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Abrahamson EPRI background sigmaWorkshop

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Abrahamson EPRI background sigmaWorkshop Powered By Docstoc
					Sigma - Background

  Norm Abrahamson
    Sep 30, 2009
            Sigma for CEUS
• EPRI (2006)
  – Truncation of log-normal distribution
  – Evaluation of Application of NGA sigma to
    CEUS
• Rhoades (2008)
  – Deviation from log-normal for the upper tail
                                        PGA Standard Deviation
Total Standard Deviation (LN units)
                                       1
                                           WUS vs CEUS
                                      0.9

                                      0.8

                                      0.7

                                      0.6

                                      0.5

                                      0.4

                                      0.3
                                              A&S 9 7 - PGA
                                      0.2
                                              Sadigh e al 1 997
                                      0.1     Toro et al 97 - PGA (Rjb >20 km)
                                              Toro et al 97 - PGA (Rjb <5 km)
                                       0
                                        4.5   5          5.5          6          6.5   7   7.5   8
                                                                    Magnitude
2005 versions of NGA Models for WUS
        Show Constant Sigma
                                        1
 Total Standard Deviation (LN units)

                                       0.9

                                       0.8

                                       0.7

                                       0.6

                                       0.5

                                       0.4

                                       0.3
                                               A&S 9 7 - PGA
                                       0.2
                                               Sadigh e al 1 997
                                       0.1     NGA - A&S 2005


                                        0
                                         4.5   5          5.5      6      6.5   7   7.5   8
                                                                   Magnitude
                                        EPRI (2004) models and AS
                                           NGA (2005 version)
                                1.2
                                                                                                         1.2
Standard Deviation (ln units)




                                                                         Standard Deviation (ln units)
                                 1
                                                                                                          1


                                0.8                                                                      0.8


                                0.6                                                                      0.6

                                         EPRI M1 (M5, R5)                                                        EPRI M1 (M6, R10)
                                0.4      EPRI M2                                                         0.4     EPRI M2
                                         EPRI M3                                                                 EPRI M3
                                0.2      EPRI M4                                                         0.2     EPRI M4
                                         NGA (A&S 2005)                                                          NGA (A&S 2005)

                                 0                                                                        0
                                  0.1        1                      10             100                     0.1       1                      10   100
                                                   Frequency (Hz)                                                          Frequency (Hz)
EPRI (2004) models and AS
   NGA (2005 version)
                                   1.2


   Standard Deviation (ln units)
                                    1


                                   0.8



                                   0.6


                                           EPRI M1 (M7, R30)
                                   0.4
                                           EPRI M2
                                           EPRI M3
                                   0.2
                                           EPRI M4
                                           NGA (A&S 2005)
                                    0
                                     0.1         1                    10   100
                                                     Frequency (Hz)
Depth Effects on Rjb-Based
         Models



          Standard Deviation (LN Units)
                                           1
                                          0.9
                                          0.8
                                          0.7
                                          0.6
                                          0.5
                                          0.4
                                          0.3
                                          0.2
                                          0.1       Toro et al Model, M=5.5 PGA

                                           0
                                                1             10                  100
                                                            Rjb (km)
Rjb-Based residuals
Flinn-Engdahl regionalization




Red = active
Blue = Oceanc
Yellow = Stable
Green = Classified Stable but considered active or oceanic
             Half Durations
   Region          N      Std dev of half
                           duration (ln
                              units)
    Active        499      0.30 ± 0.01

Stable subset 1    81         0.29 ± 0.02

Stable subset 2    59         0.27 ± 0.02

Stable subset 3    39         0.25 ± 0.03
Additional Source Parameters in
         NGA models
• NGA has additional parameters
  – Style-of-faulting
  – Hanging wall / foot wall
• Small impact on total std dev
  – Increase by less than 0.01 if these are ignored
        Path Term Variability
• Effects of Crustal Structure differences
  – Used Simulations for range of crustal structures
  – Compared std dev of resulting ground motions
Comparison of velocity structures
Stations used for Simulations
SCR Simulations
WUS Simulations
  Std Dev for Path Effects
           Active      Stable
 PGA        0.20        0.16
25 Hz       0.21        0.17
10 Hz       0.23        0.17
 5 Hz       0.23        0.21
 2 Hz       0.21        0.20
 1 Hz       0.33        0.30
0.5 Hz      0.33        0.28
Site Term Variability

