# third party imports
import numpy as np
# stdlib imports
from openquake.hazardlib.imt import PGA, PGV, SA
from shakelib.gmice.gmice import GMICE
[docs]class FM11(GMICE):
"""
Implements the ground motion intensity conversion equations (GMICE) of
Faenza and Michelini (2010, 2011).
References:
Faenza and Michelini,(2010). Regression analysis of MCS intensity and
ground motion parameters in Italy and its application in ShakeMap.
GJI, 180, 1138-1152, doi: 10.1111/j.1365-246X.2009.04467.xself
and Faenza and Michelini (2011). Regression analysis of MCS intensity
and ground motion spectral accelerations (SAs) in Italy. GJI, 186,
1415-1430, doi: 10.1111/j.1365-246X.2011.05125.x
"""
# -----------------------------------------------------------------------
# MMI = C1 + C2 * log10 (Y)
#
# Limit the distance residuals to between 0 and 160 km.
# Limit the magnitude residuals to between M3.0 and M6.9.
# These are the default in the other gmice
# Limit the distance residuals to between 10 and 300 km.
# Limit the magnitude residuals to between M3.0 and M7.3.
#
# These are calcualted on the basis of the maximum horizontal component.
# For psa 03, 10 and 30 the regression for the geometrical mean are
# available but not implemented in this modeles since the one for PGA
# and PGV are not available.
# -----------------------------------------------------------------------
def __init__(self):
super().__init__()
self.min_max = (1.0, 10.0)
self.name = "Faenza and Michelini (2010, 2011)"
self.scale = "scale_fm11.ps"
self._constants = {
self._pga: {"C1": 1.68, "C2": 2.58, "SMMI": 0.18, "SPGM": 0.31},
self._pgv: {"C1": 5.11, "C2": 2.35, "SMMI": 0.14, "SPGM": 0.22},
self._sa03: {"C1": 1.24, "C2": 2.47, "SMMI": 0.30, "SPGM": 0.42},
self._sa10: {"C1": 3.12, "C2": 2.05, "SMMI": 0.21, "SPGM": 0.31},
self._sa30: {"C1": 4.31, "C2": 2.00, "SMMI": 0.14, "SPGM": 0.26},
}
self.DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA])
self.DEFINED_FOR_SA_PERIODS = set([0.3, 1.0, 3.0])
[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, PGV and PSA
at 0.3, 1.0, and 3.0 sec periods.
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, PGV, or SA).
Supported SA periods are 0.3, 1.0, and 3.0 sec.
`[link] <http://docs.openquake.org/oq-hazardlib/master/imt.html>`
dists (ndarray):
Not used
mag (float):
Not used
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)
#
# Convert (for accelerations) from ln(g) to cm/s^2
# then take the log10
#
if imt != self._pgv:
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.log10(units) + amps * lfact
mmi = c["C1"] + c["C2"] * lamps
dmmi_damp = np.full_like(lamps, c["C2"] * lfact)
mmi = np.clip(mmi, 1.0, 10.0)
mmi[np.isnan(amps)] = 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, PGV and PSA for 0.3, 1.0, and
3.0 sec periods.
Args:
mmi (ndarray):
Macroseismic intensity.
imt (OpenQuake IMT):
IMT of the requested ground-motions intensities (must be
one of PGA, PGV, or SA).
`[link] <http://docs.openquake.org/oq-hazardlib/master/imt.html>`
dists (ndarray):
Not used
mag (float):
Not used
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()
# Set nan values to 1
ix_nan = np.isnan(mmi)
mmi[ix_nan] = 1.0
pgm = np.zeros_like(mmi)
dpgm_dmmi = np.zeros_like(mmi)
dummy_variable = np.ones(len(mmi))
#
# MMI to PGM
#
pgm = np.power(10, (mmi - c["C1"]) / c["C2"])
dpgm_dmmi = 1.0 / (c["C2"] * lfact) * dummy_variable
if imt != self._pgv:
units = 981.0
else:
units = 1.0
# Return a ln(amp) value. Convert PGA to from cm/s^2 to g
pgm /= units
pgm = np.log(pgm)
# Set nan values back from 1 to nan
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"],
self._sa03: self._constants[self._sa03]["SMMI"],
self._sa10: self._constants[self._sa10]["SMMI"],
self._sa30: self._constants[self._sa30]["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"],
self._sa03: lfact * self._constants[self._sa03]["SPGM"],
self._sa10: lfact * self._constants[self._sa10]["SPGM"],
self._sa30: lfact * self._constants[self._sa30]["SPGM"],
}
def _getConsts(self, imt):
"""
Helper function to get the constants.
"""
if (
imt != self._pga
and imt != self._pgv
and imt != self._sa03
and imt != self._sa10
and imt != self._sa30
):
raise ValueError("Invalid IMT " + str(imt))
c = self._constants[imt]
return c
