Participants of Nurmerical Benchmark Test and Misfit Criteria

for Summarizing the Results

Participants of Nurmerical Benchmark Test and Misfit Criteria

for Summarizing the Results

Seiji Tsuno (LGIT)Seiji Tsuno (LGIT)

ParticipantsParticipants  Method Case Participants

1 1D(+Nonlinear) FS fabian bonilla

2 1D FS pacific engineering

3 2D S1, S2 corinne lacave

4 2D S1, S2, W1, W2 delepine

5 2D FS pacific engineering

6 3F S1, S2, W1, W2 hideo aochi

7 3F S1, S2, W1, W2 moczo

8 3F S1, S2, W1, W2 s1642006

9 3T S1, S2, W1, W2 louie

10 3T FS stupa

11 EM S1, S2 carine sansorny

12 EM S1, FS javier ruiz

13 EM S1, FS mathieu causse

14 2D(Nonlinear)   fabian bonilla

15 3T   emmanuel chaljub

16 3T   martin

17 3F   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

OutputOutput

# 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.

Misfit criteriaMisfit 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.

Quantitative measure of the goodness-of-fit of synthetic seismograms

Proposed by John G. Anderson(13th World Conference on Earthquake Engineering )

Quantitative measure of the goodness-of-fit of synthetic seismograms

Proposed by John G. Anderson(13th 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.

CriteriaCriteria

Goodness of fit measurements Frequency bands used (Hz)• C1 Arias Duration B1 0.05 – 0.1• C2 Energy Duration B2 0.1 – 0.2• C3 Arias Integral B3 0.2 – 0.5• C4 Energy Integral B4 0.5 – 1.0• C5 Peak Acceleration B5 1.0 – 2.0• C6 Peak Velocity B6 2.0 – 5.0• C7 Peak Displacement B7 5.0 – 10.0• C8 Response Spectra B8 10.0 – 20.0• C9 Fourier Spectra B 20.0 – 50.0• C10 Cross Correlation B10 0.05 – 50.0

The similarity score (S1) is averaged by all fit criterion.

Example (application)Example (application)

Time (sec)

Acc

. (c

m/s

ec2 ) NS

0 20 40 60 80 100-400

-200

0

200

400

Time (sec)

Acc

. (c

m/s

ec2 ) EW

0 20 40 60 80 100-400

-200

0

200

400

Fig. Acceleration records of NS and EW components at PS10

PS10

Fig. Fourier spectra for acceleration records at

PS10

Fou

rier

sp

ectr

a

Frequency (Hz)

NS EW

0.1 1 101

10

100

1000

Where PS10 is 3km from the fault In the M7.9 Denali Fault, Alaska, earthquake of Nov. 3, 2002.

Individual scores -1Individual scores -1

Frequency Band (B1-10)

C1

Sim

ilarit

y sc

ore

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C2

Sim

ilarit

y sc

ore

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C3

Sim

ilarit

y sc

ore

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C4

Sim

ilarit

y sc

ore

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C5

Sim

ilari

ty s

core

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C6S

imila

rity

scor

e

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Individual scores -2Individual scores -2

Frequency Band (B1-10)

C7S

imila

rity

sco

re

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C8

Sim

ilari

ty s

core

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C9

Sim

ilarit

y sc

ore

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

C10

Sim

ilarit

y sc

ore

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Similarity scoreSimilarity score

Frequency Band (B1-10)

S2

Sim

ilari

ty s

core

0 1 2 3 4 5 6 7 8 9 10 11

123456789

10

Frequency Band (B1-10)

Bias

Bia

s

0 1 2 3 4 5 6 7 8 9 10 11-2

-1

0

1

2

S1 = 6.9811296

Definition of familiar functionDefinition of familiar function

min(p1, p2) = 100 min(p1, p2) = 50 min(p1, p2) = 25

(p1-p2)

S(p

1, p

2)

S(p1,p2) = 10exp{-[(p1-p2)/min(p1,p2)]**2}

0 40 80 120 160 200

1

2

3

4

5

6

7

8

9

10

(p1-p2)/min(p1,p2)

S(p

1,

p2

)

(0.47,8.01797)

(1.27,1.99309)

0 0.5 1 1.5 2 2.5 3

1

2

3

4

5

6

7

8

9

10

Fig. Definitions of function related to similarity score

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

Misfit criteria for quantitative comparison of seismograms

Proposed by Miriam Kristekova. et al.(Submitted to BSSA, January 2006)

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.

CriteriaCriteria

Misfit CriteriaTFEM - Time-frequency envelope misfitTFPM - Time-frequency phase misfitTEM - Time-dependent envelope misfitTPM - Time-dependent phase misfitFEM - Frequency-dependent envelope misfitFPM - Frequency-dependent phase misfitEM - Single-valued envelope misfitPM - Single-valued phase misfit

The single-value about EM, PM is obtained.

Exemple (application) -reproducedExemple (application) -reproduced

Time (sec)

Acc

. (c

m/s

ec2 ) NS

0 20 40 60 80 100-400

-200

0

200

400

Time (sec)

Acc

. (c

m/s

ec2 ) EW

0 20 40 60 80 100-400

-200

0

200

400

Fig. Acceleration records of NS and EW components at PS10

PS10

Fig. Fourier spectra for acceleration records at

PS10

Fou

rier

sp

ectr

a

Frequency (Hz)

NS EW

0.1 1 101

10

100

1000

PS10 where is 3km from the fault In the M7.9 Denali Fault, Alaska, earthquake of Nov. 3, 2002.

Continuous wavelet transform (CWT)

Continuous wavelet transform (CWT)

Time (sec)

Acc

. (c

m/s

ec2 ) NS

0 20 40 60 80-400

-200

0

200

400

5sec shifted early in each result

Misfit Criteria -1Misfit Criteria -1

TFEM - Time-frequency envelope misfit

TFPM - Time-frequency phase misfit

Misfit Criteria -2Misfit Criteria -2

Time (sec)

Pe

r.

TEM

PS10

0 20 40 60 80-100-80-60-40-20

020406080

100

Time (sec)

Pe

r.

TPM

PS10

0 20 40 60 80-100-80-60-40-20

020406080

100

Frequency (Hz)

Pe

r.

FEM

PS10

0.1 1 10-100-80-60-40-20

020406080

100

Frequency (Hz)

Pe

r.FPM

PS10

0.1 1 10-100-80-60-40-20

020406080

100

Time-dependent envelope misfit

Time-dependent phase misfit

Frequency-dependent envelope misfit

Frequency-dependent phase misfit

Misfit scoreMisfit score

EM PM RMS70.9535 46.1713 133.382

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