# coding: utf-8
# The Hazard Library
# Copyright (C) 2012-2018 GEM Foundation
#
# This program 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.
#
# This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module :mod:`openquake.hazardlib.source.rupture` defines classes
:class:`BaseRupture` and its subclasses
:class:`NonParametricProbabilisticRupture` and
:class:`ParametricProbabilisticRupture`
"""
import abc
import numpy
import math
import itertools
import collections
from openquake.baselib import general
from openquake.baselib.slots import with_slots
from openquake.hazardlib import geo
from openquake.hazardlib.geo.nodalplane import NodalPlane
from openquake.hazardlib.geo.mesh import RectangularMesh
from openquake.hazardlib.geo.point import Point
from openquake.hazardlib.geo.geodetic import geodetic_distance
from openquake.hazardlib.near_fault import (
get_plane_equation, projection_pp, directp, average_s_rad, isochone_ratio)
from openquake.hazardlib.geo.surface.base import BaseSurface
U16 = numpy.uint16
U32 = numpy.uint32
U64 = numpy.uint64
TWO16 = U64(2 ** 16)
TWO32 = U64(2 ** 32)
pmf_dt = numpy.dtype([('prob', float), ('occ', U32)])
events_dt = numpy.dtype([('eid', U64), ('rlz', U16)])
classes = {} # initialized in .init()
[docs]@with_slots
class BaseRupture(metaclass=abc.ABCMeta):
"""
Rupture object represents a single earthquake rupture.
:param mag:
Magnitude of the rupture.
:param rake:
Rake value of the rupture.
See :class:`~openquake.hazardlib.geo.nodalplane.NodalPlane`.
:param tectonic_region_type:
Rupture's tectonic regime. One of constants
in :class:`openquake.hazardlib.const.TRT`.
:param hypocenter:
A :class:`~openquake.hazardlib.geo.point.Point`, rupture's hypocenter.
:param surface:
An instance of subclass of
:class:`~openquake.hazardlib.geo.surface.base.BaseSurface`.
Object representing the rupture surface geometry.
:param rupture_slip_direction:
Angle describing rupture propagation direction in decimal degrees.
:raises ValueError:
If magnitude value is not positive, or tectonic region type is unknown.
NB: if you want to convert the rupture into XML, you should set the
attribute surface_nodes to an appropriate value.
"""
_slots_ = '''mag rake tectonic_region_type hypocenter surface
rupture_slip_direction'''.split()
serial = 0 # set to a value > 0 by the engine
_code = {}
types = {}
[docs] @classmethod
def init(cls):
"""
Initialize the class dictionaries `._code` and .`types` encoding the
bidirectional correspondence between an integer in the range 0..255
(the code) and a pair of classes (rupture_class, surface_class).
This is useful when serializing the rupture to and from HDF5.
"""
rupture_classes = [BaseRupture] + list(get_subclasses(BaseRupture))
surface_classes = list(get_subclasses(BaseSurface))
for cl in rupture_classes + surface_classes:
classes[cl.__name__] = cl
n = 0
for rup, sur in itertools.product(rupture_classes, surface_classes):
cls._code[rup, sur] = n
cls.types[n] = rup, sur
n += 1
if n >= 256:
raise ValueError('Too many rupture codes: %d' % n)
def __init__(self, mag, rake, tectonic_region_type, hypocenter,
surface, rupture_slip_direction=None):
if not mag > 0:
raise ValueError('magnitude must be positive')
NodalPlane.check_rake(rake)
self.tectonic_region_type = tectonic_region_type
self.rake = rake
self.mag = mag
self.hypocenter = hypocenter
self.surface = surface
self.rupture_slip_direction = rupture_slip_direction
@property
def code(self):
"""Returns the code (integer in the range 0 .. 255) of the rupture"""
return self._code[self.__class__, self.surface.__class__]
[docs] def get_probability_no_exceedance(self, poes):
"""
Compute and return the probability that in the time span for which the
rupture is defined, the rupture itself never generates a ground motion
value higher than a given level at a given site.
