summarizing the Results Seiji Tsuno (LGIT)

2. Participants MethodCaseParticipants 11D(+Nonlinear)FSfabian bonilla 21DFSpacific engineering 32DS1, S2corinne lacave 42DS1, S2, W1, W2delepine 52DFSpacific engineering 63FS1, S2, W1, W2hideo aochi 73FS1, S2, W1, W2moczo 83FS1, S2, W1, W2s1642006 93TS1, S2, W1, W2louie 103TFSstupa 11EMS1, S2carine sansorny 12EMS1, FSjavier ruiz 13EMS1, FSmathieu causse 142D(Nonlinear) fabian bonilla 153T emmanuel chaljub 163T martin 173F robert graves FS: at station OGFH (borehole location) for a Mw=6.0 strike-slip event occuring on the Eastern part of the Belledonne Border Fault

3. Output # Waveforms (Acceleration, velocity and displacement) # Fourier spectra # Response spectra (Pseudo-velocity response spectra; h=5%) # Maximum value of acceleration, velocity and displacement # Misfit criteria (Anderson’s method & Kristekova’s method) # Spectral ratio (for reference site;OGMU or of bore-hole;OGFB) # Standard deviation error and RMS misfit in each output.

4. Misfit criteria # We will evaluate the results estimated by participants, using the misfit criteria proposed by J. Anderson and M. Kristekova. # Mainly, J. Anderson and M. Kristekova evaluated the performance of the proposed misfit-criteria by horizontal components of observed earthquake records and canonical signals, respectively. But… # In this numerical benchmark, we can compared many theoretical seismograms estimated by participants with observation.

5. Quantitative measure of the goodness-of-fit of synthetic seismograms Proposed by John G. Anderson (13 th World Conference on Earthquake Engineering ) # He calibrated the proposal criterion, using two components of synthetic seismograms with 1000 pairs and observations with 1165 pairs. # And also, he applied this measurement system to two horizontal components of a single station recording the M8.1 Michoacan earthquake. # Lastly, this criterion was applied to a blind prediction of ground motions at a station PS10 for comparison of observation with synthetic seismograms.

6. Criteria Goodness of fit measurementsFrequency bands used (Hz) C1 Arias DurationB1 0.05 – 0.1 C2 Energy DurationB2 0.1 – 0.2 C3 Arias IntegralB3 0.2 – 0.5 C4 Energy IntegralB4 0.5 – 1.0 C5 Peak AccelerationB5 1.0 – 2.0 C6 Peak VelocityB6 2.0 – 5.0 C7 Peak DisplacementB7 5.0 – 10.0 C8 Response SpectraB8 10.0 – 20.0 C9 Fourier SpectraB 20.0 – 50.0 C10 Cross CorrelationB10 0.05 – 50.0 The similarity score (S1) is averaged by all fit criterion.

7. Example (application) Fig. Acceleration records of NS and EW components at PS10 PS10 Fig. Fourier spectra for acceleration records at PS10 Where PS10 is 3km from the fault In the M7.9 Denali Fault, Alaska, earthquake of Nov. 3, 2002.

8. Individual scores -1

9. Individual scores -2

10. Similarity score S1 = 6.9811296

11. Definition of familiar function Fig. Definitions of function related to similarity score Fig. Definitions of function related to similarity score (normalized)

12. Misfit criteria for quantitative comparison of seismograms Proposed by Miriam Kristekova. et al. (Submitted to BSSA, January 2006) # The proposal criteria are based on the time-frequency representation (TFR) of the seismograms obtained as the continuous wavelet transform (CWT) with the analyzing Morlet wavelet. # They tested properties of the misfit criteria using canonical signals, which were specifically amplitude, phase-shift, time-shift, and frequency modified. # And also, they calculated the misfit criteria for four different numerical solutions for a single layer over half-space (the SCEC LOH.3 Problem) and the reference FK (frequency-wavenumber) solution.

13. Criteria Misfit Criteria TFEM -Time-frequency envelope misfit TFPM -Time-frequency phase misfit TEM - Time-dependent envelope misfit TPM - Time-dependent phase misfit FEM - Frequency-dependent envelope misfit FPM - Frequency-dependent phase misfit EM - Single-valued envelope misfit PM - Single-valued phase misfit The single-value about EM, PM is obtained.

14. Exemple (application) -reproduced Fig. Acceleration records of NS and EW components at PS10 PS10 Fig. Fourier spectra for acceleration records at PS10 PS10 where is 3km from the fault In the M7.9 Denali Fault, Alaska, earthquake of Nov. 3, 2002.

15. Continuous wavelet transform (CWT) 5sec shifted early in each result

16. Misfit Criteria -1 TFEM -Time-frequency envelope misfit TFPM -Time-frequency phase misfit

17. Misfit Criteria -2 Time-dependent envelope misfit Time-dependent phase misfit Frequency-dependent envelope misfit Frequency-dependent phase misfit

18. Misfit score EM PMRMS 70.9535 46.1713133.382 STATION CODE EM PM RMS PS09-Alaska 63.7143 61.6312 143.93608 PS10-Alaska 70.9535 46.1713 133.38204 PS11-Alaska 64.3263 63.8550 145.66619 FA02-Alaska 73.9071 57.9291 165.12640 STATION CODE SIMILARITY SCORE(S1) M PS09-Alaska 7.1210961 7.9 PS10-Alaska 6.9811296 7.9 PS11-Alaska 7.1379919 7.9 FA02-Alaska 6.4276643 7.9