1.1
Abrahamson & Silva (1997)
1) Reference
N. A. Abrahamson and W. J. Silva, 1997, Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes, Seismological Research Letters, Vol. 68, No. 1, 94-127.
2) Estimated
physical parameter
- Peak ground acceleration (Horizontal, Vertical)
- Spectral acceleration (T=0.1 to 5 sec) (Horizontal, Vertical)
3) Used
strong motion data
- Area: World wide
- Type of earthquake: Shallow crustal
- Period: 1940 – 1994 years
- Number of events: 58
- Number of records: 655
- Magnitude: 4.4 – 7.4
- Epicentral distance: 0.1 – 200 km
4) Style
of faulting
(a) Reverse fault
(b) Reverse/ Oblique fault
(c) Otherwise
5) Ground
condition
Based on the following classification from A to E by Geomatrix.
(a) Rock or shallow soil
A: Rock (Vs>600m/s) or very thin soil (< 5m) over rock
B: Shallow Soil, Soil 5-20m thick over rock
(b) Deep soil
C:
Deep Soil in
D:
Deep Soil in
6) Definition
of magnitude
Moment magnitude
7) Definition
of source distance
Closest distance to the rupture plane
8) Definition
of horizontal component
Geometric mean of two perpendicular horizontal components
9) Applicability
written in the paper
Not specified
10) Empirical
attenuation formula
Table
1.1.1 Coefficients for the average
horizontal component
|
Period |
c4 |
a1 |
a2 |
a3 |
a4 |
a5 |
a6 |
a9 |
a10 |
a11 |
a12 |
a13 |
c1 |
c5 |
n |
|
5.00 |
3.50 |
-1.460 |
0.512 |
-0.7250 |
-0.144 |
0.400 |
-0.200 |
0.000 |
0.664 |
0.040 |
-0.2150 |
0.17 |
6.4 |
0.03 |
2 |
|
4.00 |
3.50 |
-1.130 |
0.512 |
-0.7250 |
-0.144 |
0.400 |
-0.200 |
0.039 |
0.640 |
0.040 |
-0.1956 |
0.17 |
6.4 |
0.03 |
2 |
|
3.00 |
3.50 |
-0.690 |
0.512 |
-0.7250 |
-0.144 |
0.400 |
-0.156 |
0.089 |
0.630 |
0.040 |
-0.1726 |
0.17 |
6.4 |
0.03 |
2 |
|
2.00 |
3.50 |
-0.150 |
0.512 |
-0.7250 |
-0.144 |
0.400 |
-0.094 |
0.160 |
0.610 |
0.040 |
-0.1400 |
0.17 |
6.4 |
0.03 |
2 |
|
1.50 |
3.55 |
0.260 |
0.512 |
-0.7721 |
-0.144 |
0.438 |
-0.049 |
0.210 |
0.600 |
0.040 |
-0.1200 |
0.17 |
6.4 |
0.03 |
2 |
|
1.00 |
3.70 |
0.828 |
0.512 |
-0.8383 |
-0.144 |
0.490 |
0.013 |
0.281 |
0.423 |
0.000 |
-0.1020 |
0.17 |
6.4 |
0.03 |
2 |
|
0.85 |
3.81 |
1.020 |
0.512 |
-0.8648 |
-0.144 |
0.512 |
0.038 |
0.309 |
0.370 |
-0.028 |
-0.0927 |
0.17 |
6.4 |
0.03 |
2 |
|
0.75 |
3.90 |
1.160 |
0.512 |
-0.8852 |
-0.144 |
0.528 |
0.057 |
0.331 |
0.320 |
-0.050 |
-0.0862 |
0.17 |
6.4 |
0.03 |
2 |
|
0.60 |
4.12 |
1.428 |
0.512 |
-0.9218 |
-0.144 |
0.557 |
0.091 |
0.370 |
0.194 |
-0.089 |
-0.0740 |
0.17 |
6.4 |
0.03 |
2 |
|
0.50 |
4.30 |
1.615 |
0.512 |
-0.9515 |