Such calculation is performed starting from the conditional probability
that an occurrence of the current rupture is producing a ground motion
value higher than the level of interest at the site of interest.
The actual formula used for such calculation depends on the temporal
occurrence model the rupture is associated with.
The calculation can be performed for multiple intensity measure levels
and multiple sites in a vectorized fashion.
:param poes:
2D numpy array containing conditional probabilities the the a
rupture occurrence causes a ground shaking value exceeding a
ground motion level at a site. First dimension represent sites,
second dimension intensity measure levels. ``poes`` can be obtained
calling the :meth:`method
<openquake.hazardlib.gsim.base.GroundShakingIntensityModel.get_poes>`.
"""
raise NotImplementedError
[docs] def sample_number_of_occurrences(self, n=1):
"""
Randomly sample number of occurrences from temporal occurrence model
probability distribution.
.. note::
This method is using random numbers. In order to reproduce the
same results numpy random numbers generator needs to be seeded, see
http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.seed.html
:returns:
numpy array of size n with number of rupture occurrences
"""
raise NotImplementedError
[docs]class NonParametricProbabilisticRupture(BaseRupture):
"""
Probabilistic rupture for which the probability distribution for rupture
occurrence is described through a generic probability mass function.
:param pmf:
Instance of :class:`openquake.hazardlib.pmf.PMF`. Values in the
abscissae represent number of rupture occurrences (in increasing order,
staring from 0) and values in the ordinates represent associated
probabilities. Example: if, for a given time span, a rupture has
probability ``0.8`` to not occurr, ``0.15`` to occur once, and
``0.05`` to occur twice, the ``pmf`` can be defined as ::
pmf = PMF([(0.8, 0), (0.15, 1), 0.05, 2)])
:raises ValueError:
If number of ruptures in ``pmf`` do not start from 0, are not defined
in increasing order, and if they are not defined with unit step
"""
def __init__(self, mag, rake, tectonic_region_type, hypocenter, surface,
pmf, rupture_slip_direction=None):
occ = numpy.array([occ for (prob, occ) in pmf.data])
if not occ[0] == 0:
raise ValueError('minimum number of ruptures must be zero')
if not numpy.all(numpy.sort(occ) == occ):
raise ValueError(
'numbers of ruptures must be defined in increasing order')
if not numpy.all(numpy.diff(occ) == 1):
raise ValueError(
'numbers of ruptures must be defined with unit step')
super().__init__(
mag, rake, tectonic_region_type, hypocenter, surface,
rupture_slip_direction)
# an array of probabilities with sum 1
self.probs_occur = numpy.array(
[prob for (prob, occ) in pmf.data], numpy.float32)
[docs] def get_probability_no_exceedance(self, poes):
"""
See :meth:`superclass method
<.rupture.BaseRupture.get_probability_no_exceedance>`
for spec of input and result values.
Uses the formula ::
∑ p(k|T) * p(X<x|rup)^k
where ``p(k|T)`` is the probability that the rupture occurs k times in
the time span ``T``, ``p(X<x|rup)`` is the probability that a rupture
occurrence does not cause a ground motion exceedance, and the summation
``∑`` is done over the number of occurrences ``k``.
``p(k|T)`` is given by the constructor's parameter ``pmf``, and
``p(X<x|rup)`` is computed as ``1 - poes``.
"""
# Converting from 1d to 2d
if len(poes.shape) == 1:
poes = numpy.reshape(poes, (-1, len(poes)))
p_kT = self.probs_occur
prob_no_exceed = numpy.array(
[v * ((1 - poes) ** i) for i, v in enumerate(p_kT)])
prob_no_exceed = numpy.sum(prob_no_exceed, axis=0)
prob_no_exceed[prob_no_exceed > 1.] = 1. # sanity check
prob_no_exceed[poes == 0.] = 1. # avoid numeric issues
return prob_no_exceed
[docs] def sample_number_of_occurrences(self, n=1):
"""
See :meth:`superclass method
<.rupture.BaseRupture.sample_number_of_occurrences>`
for spec of input and result values.
Uses 'Inverse Transform Sampling' method.
