Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...

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geometric effect, we expect that smaller overall ruptures would produce less effect than larger rupture, given the same values of RJB and RRUP. Previous implementations of the hanging wall effect in empirical models have reduced the effect to 0 for magnitudes less than M 6. Similarly, as the same size rupture is moved to deeper depths, we would also expect the hanging wall effect to be reduced. Both smaller rupture sizes and greater depths would tend to move make RRMS closer to RRUP, and thus, according to the analysis of Chiou et al. (2000), reduce the hanging wall effect. We propose a geometric factor, HW* = 2ψ/π, to represent the combined effect of rupture size and rupture depth. The factor is illustrated on Figure 20. The angle ψ represents the halfangle of the exposure of the surface to the fault plane and is a function of the rupture width, W, and the rupture depth, ZTOR. Using the geometry of the fault rupture, HW* is computed by the relationship: HW* 2 −1⎛ W cos( δ ) ⎞ = tan ⎜ ⎟ τ ⎝ 2( ZTOR + ζ ) ⎠ The factor ζ is included to remove singularities in the calculation and to limit the hanging wall effect for small magnitudes at shallow depths. Figure 21 show the variation of HW* with M and ZTOR with ζ set equal to 1 km. The function introduces a decrease in the hanging wall effect with increasing rupture depth that is magnitude-dependent. ZTOR W ψ Figure 20: Illustration of the hanging wall geometric factor HW*. Figure 22 shows that HW* correlates with both magnitude and ZTOR for the data selected for use in this study. One additional aspect of the hanging wall effect needs to be addressed. The function [ 1− RJB / RRUP ] produces the same level of hanging wall effect at locations on top of the rupture. However, the numerical modeling results presented in Chiou et al. (2000) and those conducted for the PEER-NGA project (Somerville et al., 2006) show the hanging wall effect tapering to zero at the fault tip for faults with surface rupture. We model this effect by multiplying the hanging wall term by tanh(0.5RRUP). C&Y2006 Page 27 δ (12)
Figure 21: Variation of HW* with magnitude, depth to top of rupture for ζ = 1 km and a range of fault dips. Figure 22: Correlation of HW* with magnitude and depth to top of rupture for the earthquakes in the PEER-NGA database selected for use in this study. The complete hanging wall function is given by: f HW = tanh( 0. 5R RUP 2 2 −1⎛ W cos( δ ) ⎞ ⎡ RJB ⎤ ) × cos ( δ ) × tan ⎜ ⎟ × ⎢1 − ⎥ (13) π ⎝ 2( ZTOR + 1) ⎠ ⎣ RRUP + 0. 001⎦ The factor of 0.001 is added in the denominator of RJB/RRUP to prevent a singularity at RRUP=0. We admit that the formulation is defined somewhat arbitrarily. However, we think that it serves the function of reducing the hanging wall effect with decreasing magnitude and C&Y2006 Page 28
Page 1 and 2: Chiou and Youngs PEER-NGA Empirical
Page 3 and 4: data are consistent with strong mot
Page 5 and 6: Figure 1: Magnitude-distance-region
Page 7 and 8: Figure 2: Empirical ground motion d
Page 9 and 10: EQID Earthquake M Table 3: Inferred
Page 11 and 12: Site Average Shear Wave Velocity: A
Page 13 and 14: Figure 6: Relationship between VS30
Page 15 and 16: 1 ) ∝ C2 × M + ( C2 − C ) × l
Page 17 and 18: Figure 9: Peak acceleration data fr
Page 19 and 20: C4+C5M slowly and the value of the
Page 21 and 22: allows the interpretation of the co
Page 23 and 24: Figure 13: Coefficients resulting f
Page 25 and 26: the top of rupture located at x = 0
Page 27: Figure 18: Intra-event residuals fo
Page 31 and 32: The interpretation of the parameter
Page 33 and 34: to the PEER-NGA pga data selected f
Page 35 and 36: EFFECT OF DATA TRUNCATION The initi
Page 37 and 38: term [ 1 Φ( y ( θ ) + τ ⋅ z ,
Page 39 and 40: Table 4: Estimate of Anelastic Atte
Page 41 and 42: data truncated at a maximum distanc
Page 43 and 44: faulting earthquakes at long period
Page 45 and 46: Slope -1.5 -1.0 -0.5 0.0 0.5 1.0 0.
Page 47 and 48: C&Y2006 Page 46 Table 5: Coefficien
Page 49 and 50: c1 of T0.010S c1 of T1.000S MODEL R
Page 51 and 52: esid 1 0 -1 -2 resid resid 1 0 -1 -
Page 53 and 54: esid resid resid 1 0 -1 -2 1 0 -1 -
Page 55 and 56: esid 2 1 0 -1 -2 SCEC Version 2 0 2
Page 57 and 58: Amplification w.r.t. Vs30 = 1130 m/
Page 59 and 60: Sa(g) Sa(g) 10 1 0.1 0.01 10 1 0.1
Page 61 and 62: Sa (g) Sa (g) 1 0.1 0.01 0.001 0.00
Page 63 and 64: Sa (g) Sa (g) 1 0.1 0.01 0.001 1 0.
Page 65 and 66: EXAMPLE CALCULATIONS FORTRAN routin
Page 67 and 68: Table 6: Example Calculations Perio
Page 69 and 70: REFERENCES Abrahamson, N.A., and Si
Page 71 and 72: Frankel, A., A. McGarr, J. Bicknell
Page 73 and 74: Appendix A Recordings from PEER-NGA
Page 75 and 76: RSN EQID Earthquake M Station No, S
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RSN EQID Earthquake M Station No, S
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Appendix B Estimation of Distance a
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Figure B-2: Data for aspect ratio v
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Probability . 0.18 0.16 0.14 0.12 0
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Appendix C Estimation of Vs30 at CW
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Percent of Total 50 40 30 20 10 0 G
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Vs30 (m/sec) 1400 1200 1000 800 600
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Figure D-1. Epicenter distribution
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PSA (g) 10^-1 10^-2 10^-3 10^-4 10^
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PSA (g) 10^-1 10^-2 10^-3 10^-4 10^
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PSA (g) 10^-1 10^-2 10^-3 10^-4 10^
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PSA (g) 10^-1 10^-2 10^-3 10^-4 10^
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PSA (g) 10^-1 10^-2 10^-3 10^-4 10^
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PSA (g) 10^-1 10^-2 10^-3 10^-4 10^
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T0.010S 1 0.1 0.01 1 0.1 0.01 1130
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T0.010S 1 0.1 0.01 1 0.1 0.01 1130
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T0.010S 1 0.1 0.01 1 0.1 0.01 1130
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T0.010S 1 0.1 0.01 1 0.1 0.01 1130
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T0.010S 1 0.1 0.01 1 0.1 0.01 1130
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T0.200S 1 0.1 0.01 1 0.1 0.01 1130
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T0.200S 1 0.1 0.01 1 0.1 0.01 1130
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1130 m/s 5
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...

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