# third party imports
import numpy as np
# stdlib imports
from openquake.hazardlib import imt
from openquake.hazardlib.imt import PGA, PGV
from shakelib.gmice.gmice import GMICE
[docs]class Wald99(GMICE):
"""
Implements the ground motion intensity conversion equations (GMICE) of
Wald et al. (1999). This module implements a simplified version in that
it only uses one of PGV or PGA, and not a combination of the two (PGV
for higher intensities, PGA for lower) as is recommended in the reference.
References:
Wald, D.J., V. Quitoriano, T.H. Heaton, and H. Kanamori (1999).
Relationships between peak gorund acceleration, peak ground
velocity, and Modified Mercalli Intensity in California,
Earthquake Spectra, Volume15, No. 3, August 1999.
"""
# -----------------------------------------------------------------------
#
# Imm = 3.66 * log10(PGA) - 1.66 for Imm >= V (e.g., log10(PGA) >= 1.82)
# Imm = 2.20 * log10(PGA) + 1.0 for Imm < 5
#
# Imm = 3.47 * log10(PGV) + 2.35 for Imm >= V
# Imm = 2.10 * log10(PGV) + 3.40 for Imm < 5
#
# -----------------------------------------------------------------------
def __init__(self):
super().__init__()
self.min_max = (1.0, 10.0)
self.name = "Wald et al. (1999)"
self.scale = "scale_wald99.ps"
self.__constants = {
self._pga: {
"C1": 3.66,
"C2": -1.66,
"C3": 2.20,
"C4": 1.00,
"T1": 1.82,
"T2": 5.00,
"SMMI": 1.08,
"SPGM": 0.295,
},
self._pgv: {
"C1": 3.47,
"C2": 2.35,
"C3": 2.10,
"C4": 3.40,
"T1": 0.76,
"T2": 5.00,
"SMMI": 0.98,
"SPGM": 0.282,
},
}
self.DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV])
self.DEFINED_FOR_SA_PERIODS = set([])
[docs] def getPreferredMI(self, df, dists=None, mag=None):
if "PGA" not in df or "PGV" not in df:
if "PGV" in df:
oqimt = imt.from_string("PGV")
return self.getMIfromGM(df["PGV"], oqimt, dists, mag)[0]
elif "PGA" in df:
oqimt = imt.from_string("PGA")
return self.getMIfromGM(df["PGA"], oqimt, dists, mag)[0]
else:
return None
oqimt = imt.from_string("PGA")
mmi_pga = self.getMIfromGM(df["PGA"], oqimt, dists, mag)[0]
ix_nan_pga = np.isnan(mmi_pga)
oqimt = imt.from_string("PGV")
mmi_pgv = self.getMIfromGM(df["PGV"], oqimt, dists, mag)[0]
ix_nan_pgv = np.isnan(mmi_pgv)
ix_nan = ix_nan_pga | ix_nan_pgv
vscale = np.zeros_like(mmi_pga)
vscale[~ix_nan] = (mmi_pga[~ix_nan] - 5) / 2
vscale[vscale < 0] = 0
vscale[vscale > 1] = 1
ascale = 1 - vscale
mmi = np.full_like(mmi_pga, np.nan)
mmi[~ix_nan] = np.clip(
mmi_pga[~ix_nan] * ascale[~ix_nan] + mmi_pgv[~ix_nan] * vscale[~ix_nan],
1,
10,
)
mmi[ix_nan_pgv] = mmi_pga[ix_nan_pgv]
mmi[ix_nan_pga] = mmi_pgv[ix_nan_pga]
ix_nan = np.isnan(mmi)
mmi95 = np.full_like(mmi, False, dtype=bool)
mmi95[~ix_nan] = mmi[~ix_nan] > 9.5
mmi[mmi95] = 10.0
return mmi
[docs] def getMIfromGM(self, amps, imt, dists=None, mag=None):
"""
Function to compute macroseismic intensity from ground-motion
intensity. Supported ground-motion IMTs are PGA and PGV
Args:
amps (ndarray):
Ground motion amplitude; natural log units; g for PGA and
PSA, cm/s for PGV.
imt (OpenQuake IMT):
Type the input amps (must be one of PGA or PGV).
`[link] <http://docs.openquake.org/oq-hazardlib/master/imt.html>`
dists (ndarray):
Numpy array of distances from rupture (km). This parameter
is ignored by this GMICE.
mag (float):
Earthquake magnitude. This parameter is ignored by this
GMICE.