"""
# compute cdf from pmf
cdf = numpy.cumsum(self.probs_occur)
n_occ = numpy.digitize(numpy.random.random(n), cdf)
return n_occ
[docs]@with_slots
class ParametricProbabilisticRupture(BaseRupture):
"""
:class:`Rupture` associated with an occurrence rate and a temporal
occurrence model.
:param occurrence_rate:
Number of times rupture happens per year.
:param temporal_occurrence_model:
Temporal occurrence model assigned for this rupture. Should
be an instance of :class:`openquake.hazardlib.tom.PoissonTOM`.
:raises ValueError:
If occurrence rate is not positive.
"""
_slots_ = BaseRupture._slots_ + [
'occurrence_rate', 'temporal_occurrence_model']
def __init__(self, mag, rake, tectonic_region_type, hypocenter, surface,
occurrence_rate, temporal_occurrence_model,
rupture_slip_direction=None):
if not occurrence_rate > 0:
raise ValueError('occurrence rate must be positive')
super().__init__(
mag, rake, tectonic_region_type, hypocenter, surface,
rupture_slip_direction)
self.temporal_occurrence_model = temporal_occurrence_model
self.occurrence_rate = occurrence_rate
[docs] def get_probability_one_or_more_occurrences(self):
"""
Return the probability of this rupture to occur one or more times.
Uses
:meth:`~openquake.hazardlib.tom.PoissonTOM.get_probability_one_or_more_occurrences`
of an assigned temporal occurrence model.
"""
tom = self.temporal_occurrence_model
rate = self.occurrence_rate
return tom.get_probability_one_or_more_occurrences(rate)
[docs] def get_probability_one_occurrence(self):
"""
Return the probability of this rupture to occur exactly one time.
Uses :meth:
`openquake.hazardlib.tom.PoissonTOM.get_probability_one_occurrence`
of an assigned temporal occurrence model.
"""
tom = self.temporal_occurrence_model
rate = self.occurrence_rate
return tom.get_probability_one_occurrence(rate)
[docs] def sample_number_of_occurrences(self, n=1):
"""
Draw a random sample from the distribution and return a number
of events to occur as an array of integers of size n.
Uses :meth:
`openquake.hazardlib.tom.PoissonTOM.sample_number_of_occurrences`
of an assigned temporal occurrence model.
"""
r = self.occurrence_rate * self.temporal_occurrence_model.time_span
return numpy.random.poisson(r, n)
[docs] def get_probability_no_exceedance(self, poes):
"""
See :meth:`superclass method
<.rupture.BaseRupture.get_probability_no_exceedance>`
for spec of input and result values.
Uses
:meth:`openquake.hazardlib.tom.PoissonTOM.get_probability_no_exceedance`
"""
tom = self.temporal_occurrence_model
rate = self.occurrence_rate
return tom.get_probability_no_exceedance(rate, poes)
[docs] def get_dppvalue(self, site):
"""
Get the directivity prediction value, DPP at
a given site as described in Spudich et al. (2013).
:param site:
:class:`~openquake.hazardlib.geo.point.Point` object
representing the location of the target site
:returns:
A float number, directivity prediction value (DPP).
