-
Notifications
You must be signed in to change notification settings - Fork 0
/
gmpe_bssa_2014.m
240 lines (209 loc) · 11.4 KB
/
gmpe_bssa_2014.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
function [median, sigma, period1] = gmpe_bssa_2014(M, T, Rjb, Fault_Type, region, z1, Vs30)
% coded by Yue Hua, [email protected]
% updated by Jack Baker, 3/3/2014
%
% BSSA14 NGA-West2 model, based on the following citation
%
% Boore, D. M., Stewart, J. P., Seyhan, E., and Atkinson, G. M. (2014).
% NGA-West2 Equations for Predicting PGA, PGV, and 5% Damped PSA for
% Shallow Crustal Earthquakes. Earthquake Spectra, 30(3), 1057-1085.
% http://www.earthquakespectra.org/doi/abs/10.1193/070113EQS184M
%
% Provides ground-mtion prediction equations for computing medians and
% standard devisations of average horizontal component internsity measures
% (IMs) for shallow crustal earthquakes in active tectonic regions.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input Variables
% M = Moment Magnitude
% T = Period (sec); Use Period = -1 for PGV computation
% Use 1000 to output the array of median with original period
% (no interpolation)
% Rjb = Joyner-Boore distance (km)
% Fault_Type = 0 for unspecified fault
% = 1 for strike-slip fault
% = 2 for normal fault
% = 3 for reverse fault
% region = 0 for global (incl. Taiwan)
% = 1 for California
% = 2 for Japan
% = 3 for China or Turkey
% = 4 for Italy
% z1 = Basin depth (km); depth from the groundsurface to the
% 1km/s shear-wave horizon.
% = 999 if unknown
% Vs30 = shear wave velocity averaged over top 30 m in m/s
%
% Output Variables
% median = Median amplitude prediction
%
% sigma = NATURAL LOG standard deviation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
period = [-1 0 0.01 0.02 0.03 0.05 0.075 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.75 1 1.5 2 3 4 5 7.5 10];
U = (Fault_Type == 0);
SS = (Fault_Type == 1);
NS = (Fault_Type == 2);
RS = (Fault_Type == 3);
if length (T) == 1 && T == 1000; % Compute median and sigma with pre-defined period
median=zeros(1,length(period)-2);
sigma=zeros(1,length(period)-2);
period1=period(3:end);
for ip=3:length(period)
[median(ip-2),sigma(ip-2)]=BSSA_2014_sub(M, ip, Rjb, U, SS, NS, RS, region, z1, Vs30);
end
else % Compute median and sigma with user-defined period
median=zeros(1, length(T));
sigma=zeros(1, length(T));
period1=T;
for i=1:length(T)
Ti = T(i);
if ( isempty(find(abs(period-Ti) < 0.0001, 1))) % The user defined period requires interpolation
T_low = max(period(period < Ti));
T_high = min(period(period > Ti));
ip_low = find(period==T_low);
ip_high = find(period==T_high);
[Sa_low, sigma_low] = BSSA_2014_sub(M, ip_low, Rjb, U, SS, NS, RS, region, z1, Vs30);
