def TpDist(saLevel, Mbar, Rbar, pidx, vs30):
'''
f(tp|Sa>x) = p1 * p2 / p3
where:
p1 = P(Sa > x | tp, Mbar, Rbar)
p2 = f(tp | Mbar)
p3 = P(Sa > x | Mbar, Rbar)
'''
T = periods[int(pidx) - 1]
Tps = np.arange(0.5, 20.5, 0.5)
# initialize variables needed for CBSB model
Ztop = 0
dip = 90
rake = 180
Zvs = 2.5
Ipulse = 1
Ppulse = 1
# Tp distribution given M , from Shahi and Baker (2013)
mulntp = -6.207 + 1.075 * Mbar
siglntp = 0.61
# compute p1
sas = np.zeros(len(Tps))
sigs = np.zeros(len(Tps))
for i in range(len(sas)):
sas[i], sigs[i] = CBSB.predict(Mbar, T, Rbar, Rbar, Ztop, dip, rake,
vs30, Zvs, Ipulse, Tps[i], Ppulse)
p1 = 1 - norm.cdf((np.log(saLevel) - np.log(sas)) / sigs)
# compute p2
p2 = norm.cdf((np.log(Tps + 0.25) - mulntp) / siglntp) - norm.cdf(
(np.log(Tps - 0.25) - mulntp) / siglntp)
# compute p3
epsUp = np.arange(-3, 3, 0.5)
epsDn = np.arange(-2.5, 3.5, 0.5)
eps = (epsUp + epsDn) / 2
Peps = norm.cdf(epsDn) - norm.cdf(epsUp)
Peps = Peps / np.sum(Peps)
p3 = 0
for i in range(len(eps)):
m, s = CBSB.predict(Mbar, T, Rbar, Rbar, Ztop, dip, rake, vs30, Zvs,
Ipulse, np.exp(mulntp + eps[i] * siglntp), Ppulse)
p3 += Peps[i] * (1 - norm.cdf((np.log(saLevel) - np.log(m)) / s))
probs = (p1 * p2) / p3
#TpDist = dict(zip(list(Tps), list(probs)))
return list(Tps), list(probs)
def TpDist(saLevel, Mbar, Rbar, pidx, vs30): ''' f(tp|Sa>x) = p1 * p2 / p3 where: p1 = P(Sa > x | tp, Mbar, Rbar) p2 = f(tp | Mbar) p3 = P(Sa > x | Mbar, Rbar) ''' T = periods[int(pidx)-1] Tps = np.arange(0.5,20.5,0.5) # initialize variables needed for CBSB model Ztop = 0 dip = 90 rake = 180 Zvs = 2.5 Ipulse = 1 Ppulse = 1 # Tp distribution given M , from Shahi and Baker (2013) mulntp = -6.207 + 1.075*Mbar siglntp = 0.61 # compute p1 sas = np.zeros(len(Tps)) sigs = np.zeros(len(Tps)) for i in range(len(sas)): sas[i],sigs[i] = CBSB.predict(Mbar,T,Rbar,Rbar,Ztop,dip,rake,vs30,Zvs,Ipulse,Tps[i],Ppulse) p1 = 1 - norm.cdf((np.log(saLevel) - np.log(sas))/sigs) # compute p2 p2 = norm.cdf((np.log(Tps + 0.25) - mulntp)/siglntp) - norm.cdf((np.log(Tps - 0.25) - mulntp)/siglntp) # compute p3 epsUp = np.arange(-3,3,0.5) epsDn = np.arange(-2.5,3.5,0.5) eps = (epsUp + epsDn)/2 Peps = norm.cdf(epsDn) - norm.cdf(epsUp) Peps = Peps/np.sum(Peps) p3 = 0 for i in range(len(eps)): m,s = CBSB.predict(Mbar,T,Rbar,Rbar,Ztop,dip,rake,vs30,Zvs,Ipulse,np.exp(mulntp + eps[i]*siglntp),Ppulse) p3 += Peps[i]*(1-norm.cdf((np.log(saLevel) - np.log(m))/s)) probs = (p1 * p2)/p3 #TpDist = dict(zip(list(Tps), list(probs))) return list(Tps),list(probs)