"""
origin = self.surface.get_resampled_top_edge()[0]
dpp_multi = []
index_patch = self.surface.hypocentre_patch_index(
self.hypocenter, self.surface.get_resampled_top_edge(),
self.surface.mesh.depths[0][0], self.surface.mesh.depths[-1][0],
self.surface.get_dip())
idx_nxtp = True
hypocenter = self.hypocenter
while idx_nxtp:
# E Plane Calculation
p0, p1, p2, p3 = self.surface.get_fault_patch_vertices(
self.surface.get_resampled_top_edge(),
self.surface.mesh.depths[0][0],
self.surface.mesh.depths[-1][0],
self.surface.get_dip(), index_patch=index_patch)
[normal, dist_to_plane] = get_plane_equation(
p0, p1, p2, origin)
pp = projection_pp(site, normal, dist_to_plane, origin)
pd, e, idx_nxtp = directp(
p0, p1, p2, p3, hypocenter, origin, pp)
pd_geo = origin.point_at(
(pd[0] ** 2 + pd[1] ** 2) ** 0.5, -pd[2],
numpy.degrees(math.atan2(pd[0], pd[1])))
# determine the lower bound of E path value
f1 = geodetic_distance(p0.longitude,
p0.latitude,
p1.longitude,
p1.latitude)
f2 = geodetic_distance(p2.longitude,
p2.latitude,
p3.longitude,
p3.latitude)
if f1 > f2:
f = f1
else:
f = f2
fs, rd, r_hyp = average_s_rad(site, hypocenter, origin,
pp, normal, dist_to_plane, e, p0,
p1, self.rupture_slip_direction)
cprime = isochone_ratio(e, rd, r_hyp)
dpp_exp = cprime * numpy.maximum(e, 0.1 * f) *\
numpy.maximum(fs, 0.2)
dpp_multi.append(dpp_exp)
# check if go through the next patch of the fault
index_patch = index_patch + 1
if (len(self.surface.get_resampled_top_edge())
<= 2) and (index_patch >=
len(self.surface.get_resampled_top_edge())):
idx_nxtp = False
elif index_patch >= len(self.surface.get_resampled_top_edge()):
idx_nxtp = False
elif idx_nxtp:
hypocenter = pd_geo
idx_nxtp = True
# calculate DPP value of the site.
dpp = numpy.log(numpy.sum(dpp_multi))
return dpp
[docs] def get_cdppvalue(self, target, buf=1.0, delta=0.01, space=2.):
"""
Get the directivity prediction value, centered DPP(cdpp) at
a given site as described in Spudich et al. (2013), and this cdpp is
used in Chiou and Young (2014) GMPE for near-fault directivity
term prediction.
:param target_site:
A mesh object representing the location of the target sites.
:param buf:
A buffer distance in km to extend the mesh borders
:param delta:
The distance between two adjacent points in the mesh
:param space:
The tolerance for the distance of the sites (default 2 km)
:returns:
The centered directivity prediction value of Chiou and Young
"""
min_lon, max_lon, max_lat, min_lat = self.surface.get_bounding_box()
min_lon -= buf
max_lon += buf
min_lat -= buf
max_lat += buf
lons = numpy.arange(min_lon, max_lon + delta, delta)
# ex shape (233,)
lats = numpy.arange(min_lat, max_lat + delta, delta)
# ex shape (204,)
mesh = RectangularMesh(*numpy.meshgrid(lons, lats))
mesh_rup = self.surface.get_min_distance(mesh).reshape(mesh.shape)
# ex shape (204, 233)
target_rup = self.surface.get_min_distance(target)
# ex shape (2,)
cdpp = numpy.zeros_like(target.lons)
for i, (target_lon, target_lat) in enumerate(
zip(target.lons, target.lats)):
# indices around target_rup[i]
around = (mesh_rup <= target_rup[i] + space) & (
mesh_rup >= target_rup[i] - space)
dpp_target = self.get_dppvalue(Point(target_lon, target_lat))
dpp_mean = numpy.mean(
[self.get_dppvalue(Point(lon, lat))
for lon, lat in zip(mesh.lons[around], mesh.lats[around])])
cdpp[i] = dpp_target - dpp_mean
return cdpp
[docs]def get_subclasses(cls):
for subclass in cls.__subclasses__():
yield subclass
for ssc in get_subclasses(subclass):
yield ssc
[docs]def get_geom(surface, is_from_fault_source, is_multi_surface,
is_gridded_surface):
"""
The following fields can be interpreted different ways,
depending on the value of `is_from_fault_source`. If
`is_from_fault_source` is True, each of these fields should
contain a 2D numpy array (all of the same shape). Each triple
of (lon, lat, depth) for a given index represents the node of
a rectangular mesh. If `is_from_fault_source` is False, each
of these fields should contain a sequence (tuple, list, or
numpy array, for example) of 4 values. In order, the triples
of (lon, lat, depth) represent top left, top right, bottom
left, and bottom right corners of the the rupture's planar
surface. Update: There is now a third case. If the rupture
originated from a characteristic fault source with a
multi-planar-surface geometry, `lons`, `lats`, and `depths`
will contain one or more sets of 4 points, similar to how
planar surface geometry is stored (see above).
