import numpy as np
from openquake.hazardlib import const
[docs]class AbrahamsonBhasin2020(object):
"""
Module to make conditional conversions from SA(T) to PGV. The user
provides a magnitude when an instance and the instance can report back
what period of SA is appropriate to use for computing PGV. The module
is based upon:
Abrahamson, N.A., and Bhasin, S. (2020) Conditional ground-motion model
for peak ground velocity for active crustal regions. PEER Report 2020/05,
Pacific Earthquake Engineering Research Center, U.C. Berkeley.
"""
def __init__(self, mag):
self.mag = mag
mag_T = [
(3.5, 0.20),
(4.5, 0.28),
(5.5, 0.40),
(6.5, 0.95),
(7.5, 1.40),
(8.5, 2.80),
]
self.Tref = 0
for mm, tt in mag_T:
if np.any(mag <= mm):
self.Tref = tt
break
if self.Tref == 0:
self.Tref = tt
self.coeff = {
"a1": 5.39,
"a2": 0.799,
"a3": 0.654,
"a4": 0.479,
"a5": -0.062,
"a6": -0.359,
"a7": -0.134,
"a8": 0.023,
"phi": 0.29,
"tau": 0.16,
"sigma": 0.33,
}
[docs] def getTref(self):
"""
Returns the period of the SA amps suitable for conversion to PGV.
Args:
None.
Returns:
(float): The period of the SA amps to supply to getPGVandSTDDEVS()
"""
return self.Tref
[docs] def getPGVandSTDDEVS(self, psa, stddevs, sdtypes, rrup, vs30):
"""
Function to compute the PGVs and inflate the uncertainties based on
the input SA amps and uncertainties.
Args:
psa (np.array): An array os SA amp of the appropriate period.
stddevs(np.arrays): A list of one or more array of standard
deviations of the psa amps. The list may also contain arrays
of the stddevs inflated by the point-source adjustments. Each
array must be the same shape as the psa array.
sdtypes (list): A list of the types of the standard deviations in
stddevs (in order). These are OpenQuake const.StdDev types.
rrup (np.array): Rupture distance to the points in psa. Must be
the same shape as psa.
vs30 (np.array): The Vs30 value at the points in psa. Must be the
same shape as psa.
Returns:
(tuple: ndarray, list): An array of PGV values, and a list of
stddev arrays corresponding to the input stddev types, now
with the uncertainty propagated through the conversion.
"""
c = self.coeff
m = self.mag
if np.any(m < 5):
f1 = c["a2"]
elif np.any(m <= 7.5):
f1 = c["a2"] + (c["a3"] - c["a2"]) * (m - 5.0) / 2.5
else:
f1 = c["a3"]
pgv = (
c["a1"]
+ f1 * psa
+ c["a4"] * (m - 6.0)
+ c["a5"] * (8.5 - m) ** 2
+ c["a6"] * np.log(rrup + 5.0 * np.exp(0.4 * (m - 6.0)))
+ (c["a7"] + c["a8"] * (m - 5.0)) * np.log(vs30 / 425)
)
#
# ShakeMap will often produce lists of stddevs that are twice
# as long as sdtypes: one set that has been inflated by the
# point-source to finite-fault factors, and one that has not.
# Here we modify both, if they are present.
#
stddevs_out = []
mytypes = sdtypes.copy()
if len(stddevs) == 2 * len(sdtypes):
mytypes.extend(sdtypes)
for i, sdtype in enumerate(mytypes):
if sdtype == const.StdDev.INTER_EVENT:
sdout = np.sqrt(f1 ** 2 * stddevs[i] ** 2 + c["tau"] ** 2)
elif sdtype == const.StdDev.INTRA_EVENT:
sdout = np.sqrt(f1 ** 2 * stddevs[i] ** 2 + c["phi"] ** 2)
else:
sdout = np.sqrt(f1 ** 2 * stddevs[i] ** 2 + c["sigma"] ** 2)
stddevs_out.append(sdout)
return pgv, stddevs_out
[docs]class AbrahamsonBhasin2020PGA(AbrahamsonBhasin2020):
"""
An alternative to AbrahamsonBhasin2020 when only PGA is available for
conversion.
"""
def __init__(self, mag):
self.mag = mag
self.Tref = 0
self.coeff = {
"a1": 4.77,
"a2": 0.738,
"a3": 0.484,
"a4": 0.275,
"a5": -0.036,
"a6": -0.332,
"a7": -0.44,
"a8": 0.0,
"phi1": 0.32,
"phi2": 0.42,
"phi": 0.0,
"tau1": 0.12,
"tau2": 0.26,
"tau": 0.0,
"sigma1": 0.34,
"sigma2": 0.49,
"sigma": 0.0,
"m1": 5.0,
"m2": 7.0,
}
c = self.coeff
mref = (self.mag - c["m1"]) / (c["m2"] - c["m1"])
#
# Here we set the magnitude-dependent phi, tau, and sigma
# to be used in the parent cless' getPGVandSTDDEVS()
#
if self.mag < c["m1"]:
c["phi"] = c["phi1"]
c["tau"] = c["tau1"]
c["sigma"] = c["sigma1"]
elif self.mag <= c["m2"]:
c["phi"] = c["phi1"] + (c["phi2"] - c["phi2"]) * mref
c["tau"] = c["tau1"] + (c["tau2"] - c["tau2"]) * mref
c["sigma"] = c["sigma1"] + (c["sigma2"] - c["sigma2"]) * mref
else:
c["phi"] = c["phi2"]
c["tau"] = c["tau2"]
c["sigma"] = c["sigma2"]
[docs]class AbrahamsonBhasin2020SA1(AbrahamsonBhasin2020):
"""
An alternative to AbrahamsonBhasin2020 when only SA(1.0) is available for
conversion.
"""
def __init__(self, mag):
self.mag = mag
self.Tref = 1.0
self.coeff = {
"a1": 4.80,
"a2": 0.82,
"a3": 0.55,
"a4": 0.27,
"a5": 0.054,
"a6": -0.382,
"a7": -0.21,
"a8": 0.0,
"phi1": 0.28,
"phi2": 0.38,
"phi": 0.0,
"tau1": 0.12,
"tau2": 0.17,
"tau": 0.0,
"sigma1": 0.30,
"sigma2": 0.42,
"sigma": 0.0,
"m1": 5.0,
"m2": 7.0,
}
c = self.coeff
mref = (self.mag - c["m1"]) / (c["m2"] - c["m1"])
#
# Here we set the magnitude-dependent phi, tau, and sigma
# to be used in the parent cless' getPGVandSTDDEVS()
#
if self.mag < c["m1"]:
c["phi"] = c["phi1"]
c["tau"] = c["tau1"]
c["sigma"] = c["sigma1"]
elif self.mag <= c["m2"]:
c["phi"] = c["phi1"] + (c["phi2"] - c["phi2"]) * mref
c["tau"] = c["tau1"] + (c["tau2"] - c["tau2"]) * mref
c["sigma"] = c["sigma1"] + (c["sigma2"] - c["sigma2"]) * mref
else:
c["phi"] = c["phi2"]
c["tau"] = c["tau2"]
c["sigma"] = c["sigma2"]
