The Generation of the Target Aftershock Spectrum Based on the Conditional Mean Spectrum of Aftershocks
Abstract
:1. Introduction
2. The Target Aftershock Spectrum
3. Determination of Aftershock Seismic Parameters
3.1. The Parameters Related to the Source
3.2. The Parameters Related to the Distance
3.3. Other Parameters
4. Conditional Mean Spectrum of the Aftershocks
4.1. The Aftershock Magnitude Is Known
4.1.1. The Simulated Seismic Parameters for the Aftershock Ground Motions
4.1.2. The Response Spectrum of the Aftershock Ground Motions
4.2. The Aftershock Magnitude Is Unknown
4.2.1. The Simulated Seismic Parameters for the Aftershock Ground Motions
4.2.2. The Response Spectrum of the Aftershock Ground Motions
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
List of Abbreviations and Symbols
Abbreviations: | (Alphabetically!!) |
AS | Aftershock |
ASK14 | GMPE proposed by Abrahamson et al. in 2014 [31] |
CMSA | Conditional mean spectrum of aftershocks |
ETAS | Epidemic-type aftershock sequence |
GMPE | Ground motion prediction equation |
MS | Main shock |
Probability density function | |
Symbols: | (Alphabetically!!) |
A | Area of the circular region (km2) |
a, b | Regression coefficients of the rupture length and rupture width |
Beta function for the corresponding elements 2.2 and 2.3 | |
CRJB | Centroid Joyner–Boore distance |
FW | Site within the footwall region |
HW | Site within the hanging wall region |
L | Rupture length |
LA | Rupture length of the aftershock |
LM | Rupture length of the main shock |
MA | Magnitude of the aftershock |
MM | Magnitude of the main shock |
NU | Site within the neutral region |
PDF of the selected beta distribution | |
RA | Source-to-site distance of an aftershock |
Rerror | Relative error |
Rrup, A | Rupture distance of the aftershock |
Rrup, M | Rupture distance of the main shock |
RX | Distance measured perpendicular to the fault strike from the surface projection of the up-dip edge of the fault plane |
Sa,A | Spectral accelerations of the aftershock |
Sa,M | Spectral accelerations of the mainshock |
Ti | The ith period of the response spectrum |
W | Rupture width |
WA | Rupture width of the aftershock |
WM | Rupture width of the main shock |
Δm | Magnitude difference between the mainshock and its largest aftershock |
Epsilon values of the aftershock | |
Epsilon values of the mainshock | |
Mean of lnSa,A predicted using the GMPE | |
Conditional mean of the lnSa,A conditioned on the lnSa,M at the period Ti | |
Mean of the logarithm of the recorded response spectrum for the aftershock ground motions | |
Mean of the logarithm of the predicted response spectrum | |
at the period | |
at the period Ti | |
at the period | |
Correlation coefficient between and at the period | |
Standard deviation of lnSa,A predicted using the GMPE | |
at the period | |
at the period |
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L (km) | W (km) | ||||
---|---|---|---|---|---|
Type of the Rupture | a | b | Type of the Rupture | a | b |
Strike slip | −2.57 | 0.62 | Strike slip | −0.76 | 0.27 |
Reverse | −2.42 | 0.58 | Reverse | −1.61 | 0.41 |
Normal | −1.88 | 0.50 | Normal | −1.14 | 0.35 |
All | −2.44 | 0.59 | All | −1.01 | 0.32 |
EQID | Earthquake Name | Number of Stations | MW | Class | CRJB (km) |
---|---|---|---|---|---|
40 | Friuli, Italy-01 | 0.5 | 6.5 | C1 | 0 |
43 | Friuli, Italy-02 | 0.5 | 5.91 | C2-0040 | 8.79 |
50 | Imperial Valley-06 | 12 | 6.53 | C1 | 0 |
51 | Imperial Valley-07 | 12 | 5.01 | C2-0050 | 0 |
53 | Livermore-01 | 1 | 5.8 | C1 | 0 |
54 | Livermore-02 | 1 | 5.42 | C2-0053 | 10.75 |
56 | Mammoth Lakes-01 | 1 | 6.06 | C1 | 0 |
61 | Mammoth Lakes-06 | 1 | 5.94 | C2-0056 | 5.24 |
68 | Irpinia, Italy-01 | 2 | 6.9 | C1 | 0 |
69 | Irpinia, Italy-02 | 2 | 6.2 | C2-0068 | 2.41 |
76 | Coalinga-01 | 0.5 | 6.36 | C1 | 0 |
80 | Coalinga-05 | 0.5 | 5.77 | C2-0076 | 0 |
103 | Chalfant Valley-02 | 1 | 6.19 | C1 | 0 |
104 | Chalfant Valley-03 | 1 | 5.65 | C2-0103 | 4.01 |
113 | Whittier Narrows-01 | 1 | 5.99 | C1 | 0 |
114 | Whittier Narrows-02 | 1 | 5.27 | C2-0113 | 0 |
136 | Kocaeli, Turkey | 5 | 7.51 | C1 | 0 |
138 | Duzce, Turkey | 5 | 7.14 | C2-0136 | 15.68 |
137 | Chi-Chi, Taiwan | 40 | 7.62 | C1 | 0 |
175 | Chi-Chi, Taiwan-06 | 40 | 6.3 | C2-0137 | 0 |
234 | Umbria Marche, Italy | 4 | 6 | C1 | 0 |
237 | Umbria Marche (aftershock 1), Italy | 4 | 5.5 | C2-0234 | 0 |
274 | L’Aquila, Italy | 4 | 6.3 | C1 | 0 |
275 | L’Aquila (aftershock 1), Italy | 4 | 5.6 | C2-0274 | 0 |
281 | Darfield, New Zealand | 3 | 7 | C1 | 0 |
346 | Christchurch, New Zealand | 3 | 6.2 | C2-0281 | 23.68 |
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Zhu, R.; Du, B.; Yang, Y.; Lu, D. The Generation of the Target Aftershock Spectrum Based on the Conditional Mean Spectrum of Aftershocks. Buildings 2023, 13, 2660. https://doi.org/10.3390/buildings13102660
Zhu R, Du B, Yang Y, Lu D. The Generation of the Target Aftershock Spectrum Based on the Conditional Mean Spectrum of Aftershocks. Buildings. 2023; 13(10):2660. https://doi.org/10.3390/buildings13102660
Chicago/Turabian StyleZhu, Ruiguang, Bohan Du, Yekai Yang, and Dagang Lu. 2023. "The Generation of the Target Aftershock Spectrum Based on the Conditional Mean Spectrum of Aftershocks" Buildings 13, no. 10: 2660. https://doi.org/10.3390/buildings13102660