                F=25 Hz Std Dev for
                Hard -rock (0.55) is
                larger than for soft-rock
                (0.51)

                5-10 hz for soft-rock
                is 0.55 - 0.65
Std Dev from Stress-Param
       Variability

                    High Freq
                    Inter-Event
                    Std Dev = 0.43

                    Compared to NGA
                    values of 0.4
           EUS Sigma Models
• Intra-Event Std Dev (R>20 km)
  – NGA models considered to be applicable with
    following modifications
     • Increase the std dev to account for source parameters included
       in NGA that are not available for CEUS (0.01 units)
     • Increase std dev at high frequencies to account for freq content
       difference
  – Alternative models
     • More homogeneous crust in CUES (reduce 0.03 units)
     • No reduction
          EUS Sigma Models
• Inter-Event Std Dev models
  – NGA models are applicable without change based on
    teleseismic comparison
  – Use std dev from point-source stress parameters
    distribution
            EUS Sigma Models
• Intra-Event Standard Deviation at Short distances
   – No increase
   – Some Increase
      • Based on trends from European data
   – Increase Increase
                                   EPRI (2006) model R>20 km
                           0.9

                           0.8
Total Std Dev (Ln units)




                           0.7

                           0.6

                           0.5

                           0.4

                                     model 1a (NGA tau, NGA sigma, wt=0.42)
                           0.3
                                     model 1b (pt source tau, NGA sigma, wt=0.28)
                           0.2       model 1c (NGA tau, reduced sigma, wt=0.18)
                                     model 1b (pt source tau, reduced sigma, wt=0.12)
                           0.1

                            0
                            0.01      0.1              1                 10             100
                                                 Frequency (hz)
                                         Short Distance Sigma
                              0.25
                                          Adjustment Model
                                                                    Model 2A (wt=0.6)
Additional Sigma (ln units)




                                                                    Model 2B (wt=0.3)
                               0.2
                                                                    Model 2C (wt=0.1)



                              0.15




                               0.1




                              0.05




                                0
                                     0     5   10     15       20           25          30
                                                    Rjb (km)
                             Total Std Dev Models
                           0.9

                           0.8
Total Std Dev (Ln units)




                           0.7

                           0.6

                           0.5

                                   M1a - M2a        M1c - M2b
                           0.4
                                   M1b - M2a        M1d-M2b
                           0.3     M1c - M2a        M1a - M2c
                                   M1d-M2a          M1b - M2c
                           0.2
                                   M1a - M2b        M1c - M2c

                           0.1     M1b - M2b        M1d-M2c


                            0
                            0.01   0.1               1          10   100
                                               Frequency (hz)
                                        EPRI (2004) models and AS
                                           NGA (2005 version)
                                1.2
                                                                                                         1.2
Standard Deviation (ln units)




                                                                         Standard Deviation (ln units)
                                 1
                                                                                                          1


                                0.8                                                                      0.8


                                0.6                                                                      0.6

                                         EPRI M1 (M5, R5)                                                        EPRI M1 (M6, R10)
                                0.4      EPRI M2                                                         0.4     EPRI M2
                                         EPRI M3                                                                 EPRI M3
                                0.2      EPRI M4                                                         0.2     EPRI M4
                                         NGA (A&S 2005)                                                          NGA (A&S 2005)

                                 0                                                                        0
                                  0.1        1                      10             100                     0.1       1                      10   100
                                                   Frequency (Hz)                                                          Frequency (Hz)
      Mag Dependent Sigma?
• After EPRI (2006) study, some NGA
  models revised to use mag-dependent sigma
  – AS08, CY08, I08
  – Based on inclusion of aftershocks
   Standard Deviation
(RJB=30 km, VS30=760)
Rhoades et al (2008) Method
                               n
                               I yi  ln( z )
      Ratio (z ) n i 1
          1

                  i 1
                              
                   P yi  ln( z) yi , Ti
                                  ˆ                 

 