-0.144 |
0.581 |
0.119 |
0.370 |
0.085 |
-0.121 |
-0.0635 |
0.17 |
6.4 |
0.03 |
2 |
|
0.46 |
4.38 |
1.717 |
0.512 |
-0.9652 |
-0.144 |
0.592 |
0.132 |
0.370 |
0.020 |
-0.136 |
-0.0594 |
0.17 |
6.4 |
0.03 |
2 |
|
0.40 |
4.52 |
1.860 |
0.512 |
-0.9880 |
-0.144 |
0.610 |
0.154 |
0.370 |
-0.065 |
-0.160 |
-0.0518 |
0.17 |
6.4 |
0.03 |
2 |
|
0.36 |
4.62 |
1.955 |
0.512 |
-1.0052 |
-0.144 |
0.610 |
0.170 |
0.370 |
-0.123 |
-0.173 |
-0.0460 |
0.17 |
6.4 |
0.03 |
2 |
|
0.30 |
4.80 |
2.114 |
0.512 |
-1.0350 |
-0.144 |
0.610 |
0.198 |
0.370 |
-0.219 |
-0.195 |
-0.0360 |
0.17 |
6.4 |
0.03 |
2 |
|
0.24 |
4.97 |
2.293 |
0.512 |
-1.0790 |
-0.144 |
0.610 |
0.232 |
0.370 |
-0.350 |
-0.223 |
-0.0238 |
0.17 |
6.4 |
0.03 |
2 |
|
0.20 |
5.10 |
2.406 |
0.512 |
-1.1150 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.445 |
-0.245 |
-0.0138 |
0.17 |
6.4 |
0.03 |
2 |
|
0.17 |
5.19 |
2.430 |
0.512 |
-1.1350 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.522 |
-0.265 |
-0.0040 |
0.17 |
6.4 |
0.03 |
2 |
|
0.15 |
5.27 |
2.407 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.577 |
-0.280 |
0.0050 |
0.17 |
6.4 |
0.03 |
2 |
|
0.12 |
5.39 |
2.272 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.591 |
-0.280 |
0.0180 |
0.17 |
6.4 |
0.03 |
2 |
|
0.10 |
5.50 |
2.160 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.598 |
-0.280 |
0.0280 |
0.17 |
6.4 |
0.03 |
2 |
|
0.09 |
5.54 |
2.100 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.609 |
-0.280 |
0.0300 |
0.17 |
6.4 |
0.03 |
2 |
|
0.075 |
5.58 |
2.037 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.628 |
-0.280 |
0.0300 |
0.17 |
6.4 |
0.03 |
2 |
|
0.06 |
5.60 |
1.940 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.665 |
-0.280 |
0.0300 |
0.17 |
6.4 |
0.03 |
2 |
|
0.05 |
5.60 |
1.870 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.620 |
-0.267 |
0.0280 |
0.17 |
6.4 |
0.03 |
2 |
|
0.04 |
5.60 |
1.780 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.555 |
-0.251 |
0.0245 |
0.17 |
6.4 |
0.03 |
2 |
|
0.03 |
5.60 |
1.690 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.470 |
-0.230 |
0.0143 |
0.17 |
6.4 |
0.03 |
2 |
|
0.02 |
5.60 |
1.640 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.417 |
-0.230 |
0.0000 |
0.17 |
6.4 |
0.03 |
2 |
|
0.01 |
5.60 |
1.640 |
0.512 |
-1.1450 |
-0.144 |
0.610 |
0.260 |
0.370 |
-0.417 |
-0.230 |
0.0000 |
0.17 |
6.4 |
0.03 |
2 |
Table
1.1.2 Coefficients for standard
errors for the averaged horizontal component
|
Period |
b5 |
b6 |
|
5.00 |
0.89 |
0.087 |
|
4.00 |
0.88 |
0.092 |
