# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2025 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.
"""
Module :mod:`openquake.hazardlib.imt` defines different intensity measure
types.
"""
import re
import collections
import numpy
from openquake.baselib.general import DictArray
FREQUENCY_PATTERN = '^(EAS|FAS|DRVT|AvgSA)\\((\\d+\\.*\\d*)\\)'
[docs]def positivefloat(val):
"""
Raise a ValueError if val <= 0
"""
if val <= 0:
raise ValueError(val)
[docs]def imt2tup(string):
"""
>>> imt2tup('PGA')
('PGA',)
>>> imt2tup('SA(1.0)')
('SA(1.0)', 1.0)
>>> imt2tup('SA(1)')
('SA(1.0)', 1.0)
"""
s = string.strip()
name, *rest = s.split('(')
if name not in globals():
raise KeyError(name)
elif len(name) > 12:
raise NameError('IMT class name longer than 12 chars: %s' % name)
elif not rest:
if name == 'SA':
raise ValueError('Missing period in SA')
# no parenthesis, PGA is considered the same as PGA()
return (s,)
if len(rest[0][:-1].split(',')) == 1:
period = float(rest[0][:-1])
elif len(rest[0][:-1].split(',')) == 2:
period = float(rest[0][:-1].split(',')[0])
strength_ratio = float(rest[0][:-1].split(',')[1])
else:
raise NameError('IMT attributes not recognizable: %s' % rest[0][:-1])
if name.startswith("Sa_avg2") or name.startswith("SA_avg2"):
return ('Sa_avg2(%s)' % period, period)
elif name.startswith("Sa_avg3") or name.startswith("SA_avg3"):
return ('Sa_avg3(%s)' % period, period)
elif name.startswith("SA") or name.startswith("Sa"):
return ('SA(%s)' % period, period)
elif name.startswith("FIV3"):
return ('FIV3(%s)' % period, period)
elif name.startswith("SDi"):
return ('SDi(%s,%s)' % (period, strength_ratio), period, strength_ratio)
else:
raise NameError('IMT class name not recognizable: %s' % name)
[docs]def from_string(imt, _damping=5.0):
"""
Convert an IMT string into an hazardlib object.
:param str imt:
Intensity Measure Type.
"""
m = re.match(FREQUENCY_PATTERN, imt)
if m: # passed float interpreted as frequency
if m.group(1) == 'EAS':
im = EAS(float(m.group(2)))
elif m.group(1) == 'FAS':
im = FAS(float(m.group(2)))
elif m.group(1) == 'DRVT':
im = DRVT(float(m.group(2)))
elif m.group(1) == 'AvgSA':
im = AvgSA(float(m.group(2)))
return im
elif re.match(r'^SDi\((\d+\.?\d*),(\d+\.?\d*)\)$', imt):
m = re.match(r'^SDi\((\d+\.?\d*),(\d+\.?\d*)\)$', imt)
return SDi(float(m.group(1)), float(m.group(2)))
elif re.match(r'[ \+\d\.]+', imt): # passed float interpreted as period
return SA(float(imt))
return IMT(*imt2tup(imt))
[docs]def sort_by_imt(imtls):
"""
:param imtls: a dictionary keyed by IMT string
:returns: a new dictionary with the keys sorted by period
>>> sort_by_imt({'SA(10.0)': 1, 'SA(2.0)': 2})
{'SA(2.0)': 2, 'SA(10.0)': 1}
"""
imts = sorted(imtls, key=lambda imt: from_string(imt).period)
return {imt: imtls[imt] for imt in imts}
[docs]def dictarray(imtls):
"""
:returns: a DictArray sorted by IMT
"""
return DictArray(sort_by_imt(imtls))
[docs]def repr(self):
if self.period and self.damping != 5.0:
if self.string.startswith('SDi'):
return 'SDi(%s, %s, %s)' % (self.period, self.strength_ratio,
self.damping)
return 'SA(%s, %s)' % (self.period, self.damping)
return self.string
IMT = collections.namedtuple('IMT', 'string period damping strength_ratio')
IMT.__new__.__defaults__ = (0., 5.0, None)
IMT.__lt__ = lambda self, other: self[1] < other[1]
IMT.__gt__ = lambda self, other: self[1] > other[1]
IMT.__le__ = lambda self, other: self[1] <= other[1]
IMT.__ge__ = lambda self, other: self[1] >= other[1]
IMT.__repr__ = repr
IMT.frequency = property(lambda self: 1. / self.period)
[docs]def PGA():
"""
Peak ground acceleration during an earthquake measured in units
of ``g``, times of gravitational acceleration.
"""
return IMT('PGA')
[docs]def PGV():
"""
Peak ground velocity during an earthquake measured in units of ``cm/sec``.
"""
return IMT('PGV')
[docs]def PGD():
"""
Peak ground displacement during an earthquake measured in units of ``cm``.
"""
return IMT('PGD')
[docs]def EAS(frequency):
"""
Effective Amplitude Spectrum in terms of a frequency (in Hz).
"""
period = 1. / frequency
return IMT('EAS(%.6f)' % frequency, period, 5.0)
[docs]def FAS(frequency):
"""
Fourier Amplitude Spectrum in terms of a frequency (in Hz).