def ppulse(saLevel, Mbar, Rbar, pidx, vs30):
'''
P(pulse|Sa>x) = p1 * p2 / p3
where:
p1 = P(Sa > x | directivity, Mbar, Rbar)
p2 = P(directivity | Mbar, Rbar)
p3 = P(Sa > x | Mbar, Rbar)
'''
T = periods[int(pidx) - 1]
mulntp = -6.207 + 1.075 * Mbar
siglntp = 0.61
epsUp = np.arange(-3, 3, 0.5)
epsDn = np.arange(-2.5, 3.5, 0.5)
eps = (epsUp + epsDn) / 2
Peps = norm.cdf(epsDn) - norm.cdf(epsUp)
Peps = Peps / np.sum(Peps)
sas = np.zeros(len(eps))
sigs = np.zeros(len(eps))
Ztop = 0
dip = 90
rake = 180
Zvs = 2.5
p1 = 0
Ipulse = 1
Ppulse = 1
for i in range(len(eps)):
m, s = CBSB.predict(Mbar, T, Rbar, Rbar, Ztop, dip, rake, vs30, Zvs,
Ipulse, np.exp(mulntp + eps[i] * siglntp), Ppulse)
p1 += Peps[i] * (1 - norm.cdf((np.log(saLevel) - np.log(m)) / s))
p2 = PpulseGivenMR(Mbar, Rbar)
p3pulse = p1
Ipulse = 0
Ppulse = 0
m, s = CBSB.predict(Mbar, T, Rbar, Rbar, Ztop, dip, rake, vs30, Zvs,
Ipulse, np.exp(mulntp + eps[i] * siglntp), Ppulse)
p3nopulse = (1 - norm.cdf((np.log(saLevel) - np.log(m)) / s))
p3 = p2 * p3pulse + (1 - p2) * p3nopulse
return p1 * p2 / p3
def ppulse(saLevel, Mbar, Rbar, pidx, vs30): ''' P(pulse|Sa>x) = p1 * p2 / p3 where: p1 = P(Sa > x | directivity, Mbar, Rbar) p2 = P(directivity | Mbar, Rbar) p3 = P(Sa > x | Mbar, Rbar) ''' T = periods[int(pidx)-1] mulntp = -6.207 + 1.075*Mbar siglntp = 0.61 epsUp = np.arange(-3,3,0.5) epsDn = np.arange(-2.5,3.5,0.5) eps = (epsUp + epsDn)/2 Peps = norm.cdf(epsDn) - norm.cdf(epsUp) Peps = Peps/np.sum(Peps) sas = np.zeros(len(eps)) sigs = np.zeros(len(eps)) Ztop = 0 dip = 90 rake = 180 Zvs = 2.5 p1 = 0 Ipulse = 1 Ppulse = 1 for i in range(len(eps)): m,s = CBSB.predict(Mbar,T,Rbar,Rbar,Ztop,dip,rake,vs30,Zvs,Ipulse,np.exp(mulntp + eps[i]*siglntp),Ppulse) p1 += Peps[i]*(1-norm.cdf((np.log(saLevel) - np.log(m))/s)) p2 = PpulseGivenMR(Mbar,Rbar) p3pulse = p1 Ipulse = 0 Ppulse = 0 m,s = CBSB.predict(Mbar,T,Rbar,Rbar,Ztop,dip,rake,vs30,Zvs,Ipulse,np.exp(mulntp + eps[i]*siglntp),Ppulse) p3nopulse = (1-norm.cdf((np.log(saLevel) - np.log(m))/s)) p3 = p2*p3pulse + (1-p2)*p3nopulse return p1 * p2 / p3