[Sa_high, sigma_high] = BSSA_2014_sub(M, ip_high, Rjb, U, SS, NS, RS, region, z1, Vs30);
x = [log(T_low) log(T_high)];
Y_sa = [log(Sa_low) log(Sa_high)];
Y_sigma = [sigma_low sigma_high];
median(i) = exp(interp1(x, Y_sa, log(Ti)));
sigma(i) = interp1(x, Y_sigma, log(Ti));
else
ip_T = find(abs((period- Ti)) < 0.0001);
[median(i), sigma(i)] = BSSA_2014_sub(M, ip_T, Rjb, U, SS, NS, RS, region, z1, Vs30);
end
end
end
function [median, sigma]=BSSA_2014_sub (M, ip, Rjb, U, SS, NS, RS, region, z1, Vs30)
%% Coefficients
mref=4.5;
rref=1;
v_ref=760;
f1=0;
f3=0.1;
v1=225;
v2=300;
period = [-1 0 0.01 0.02 0.03 0.05 0.075 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.75 1 1.5 2 3 4 5 7.5 10];
mh=[6.2 5.5 5.5 5.5 5.5 5.5 5.5 5.54 5.74 5.92 6.05 6.14 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.2];
e0=[5.037 0.4473 0.4534 0.48598 0.56916 0.75436 0.96447 1.1268 1.3095 1.3255 1.2766 1.2217 1.1046 0.96991 0.66903 0.3932 -0.14954 -0.58669 -1.1898 -1.6388 -1.966 -2.5865 -3.0702];
e1=[5.078 0.4856 0.4916 0.52359 0.6092 0.79905 1.0077 1.1669 1.3481 1.359 1.3017 1.2401 1.1214 0.99106 0.69737 0.4218 -0.11866 -0.55003 -1.142 -1.5748 -1.8882 -2.4874 -2.9537];
e2=[4.849 0.2459 0.2519 0.29707 0.40391 0.60652 0.77678 0.8871 1.0648 1.122 1.0828 1.0246 0.89765 0.7615 0.47523 0.207 -0.3138 -0.71466 -1.23 -1.6673 -2.0245 -2.8176 -3.3776];
e3=[5.033 0.4539 0.4599 0.48875 0.55783 0.72726 0.9563 1.1454 1.3324 1.3414 1.3052 1.2653 1.1552 1.012 0.69173 0.4124 -0.1437 -0.60658 -1.2664 -1.7516 -2.0928 -2.6854 -3.1726];
e4=[1.073 1.431 1.421 1.4331 1.4261 1.3974 1.4174 1.4293 1.2844 1.1349 1.0166 0.95676 0.96766 1.0384 1.2871 1.5004 1.7622 1.9152 2.1323 2.204 2.2299 2.1187 1.8837];
e5=[-0.1536 0.05053 0.04932 0.053388 0.061444 0.067357 0.073549 0.055231 -0.042065 -0.11096 -0.16213 -0.1959 -0.22608 -0.23522 -0.21591 -0.18983 -0.1467 -0.11237 -0.04332 -0.014642 -0.014855 -0.081606 -0.15096 ];
e6=[0.2252 -0.1662 -0.1659 -0.16561 -0.1669 -0.18082 -0.19665 -0.19838 -0.18234 -0.15852 -0.12784 -0.092855 -0.023189 0.029119 0.10829 0.17895 0.33896 0.44788 0.62694 0.76303 0.87314 1.0121 1.0651];
c1=[-1.24300 -1.13400 -1.13400 -1.13940 -1.14210 -1.11590 -1.08310 -1.06520 -1.05320 -1.06070 -1.07730 -1.09480 -1.12430 -1.14590 -1.17770 -1.19300 -1.20630 -1.21590 -1.21790 -1.21620 -1.21890 -1.25430 -1.32530];
c2=[0.14890 0.19170 0.19160 0.18962 0.18842 0.18709 0.18225 0.17203 0.15401 0.14489 0.13925 0.13388 0.12512 0.12015 0.11054 0.10248 0.09645 0.09636 0.09764 0.10218 0.10353 0.12507 0.15183];
c3=[-0.00344 -0.00809 -0.00809 -0.00807 -0.00834 -0.00982 -0.01058 -0.01020 -0.00898 -0.00772 -0.00652 -0.00548 -0.00405 -0.00322 -0.00193 -0.00121 -0.00037 0.00000 0.00000 -0.00005 0.00000 0.00000 0.00000];