|
3.00 |
0.87 |
0.097 |
|
2.00 |
0.85 |
0.105 |
|
1.50 |
0.84 |
0.110 |
|
1.00 |
0.83 |
0.118 |
|
0.85 |
0.82 |
0.121 |
|
0.75 |
0.81 |
0.123 |
|
0.60 |
0.81 |
0.127 |
|
0.50 |
0.80 |
0.130 |
|
0.46 |
0.80 |
0.132 |
|
0.40 |
0.79 |
0.135 |
|
0.36 |
0.79 |
0.135 |
|
0.30 |
0.78 |
0.135 |
|
0.24 |
0.77 |
0.135 |
|
0.20 |
0.77 |
0.135 |
|
0.17 |
0.76 |
0.135 |
|
0.15 |
0.75 |
0.135 |
|
0.12 |
0.75 |
0.135 |
|
0.10 |
0.74 |
0.135 |
|
0.09 |
0.74 |
0.135 |
|
0.075 |
0.73 |
0.135 |
|
0.06 |
0.72 |
0.135 |
|
0.05 |
0.71 |
0.135 |
|
0.04 |
0.71 |
0.135 |
|
0.03 |
0.70 |
0.135 |
|
0.02 |
0.70 |
0.135 |
|
0.01 |
0.70 |
0.135 |
Table
1.1.3 Coefficients for the vertical
component
|
Period |
c4 |
a1 |
a2 |
a3 |
a4 |
a5 |
a6 |
a9 |
a10 |
a11 |
a12 |
a13 |
c1 |
c5 |
n |
|
5.00 |
2.50 |
-2.053 |
0.909 |
-0.7200 |
0.275 |
0.260 |
-0.100 |
0.240 |
0.040 |
-0.220 |
-0.0670 |
0.06 |
6.4 |
0.3 |
3 |
|
4.00 |
2.50 |
-1.857 |
0.909 |
-0.7200 |
0.275 |
0.260 |
-0.100 |
0.240 |
0.040 |
-0.220 |
-0.0565 |
0.06 |
6.4 |
0.3 |
3 |
|
3.00 |
2.50 |
-1.581 |
0.909 |
-0.7200 |
0.275 |
0.260 |
-0.100 |
0.240 |
0.040 |
-0.220 |
-0.0431 |
0.06 |
6.4 |
0.3 |
3 |
|
2.00 |
2.50 |
-1.224 |
0.909 |
-0.7200 |
0.275 |
0.260 |
-0.008 |
0.240 |
0.040 |
-0.220 |
-0.0240 |
0.06 |
6.4 |
0.3 |
3 |
|
1.50 |
2.50 |
-0.966 |
0.909 |
-0.7285 |
0.275 |
0.260 |
0.058 |
0.240 |
0.025 |
-0.220 |
-0.0180 |
0.06 |
6.4 |
0.3 |
3 |
|
1.00 |
2.50 |
-0.602 |
0.909 |
-0.7404 |
0.275 |
0.260 |
0.150 |
0.240 |
0.004 |
-0.220 |
-0.0115 |
0.06 |
6.4 |
0.3 |
3 |
|
0.85 |
2.50 |
-0.469 |
0.909 |
-0.7451 |
0.275 |
0.309 |
0.150 |
0.273 |
-0.004 |
-0.220 |
-0.0097 |
0.06 |
6.4 |
0.3 |
3 |
|
0.75 |
2.50 |
-0.344 |
0.909 |
-0.7488 |
0.275 |
0.348 |
0.150 |
0.299 |
-0.010 |
-0.220 |
-0.0083 |
0.06 |
6.4 |
0.3 |
3 |
|
0.60 |
2.85 |
-0.087 |
0.909 |
-0.7896 |
0.275 |
0.416 |
0.150 |
0.345 |
-0.022 |
-0.220 |
-0.0068 |
0.06 |
6.4 |
0.3 |
3 |
|
0.50 |
3.26 |
0.145 |
0.909 |
-0.8291 |
0.275 |
0.471 |
0.150 |
0.383 |
-0.031 |
-0.220 |
-0.0060 |
0.06 |
6.4 |
0.3 |
3 |
|
0.46 |
3.45 |
0.271 |
0.909 |
-0.8472 |
0.275 |
0.497 |
0.150 |
0.400 |
-0.035 |
-0.220 |
-0.0056 |
0.06 |
6.4 |
0.3 |
3 |
|
0.40 |
3.77 |
0.478 |
0.909 |
-0.8776 |
0.275 |
0.539 |
0.150 |
0.428 |
-0.043 |
-0.220 |
-0.0050 |
0.06 |
6.4 |
0.3 |
3 |
|
0.36 |
4.01 |
0.617 |
0.909 |
-0.9004 |
0.275 |
0.571 |
0.150 |
0.450 |
-0.048 |
-0.220 |
-0.0047 |
0.06 |
6.4 |
0.3 |
3 |
|
0.30 |
4.42 |
0.878 |
0.909 |
-0.9400 |
0.275 |
0.580 |
0.150 |
0.488 |
-0.057 |
-0.220 |
-0.0042 |
0.06 |
6.4 |
0.3 |
3 |