"""
period = 1. / frequency
return IMT('FAS(%.6f)' % frequency, period, 5.0)
[docs]def DRVT(frequency):
"""
Duration as defined in Bora et al. (2019)
"""
period = 1. / frequency
return IMT('DRVT(%.6f)' % frequency, period, 5.0)
[docs]def SA(period, damping=5.0):
"""
Spectral acceleration, defined as the maximum acceleration of a damped,
single-degree-of-freedom harmonic oscillator. Units are ``g``, times
of gravitational acceleration.
"""
period = float(period)
return IMT('SA(%s)' % period, period, damping)
[docs]def FIV3(period, damping=5.0):
"""
Filtered incremental velocity, as defined in: Dávalos, H. and Miranda,
E. (2019) ‘Filtered incremental velocity: A novel approach in
intensity measures for seismic collapse estimation’, Earthquake
Engineering and Structural Dynamics, 48(12), pp. 1384–1405. Available
at: https://doi.org/10.1002/eqe.3205. Units are ``cm/s``.
"""
period = float(period)
return IMT('FIV3(%s)' % period, period, damping)
[docs]def Sa_avg2(period, damping=5.0):
period = float(period)
return IMT('Sa_avg2(%s)' % period, period, damping)
[docs]def Sa_avg3(period, damping=5.0):
period = float(period)
return IMT('Sa_avg3(%s)' % period, period, damping)
[docs]def SDi(period, strength_ratio, damping=5.0):
"""
Inelastic spectral displacement, defined as the maximum displacement
of a damped, single-degree-of-freedom inelastic oscillator. Units
are ``cm``.
"""
period = float(period)
strength_ratio = float(strength_ratio)
return IMT('SDi(%s,%s)' % (period, strength_ratio), period, damping,
strength_ratio)
[docs]def AvgSA(period=None, damping=5.0):
"""
Dummy spectral acceleration to compute average ground motion over
several spectral ordinates. Depending on the choice of AvgSA GMPE, this
can operate as a scalar value or as a vector quantity.
"""
return IMT('AvgSA(%s)' % period, period, damping)\
if period else IMT('AvgSA')
[docs]def IA():
"""
Arias intensity. Determines the intensity of shaking by measuring
the acceleration of transient seismic waves. Units are ``m/s``.
"""
return IMT('IA')
[docs]def CAV():
"""
Cumulative Absolute Velocity. Defins the integral of the absolute
acceleration time series. Units are "g-sec"
"""
return IMT('CAV')
[docs]def RSD():
"""
Relative significant duration, 5-95% of :class:`Arias intensity<IA>`,
in seconds.
"""
return IMT('RSD')
[docs]def RSD595():
"""
Alias for RSD
"""
return IMT('RSD595')
[docs]def RSD575():
"""
Relative significant duration, 5-75% of :class:`Arias intensity<IA>`,
in seconds.
"""
return IMT('RSD575')
[docs]def RSD2080():
"""
Relative significant duration, 20-80% of :class:`Arias intensity<IA>`,
in seconds.
"""
return IMT('RSD2080')
[docs]def MMI():
"""
Modified Mercalli intensity, a Roman numeral describing the severity
of an earthquake in terms of its effects on the earth's surface
and on humans and their structures.
"""
return IMT('MMI')
[docs]def JMA():
"""
Modified Mercalli intensity, a Roman numeral describing the severity
of an earthquake in terms of its effects on the earth's surface
and on humans and their structures.
"""
return IMT('JMA')
# secondary IMTs
sec_imts = '''ASH LAVA LAHAR PYRO
Disp DispProb LiqProb LiqOccur LSE PGDMax LSD PGDGeomMean LsProb
'''.split()
for sec in sec_imts:
assert '_' not in sec, sec
# Volcanic IMTs
[docs]def ASH():
"""
Level of the ash fall in millimeters
"""
return IMT('ASH')
[docs]def LAVA():
"""
Lava Intensity
"""
return IMT('LAVA')
[docs]def LAHAR():
"""
Lahar Intensity
"""
return IMT('LAHAR')
[docs]def PYRO():
"""
Pyroclastic Flow Intensity
"""
return IMT('PYRO')
# Liquefaction IMTs
[docs]def Disp():
"""
Displacement
"""
return IMT('Disp')
[docs]def DispProb():
"""
Displacement probability
"""
return IMT('DispProb')
[docs]def LiqProb():
"""
Liquefaction probability
"""
return IMT('LiqProb')
[docs]def LiqOccur():
"""
Liquefaction occurrence class
"""
return IMT('LiqOccur')
[docs]def LSE():
"""
Liquefaction or Landslide spatial extent.
"""
return IMT('LSE')
[docs]def PGDMax(vert_settlement, lat_spread):
"""
Maximum between vert_settlement and lat_spread
"""
return numpy.maximum(vert_settlement, lat_spread)
[docs]def LSD():
"""
Liquefaction-induced lateral spread displacements measured in units of
``m``.
"""
return IMT('LSD')
[docs]def PGDGeomMean(vert_settlement, lat_spread):
"""
Geometric mean between vert_settlement and lat_spread
"""
return numpy.sqrt(vert_settlement * lat_spread)
[docs]def LsProb():
"""
Probability of landsliding.
"""
return IMT('LsProb')