Returns:
ndarray of Modified Mercalli Intensity and ndarray of
dMMI / dln(amp) (i.e., the slope of the relationship at the
point in question).
""" # noqa
lfact = np.log10(np.e)
c = self._getConsts(imt)
ix_nan = np.isnan(amps)
#
# Convert (for accelerations) from ln(g) to cm/s^2
# then take the log10
#
if imt == self._pga:
units = 981.0
else:
units = 1.0
#
# Math: log10(981 * exp(amps)) = log10(981) + log10(exp(amps))
# = log10(981) + amps * log10(e)
# For PGV, just convert ln(amp) to log10(amp) by multiplying
# by log10(e)
#
lamps = np.zeros_like(amps)
lamps[~ix_nan] = np.log10(units) + amps[~ix_nan] * lfact
mmi = np.full_like(amps, np.nan)
dmmi_damp = np.zeros_like(amps)
#
# This is the upper segment of the bi-linear fit
#
idx = lamps >= c["T1"]
mmi[idx] = c["C2"] + c["C1"] * lamps[idx]
dmmi_damp[idx] = c["C1"] * lfact
#
# This is the lower segment of the bi-linear fit
#
idx = lamps < c["T1"]
mmi[idx] = c["C4"] + c["C3"] * lamps[idx]
dmmi_damp[idx] = c["C3"] * lfact
mmi = np.clip(mmi, 1.0, 10.0)
mmi[ix_nan] = np.nan
return mmi, dmmi_damp
[docs] def getGMfromMI(self, mmi, imt, dists=None, mag=None):
"""
Function to tcompute ground-motion intensity from macroseismic
intensity. Supported IMTs are PGA and PGV.
Args:
mmi (ndarray):
Macroseismic intensity.
imt (OpenQuake IMT):
IMT of the requested ground-motions intensities (must be
one of PGA or PGV).
`[link] <http://docs.openquake.org/oq-hazardlib/master/imt.html>`
dists (ndarray):
Rupture distances (km) to the corresponding MMIs. This
parameter is ignored by this GMICE.
mag (float):
Earthquake magnitude. This parameter is ignored by this
GMICE.
Returns:
Ndarray of ground motion intensity in natural log of g for PGA
and PSA, and natural log cm/s for PGV; ndarray of dln(amp) / dMMI
(i.e., the slope of the relationship at the point in question).
""" # noqa
lfact = np.log10(np.e)
c = self._getConsts(imt)
mmi = mmi.copy()
ix_nan = np.isnan(mmi)
mmi[ix_nan] = 1.0
pgm = np.zeros_like(mmi)
dpgm_dmmi = np.zeros_like(mmi)
#
# Upper segment of bi-linear relationship
#
idx = mmi >= c["T2"]
pgm[idx] = np.power(10, (mmi[idx] - c["C2"]) / c["C1"])
dpgm_dmmi[idx] = 1.0 / (c["C1"] * lfact)
#
# Lower segment of bi-linear relationship
#
idx = mmi < c["T2"]
pgm[idx] = np.power(10, (mmi[idx] - c["C4"]) / c["C3"])
dpgm_dmmi[idx] = 1.0 / (c["C3"] * lfact)
if imt != self._pgv:
units = 981.0
else:
units = 1.0
pgm /= units
pgm = np.log(pgm)
pgm[ix_nan] = np.nan
dpgm_dmmi[ix_nan] = np.nan
return pgm, dpgm_dmmi
[docs] def getGM2MIsd(self):
"""
Return a dictionary of standard deviations for the ground-motion
to MMI conversion. The keys are the ground motion types.
Returns:
Dictionary of GM to MI sigmas (in MMI units).
"""
return {
self._pga: self.__constants[self._pga]["SMMI"],
self._pgv: self.__constants[self._pgv]["SMMI"],
}
[docs] def getMI2GMsd(self):
"""
Return a dictionary of standard deviations for the MMI
to ground-motion conversion. The keys are the ground motion
types.
Returns:
Dictionary of MI to GM sigmas (ln(PGM) units).
"""
#
# Need to convert log10 to ln units
#
lfact = np.log(10.0)
return {
self._pga: lfact * self.__constants[self._pga]["SPGM"],
self._pgv: lfact * self.__constants[self._pgv]["SPGM"],
}
def _getConsts(self, imt):
"""
Helper function to get the constants.
"""
if imt != self._pga and imt != self._pgv:
raise ValueError("Invalid IMT " + str(imt))
return self.__constants[imt]