h=[5.3 4.5 4.5 4.5 4.49 4.2 4.04 4.13 4.39 4.61 4.78 4.93 5.16 5.34 5.6 5.74 6.18 6.54 6.93 7.32 7.78 9.48 9.66];
deltac3_gloCATW=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000];
deltac3_CHTU=[0.004350 0.002860 0.002820 0.002780 0.002760 0.002960 0.002960 0.002880 0.002790 0.002610 0.002440 0.002200 0.002110 0.002350 0.002690 0.002920 0.003040 0.002920 0.002620 0.002610 0.002600 0.002600 0.003030];
deltac3_ITJA=[-0.000330 -0.002550 -0.002440 -0.002340 -0.002170 -0.001990 -0.002160 -0.002440 -0.002710 -0.002970 -0.003140 -0.003300 -0.003210 -0.002910 -0.002530 -0.002090 -0.001520 -0.001170 -0.001190 -0.001080 -0.000570 0.000380 0.001490];
c=[-0.8400 -0.6000 -0.6037 -0.5739 -0.5341 -0.4580 -0.4441 -0.4872 -0.5796 -0.6876 -0.7718 -0.8417 -0.9109 -0.9693 -1.0154 -1.0500 -1.0454 -1.0392 -1.0112 -0.9694 -0.9195 -0.7766 -0.6558];
vc=[1300.00 1500.00 1500.20 1500.36 1502.95 1501.42 1494.00 1479.12 1442.85 1392.61 1356.21 1308.47 1252.66 1203.91 1147.59 1109.95 1072.39 1009.49 922.43 844.48 793.13 771.01 775.00];
f4=[-0.1000 -0.1500 -0.1483 -0.1471 -0.1549 -0.1963 -0.2287 -0.2492 -0.2571 -0.2466 -0.2357 -0.2191 -0.1958 -0.1704 -0.1387 -0.1052 -0.0679 -0.0361 -0.0136 -0.0032 -0.0003 -0.0001 0.0000];
f5=[-0.00844 -0.00701 -0.00701 -0.00728 -0.00735 -0.00647 -0.00573 -0.00560 -0.00585 -0.00614 -0.00644 -0.00670 -0.00713 -0.00744 -0.00812 -0.00844 -0.00771 -0.00479 -0.00183 -0.00152 -0.00144 -0.00137 -0.00136];
f6=[-9.900 -9.900 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 0.092 0.367 0.638 0.871 1.135 1.271 1.329 1.329 1.183];
f7=[-9.900 -9.900 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 0.059 0.208 0.309 0.382 0.516 0.629 0.738 0.809 0.703];
tau1=[0.4010 0.3980 0.4020 0.4090 0.4450 0.5030 0.4740 0.4150 0.3540 0.3440 0.3500 0.3630 0.3810 0.4100 0.4570 0.4980 0.5250 0.5320 0.5370 0.5430 0.5320 0.5110 0.4870];
tau2=[0.3460 0.3480 0.3450 0.3460 0.3640 0.4260 0.4660 0.4580 0.3880 0.3090 0.2660 0.2290 0.2100 0.2240 0.2660 0.2980 0.3150 0.3290 0.3440 0.3490 0.3350 0.2700 0.2390];
phi1=[0.6440 0.6950 0.6980 0.7020 0.7210 0.7530 0.7450 0.7280 0.7200 0.7110 0.6980 0.6750 0.6430 0.6150 0.5810 0.5530 0.5320 0.5260 0.5340 0.5360 0.5280 0.5120 0.5100];
phi2=[0.5520 0.4950 0.4990 0.5020 0.5140 0.5320 0.5420 0.5410 0.5370 0.5390 0.5470 0.5610 0.5800 0.5990 0.6220 0.6250 0.6190 0.6180 0.6190 0.6160 0.6220 0.6340 0.6040];
dphiR=[0.082 0.100 0.096 0.092 0.081 0.063 0.064 0.087 0.120 0.136 0.141 0.138 0.122 0.109 0.100 0.098 0.104 0.105 0.088 0.070 0.061 0.058 0.060];
dphiV=[0.080 0.070 0.070 0.030 0.029 0.030 0.022 0.014 0.015 0.045 0.055 0.050 0.049 0.060 0.070 0.020 0.010 0.008 0.000 0.000 0.000 0.000 0.000];