|
0.24 |
4.93 |
1.312 |
0.909 |
-1.0274 |
0.275 |
0.580 |
0.109 |
0.533 |
-0.069 |
-0.220 |
-0.0035 |
0.06 |
6.4 |
0.3 |
3 |
|
0.20 |
5.35 |
1.648 |
0.909 |
-1.0987 |
0.275 |
0.580 |
0.076 |
0.571 |
-0.078 |
-0.220 |
-0.0030 |
0.06 |
6.4 |
0.3 |
3 |
|
0.17 |
5.72 |
1.960 |
0.909 |
-1.1623 |
0.275 |
0.580 |
0.047 |
0.604 |
-0.087 |
-0.220 |
-0.0025 |
0.06 |
6.4 |
0.3 |
3 |
|
0.15 |
6.00 |
2.170 |
0.909 |
-1.2113 |
0.275 |
0.580 |
0.024 |
0.630 |
-0.093 |
-0.220 |
-0.0022 |
0.06 |
6.4 |
0.3 |
3 |
|
0.12 |
6.00 |
2.480 |
0.909 |
-1.2986 |
0.275 |
0.580 |
-0.017 |
0.630 |
-0.104 |
-0.220 |
-0.0015 |
0.06 |
6.4 |
0.3 |
3 |
|
0.10 |
6.00 |
2.700 |
0.909 |
-1.3700 |
0.275 |
0.580 |
-0.050 |
0.630 |
-0.114 |
-0.220 |
-0.0010 |
0.06 |
6.4 |
0.3 |
3 |
|
0.09 |
6.00 |
2.730 |
0.909 |
-1.3700 |
0.275 |
0.567 |
-0.050 |
0.630 |
-0.119 |
-0.220 |
-0.0009 |
0.06 |
6.4 |
0.3 |
3 |
|
0.075 |
6.00 |
2.750 |
0.909 |
-1.3700 |
0.275 |
0.545 |
-0.050 |
0.630 |
-0.129 |
-0.220 |
-0.0007 |
0.06 |
6.4 |
0.3 |
3 |
|
0.06 |
6.00 |
2.710 |
0.909 |
-1.3700 |
0.275 |
0.518 |
-0.050 |
0.630 |
-0.140 |
-0.220 |
-0.0004 |
0.06 |
6.4 |
0.3 |
3 |
|
0.05 |
6.00 |
2.620 |
0.909 |
-1.3700 |
0.275 |
0.496 |
-0.050 |
0.630 |
-0.140 |
-0.220 |
-0.0002 |
0.06 |
6.4 |
0.3 |
3 |
|
0.04 |
6.00 |
2.420 |
0.909 |
-1.3700 |
0.275 |
0.469 |
-0.050 |
0.630 |
-0.140 |
-0.220 |
0.0000 |
0.06 |
6.4 |
0.3 |
3 |
|
0.03 |
6.00 |
2.100 |
0.909 |
-1.3168 |
0.275 |
0.432 |
-0.050 |
0.630 |
-0.140 |
-0.220 |
0.0000 |
0.06 |
6.4 |
0.3 |
3 |
|
0.02 |
6.00 |
1.642 |
0.909 |
-1.2520 |
0.275 |
0.390 |
-0.050 |
0.630 |
-0.140 |
-0.220 |
0.0000 |
0.06 |
6.4 |
0.3 |
3 |
|
0.01 |
6.00 |
1.642 |
0.909 |
-1.2520 |
0.275 |
0.390 |
-0.050 |
0.630 |
-0.140 |
-0.220 |
0.0000 |
0.08 |
6.4 |
0.3 |
3 |
Table
1.1.4 Coefficients for standard
errors for the vertical component
|
Period |
b5 |
b6 |
|
5.00 |
0.78 |
0.050 |
|
4.00 |
0.75 |
0.050 |
|
3.00 |
0.72 |
0.050 |
|
2.00 |
0.69 |
0.050 |
|
1.50 |
0.69 |
0.050 |
|
1.00 |
0.69 |
0.050 |
|
0.85 |
0.69 |
0.050 |
|
0.75 |
0.69 |
0.050 |
|
0.60 |
0.69 |
0.050 |
|
0.50 |
0.69 |
0.050 |
|
0.46 |
0.69 |
0.050 |
|
0.40 |
0.69 |
0.050 |
|
0.36 |
0.69 |
0.050 |
|
0.30 |
0.69 |
0.050 |
|
0.24 |
0.69 |
0.050 |
|
0.20 |
0.69 |
0.050 |
|
0.17 |
0.70 |
0.056 |
|
0.15 |
0.72 |
0.063 |
|
0.12 |
0.74 |
0.075 |
|
0.10 |
0.76 |
0.085 |
|
0.09 |
0.76 |
0.085 |
|
0.075 |
0.76 |
0.085 |
|
0.06 |
0.76 |
0.085 |
|
0.05 |
0.76 |
0.085 |
|
0.04 |
0.76 |
0.085 |
|
0.03 |
0.76 |
0.085 |
|
0.02 |
0.76 |
0.085 |
|
0.01 |
0.76 |
0.085 |