                       QuickTime™ and a
                         decompressor
                 are neede d to see this picture.
Problems Using Total Residuals
AS08 Model Using Intra-Event
        Residuals                                               1000
                                        Number of Exceedances          B


                                                                             B

                                                                                 B

                                                                100                        B

                                                                                                B
                                                                                                    B

                                                                                                        B


                                                                  10                                        B
                                                                                                                B
                                                                                                                    B
                                                                                                                        B
                                                                                                                            BB
                                                                                                                                 B
   Ratio of Actual to Expected Number




                                                                                                                                     BB
                                                                       0.1                                          1                               2
                                                                                       Peak Acc (g)

                                                                  3

                                                                 2.5
                                                                                                                                         B
                                                                  2                                                             BB


                                                                 1.5                                                                 B
                                                                                                                            B
                                                                                                                        B
                                                                  1    B     B   B        B    B    B   B
                                                                                                                    B
                                                                                                            B B
                                                                 0.5

                                                                  0                                                                          B BB
                                                                   0.1                                              1                               2
                                                                                     Spectral Acc (g)
                                                               AS08 Intra-Event std dev




                                                                                                                                                                                Ratio of Actual to Expected Number
Ratio of Actual to Expected Number




                                      3                                            B                3                                                                                                                  3                                                       3
                                               T=0.05                                  B                                                                                                                                        T=0.3
                                                                                   B                        T=0.075                         B                                                                                                                                          T=0.4
                                     2.5                                                           2.5                                                                                                                2.5                                                     2.5
                                                                                       B
                                                                                   B
                                      2                                                             2                                       B                                                                          2                                                       2
                                                                               B
                                     1.5                                                           1.5                                      B                                                                         1.5                                                     1.5
                                                                              BB                                                          B
                                                                         B BBB                                                      BBB B B                                                                                                                        B
                                                             B BBBB B
                                                                     B                                                                                                                                                                                         B BB B
                                                                                                                                                                                                                                                                 B
                                      1    B B B B B B B BBBB B BBBB           B                    1                      B
                                                                                                                          B BBB
                                                                                                         B B B B B B BBBBB BBBBBB B    BB                                                                              1    B B B B B B B BBBBB B BBB BB B BBBB B BB
                                                                                                                                                                                                                                               B BBBB                          1                                       B
                                                                                                                                                                                                                                                                                    B B B B B B BBBBB B BBB BB B BBBB B B
                                                                                                                                                                                                                                                                                                     B BBBB          B B
                                                                                                                                                                                                                                                                                                                         BBB
                                                                                                                                                                                                                                                                    B
                                                                                                                                                                                                                                                                    B                                                     BB B
                                                                                                                                                                                                                                                                    BB                                                       B
                                     0.5                                                           0.5                                                                                                                0.5                                            BB       0.5                                           BB
                                                                                                                                                                                                                                                                                                                             B




                                                                                                                                                         Ratio of Actual to Expected Number
Ratio of Actual to Expected Number




                                      0                                                    B        0                                           B                                                                      0                                                       0
                                      0.03          0.1              1                         3    0.03        0.1               1                 3                                                                  0.03           0.1               1                 3    0.03        0.1               1                   3
                                                    Spectral Acc (g)                                             Spectral Acc (g)                                                                                                      Spectral Acc (g)                                     Spectral Acc (g)

                                      3                                                              3                                                                                                                3                                                         3
                                                                                           B
                                     2.5       T=0.1                                               2.5      T=0.15                                                                                                   2.5        T=0.5                                         2.5      T=0.75
                                                                                        B
                                      2                                               B              2                                                                                                                2                                                         2
                                                                                      B
                                                                                        B
                                                                                     B
                                     1.5                                            BB             1.5                                                                                                               1.5                                                      1.5                                       BB
                                                                         B          B                                                            B                                                                                                                                                                  B
                                                                                                                                B BBBBBB B
                                                                                                                                        BB                                                                                                                                                                            B
                                                                                                                                                                                                                                                                                                                 BBB B B
                                                              B BBBBBB BB B
                                                               BBBB                B
                                                                                                         B B B B B B BBBBB BBBB B                                                                                     1      B B B B B B BBBB B BBBBBB B BBBBB B
                                                                                                                                                                                                                                             B BBBB           B
                                      1      B B B B B B BBBBB               B
                                                                           BB B
                                                                                                     1                    B BBBB                B                                                                                                               B               1   B B B B B B BBBB B BBBBBB B B
                                                                                                                                                                                                                                                                                                    B B BBB
                                                                               B                                                                B
                                                                                                                                            BBB
                                                                                                                                           BBB B                                                                                                                 B
                                                                                                                                                                                                                                                                  BB                                                     B
                                     0.5                                                           0.5                                        B                                                                      0.5                                          BBBB
                                                                                                                                                                                                                                                                   B B        0.5                                        B
                                                                                                                                                                                                                                                                     B                                                    B