R1=[105.000 110.000 111.670 113.100 112.130 97.930 85.990 79.590 81.330 90.910 97.040 103.150 106.020 105.540 108.390 116.390 125.380 130.370 130.360 129.490 130.220 130.720 130.000];
R2=[272.000 270.000 270.000 270.000 270.000 270.000 270.040 270.090 270.160 270.000 269.450 268.590 266.540 265.000 266.510 270.000 262.410 240.140 195.000 199.450 230.000 250.390 210.000];
%% The source(event function):
if M <= mh (ip);
F_E = e0(ip) * U + e1(ip) * SS + e2(ip) * NS + e3(ip) * RS + e4(ip) * (M - mh(ip)) + e5(ip) * (M - mh(ip))^2;
else
F_E = e0(ip) * U + e1(ip) * SS + e2(ip) * NS + e3(ip) * RS + e6(ip) * (M - mh(ip));
end;
%% The path function:
if region == 0 || region == 1
deltac3 = deltac3_gloCATW;
elseif region == 3
deltac3 = deltac3_CHTU;
elseif region == 2 || region == 4
deltac3 = deltac3_ITJA;
end
r=sqrt(Rjb^2+h(ip)^2);
F_P= (c1(ip) + c2(ip) * (M - mref)) * log (r / rref) + (c3(ip) + deltac3(ip)) * (r - rref);
%% FIND PGAr
if Vs30~=v_ref || ip~=2;
[PGA_r,sigma_r] =BSSA_2014_sub(M, 2, Rjb, U, SS, NS, RS, region, z1, v_ref);
%% The site function:
% Linear component
if Vs30<= vc(ip)
ln_Flin = c(ip) * log(Vs30 / v_ref);
else
ln_Flin = c(ip) * log(vc(ip)/ v_ref);
end
% Nonlinear component
f2=f4(ip)*(exp(f5(ip)*(min(Vs30,760)-360))-exp(f5(ip)*(760-360)));
ln_Fnlin=f1+f2*log((PGA_r+f3)/f3);
% Effect of basin depth
if z1 ~= 999
if region == 1 % if in California
mu_z1=exp(-7.15/4*log((Vs30^4+570.94^4)/(1360^4+570.94^4)))/1000;
else if region == 2 % if in Japan
mu_z1=exp(-5.23/2*log((Vs30^2+412.39^2)/(1360^2+412.39^2)))/1000;
else
mu_z1=exp(-7.15/4*log((Vs30^4+570.94^4)/(1360^4+570.94^4)))/1000;
end
end
dz1=z1-mu_z1;
else
dz1=0;
end
if z1 ~= 999
if period(ip) <0.65
F_dz1=0;
else if period(ip) >= 0.65 && abs(dz1) <= f7(ip)/f6(ip)
F_dz1=f6(ip)*dz1;
else
F_dz1=f7(ip);
end
end
else
F_dz1=0;
end
F_S=ln_Flin+ln_Fnlin+F_dz1;
ln_Y=F_E + F_P + F_S;
median=exp(ln_Y);
else
ln_y=F_E + F_P;
median = exp(ln_y);
end
%% Aleatory - uncertainty function
if M <= 4.5
tau = tau1(ip);
phi_M = phi1(ip);
else if 4.5 < M && M < 5.5
tau = tau1(ip)+(tau2(ip)-tau1(ip))*(M-4.5);
phi_M = phi1(ip)+(phi2(ip)-phi1(ip))*(M-4.5);
else if M >= 5.5
tau = tau2(ip);
phi_M = phi2(ip);
end
end
end
if Rjb <= R1(ip)
phi_MR = phi_M;
else if R1(ip) < Rjb && Rjb <= R2(ip)
phi_MR = phi_M + dphiR(ip)*(log(Rjb/R1(ip))/log(R2(ip)/R1(ip)));
else if Rjb > R2(ip)
phi_MR = phi_M + dphiR(ip);
end
end
end
if Vs30 >= v2
phi_MRV = phi_MR;
else if v1 <= Vs30 && Vs30 <= v2
phi_MRV = phi_MR - dphiV(ip)*(log(v2/Vs30)/log(v2/v1));
else if Vs30 <= v1
phi_MRV = phi_MR - dphiV(ip);
end
end
end
sigma = sqrt(phi_MRV^2 + tau^2);