:param surface: a Surface instance
:param is_from_fault_source: a boolean
:param is_multi_surface: a boolean
"""
if is_from_fault_source:
# for simple and complex fault sources,
# rupture surface geometry is represented by a mesh
surf_mesh = surface.mesh
lons = surf_mesh.lons
lats = surf_mesh.lats
depths = surf_mesh.depths
else:
if is_multi_surface:
# `list` of
# openquake.hazardlib.geo.surface.planar.PlanarSurface
# objects:
surfaces = surface.surfaces
# lons, lats, and depths are arrays with len == 4*N,
# where N is the number of surfaces in the
# multisurface for each `corner_*`, the ordering is:
# - top left
# - top right
# - bottom left
# - bottom right
lons = numpy.concatenate([x.corner_lons for x in surfaces])
lats = numpy.concatenate([x.corner_lats for x in surfaces])
depths = numpy.concatenate([x.corner_depths for x in surfaces])
elif is_gridded_surface:
# the surface mesh has shape (1, N)
lons = surface.mesh.lons[0]
lats = surface.mesh.lats[0]
depths = surface.mesh.depths[0]
else:
# For area or point source,
# rupture geometry is represented by a planar surface,
# defined by 3D corner points
lons = numpy.zeros((4))
lats = numpy.zeros((4))
depths = numpy.zeros((4))
# NOTE: It is important to maintain the order of these
# corner points. TODO: check the ordering
for i, corner in enumerate((surface.top_left,
surface.top_right,
surface.bottom_left,
surface.bottom_right)):
lons[i] = corner.longitude
lats[i] = corner.latitude
depths[i] = corner.depth
return lons, lats, depths
[docs]class ExportedRupture(object):
"""
Simplified Rupture class with attributes rupid, events_by_ses, indices
and others, used in export.
:param rupid: rupture serial ID
:param events_by_ses: dictionary ses_idx -> event records
:param indices: site indices
"""
def __init__(self, rupid, events_by_ses, indices=None):
self.rupid = rupid
self.events_by_ses = events_by_ses
self.indices = indices
[docs]def get_eids(rup_array, samples_by_grp, num_rlzs_by_grp):
"""
:param rup_array: a composite array with fields serial, n_occ and grp_id
:param samples_by_grp: a dictionary grp_id -> samples
:param num_rlzs_by_grp: a dictionary grp_id -> num_rlzs
"""
all_eids = []
for rup in rup_array:
grp_id = rup['grp_id']
samples = samples_by_grp[grp_id]
num_rlzs = num_rlzs_by_grp[grp_id]
num_events = rup['n_occ'] if samples > 1 else rup['n_occ'] * num_rlzs
eids = TWO32 * U64(rup['serial']) + numpy.arange(num_events, dtype=U64)
all_eids.append(eids)
return numpy.concatenate(all_eids)
[docs]class EBRupture(object):
"""
An event based rupture. It is a wrapper over a hazardlib rupture
object, containing an array of site indices affected by the rupture,
as well as the IDs of the corresponding seismic events.