                                                                                                                                                                                Ratio of Actual to Expected Number
                                                                                                                                                                                                                      0
Ratio of Actual to Expected Number




                                      0                                                              0                                                                                                                                                                B         0                                            B
                                      0.03          0.1               1                        3     0.03        0.1              1                  3                                                                0.03          0.1               1                   3     0.03        0.1              1                   3
                                                     Spectral Acc (g)                                            Spectral Acc (g)                                                                                                    Spectral Acc (g)                                       Spectral Acc (g)

                                      3                                                              3                                                                                                                 3                                                        3

                                     2.5       T=0.20                                              2.5      T=0.25                                                                                                    2.5       T=1.0                                         2.5      T=1.5

                                      2                                                              2                                                                                                                 2                                                        2

                                     1.5                                                           1.5                                                                                                                1.5                                         B
                                                                                                                                                                                                                                                                              1.5
                                                                           B                                                                                                                                                                             B
                                                                          B BB B                                                       B B                                                                                                                        B                                           B
                                      1      B B B B B B BBBBB BBBB BB BB
                                                              B BBBB
                                                                              BB                     1   B B B B B B BBBBB BBBB B BBBBB B BB B
                                                                                                                          B BBBB B       B BB B                                                                        1                      B B BB
                                                                                                                                                                                                                              B B B B B B BBBB B BBBBBB B B
                                                                                                                                                                                                                                                    B                           1   B B B B B B BBBB B BB
                                                                                                                                                                                                                                                                                                    B BB B
                                                                                 BB B B                                                     BB B
                                                                                                                                             B                                                                                                              BB B
                                                                                                                                                                                                                                                              B                                         BB B
                                                                                                                                                                                                                                                                                                         B
                                                                                   B BB                                                        B                                                                                                           B B                                             BB
                                                                                  BB B
                                                                                    B                                                                                                                                                                           B                                               B
                                     0.5                                                           0.5                                                                                                                0.5                                       B             0.5                              B
                                                                                                                                                                                                                                                                                                                 B

                                      0                                                              0                                                                                                                 0                                           B            0                                    B

                                      0.03          0.1               1                        3     0.03        0.1              1                  3                                                                 0.03           0.1              1                  3     0.03        0.1              1                   3
                                                     Spectral Acc (g)                                            Spectral Acc (g)                                                                                                     Spectral Acc (g)                                      Spectral Acc (g)
Standard Deviation
(M=7, VS30=270)
Ratio of Actual to Expected Number   Non-linear site effects
                                          T=0.15 sec
                                      2
                                     1.8     2   With Nonlinear Effects on Std Dev
                                     1.6     E   Without Nonlinear Effects on Std Dev
                                     1.4
                                     1.2                                                     2 2 22     2            2
                                                                                       2   2 E E E 222
                                      12
                                       E     E
                                             2   E E
                                                 2 2    E
                                                        2   2 2 2 2 2 2 2 2 2 22
                                                            E E E E E E E E E EE 22222 E 2 E
                                                                                 EEEEE E          EE                 2
                                                                                                     E EE
                                     0.8                                                                         2
                                                                                                             22 E
                                                                                                        2 222 2
                                     0.6                                                                          E
                                                                                                               2
                                                                                                        EE EEE E
                                                                                                            E    E
                                     0.4                                                                        E

                                     0.2
                                      0
                                      0.03                  0.1                                   1                      3
                                                                  Spectral Acceleration (g)
Evaluation of Inter-Event

				
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