"""
def __init__(self, rupture, srcidx, grp_id, n_occ, samples=1):
assert rupture.serial # sanity check
self.rupture = rupture
self.srcidx = srcidx
self.grp_id = grp_id
self.n_occ = n_occ
self.samples = samples
@property
def serial(self):
"""
Serial number of the rupture
"""
return self.rupture.serial
[docs] def get_eids_by_rlz(self, rlzs_by_gsim):
"""
:param n_occ: number of occurrences
:params rlzs_by_gsim: a dictionary gsims -> rlzs array
:param samples: number of samples in current source group
:returns: a dictionary rlz index -> eids array
"""
j = 0
dic = {}
if self.samples == 1: # full enumeration or akin to it
for rlzs in rlzs_by_gsim.values():
for rlz in rlzs:
dic[rlz] = numpy.arange(j, j + self.n_occ, dtype=U64) + (
TWO32 * U64(self.serial))
j += self.n_occ
else: # associated eids to the realizations
rlzs = numpy.concatenate(list(rlzs_by_gsim.values()))
assert len(rlzs) == self.samples, (len(rlzs), self.samples)
histo = general.random_histogram(
self.n_occ, self.samples, self.serial)
for rlz, n in zip(rlzs, histo):
dic[rlz] = numpy.arange(j, j + n, dtype=U64) + (
TWO32 * U64(self.serial))
j += n
return dic
[docs] def get_events(self, rlzs_by_gsim):
"""
:returns: an array of events with fields eid, rlz
"""
all_eids, rlzs = [], []
for rlz, eids in self.get_eids_by_rlz(rlzs_by_gsim).items():
all_eids.extend(eids)
rlzs.extend([rlz] * len(eids))
return numpy.fromiter(zip(all_eids, rlzs), events_dt)
[docs] def get_eids(self, num_rlzs):
"""
:param num_rlzs: the number of realizations for the given group
:returns: an array of event IDs
"""
num_events = self.n_occ if self.samples > 1 else self.n_occ * num_rlzs
return TWO32 * U64(self.serial) + numpy.arange(num_events, dtype=U64)
[docs] def get_events_by_ses(self, events, num_ses):
"""
:returns: a dictionary ses index -> events array
"""
numpy.random.seed(self.serial)
sess = numpy.random.choice(num_ses, len(events)) + 1
events_by_ses = collections.defaultdict(list)
for ses, event in zip(sess, events):
events_by_ses[ses].append(event)
for ses in events_by_ses:
events_by_ses[ses] = numpy.array(events_by_ses[ses])
return events_by_ses
[docs] def get_ses_by_eid(self, rlzs_by_gsim, num_ses):
events = self.get_events(rlzs_by_gsim)
numpy.random.seed(self.serial)
sess = numpy.random.choice(num_ses, len(events)) + 1
return dict(zip(events['eid'], sess))
[docs] def export(self, mesh, rlzs_by_gsim, num_ses):
"""
Yield :class:`Rupture` objects, with all the
attributes set, suitable for export in XML format.
"""
rupture = self.rupture
events = self.get_events(rlzs_by_gsim)
events_by_ses = self.get_events_by_ses(events, num_ses)
new = ExportedRupture(self.serial, events_by_ses)
new.mesh = mesh[()]
if isinstance(rupture.surface, geo.ComplexFaultSurface):
new.typology = 'complexFaultsurface'
elif isinstance(rupture.surface, geo.SimpleFaultSurface):
new.typology = 'simpleFaultsurface'
elif isinstance(rupture.surface, geo.GriddedSurface):
new.typology = 'griddedRupture'
elif isinstance(rupture.surface, geo.MultiSurface):
new.typology = 'multiPlanesRupture'
else:
new.typology = 'singlePlaneRupture'
new.is_from_fault_source = iffs = isinstance(
rupture.surface, (geo.ComplexFaultSurface,
geo.SimpleFaultSurface))
new.is_gridded_surface = igs = isinstance(
rupture.surface, geo.GriddedSurface)
new.is_multi_surface = ims = isinstance(
rupture.surface, geo.MultiSurface)
new.lons, new.lats, new.depths = get_geom(
rupture.surface, iffs, ims, igs)
new.surface = rupture.surface
new.strike = rupture.surface.get_strike()
new.dip = rupture.surface.get_dip()
new.rake = rupture.rake
new.hypocenter = rupture.hypocenter
new.tectonic_region_type = rupture.tectonic_region_type
new.magnitude = new.mag = rupture.mag
new.top_left_corner = None if iffs or ims or igs else (
new.lons[0], new.lats[0], new.depths[0])
new.top_right_corner = None if iffs or ims or igs else (
new.lons[1], new.lats[1], new.depths[1])
new.bottom_left_corner = None if iffs or ims or igs else (
new.lons[2], new.lats[2], new.depths[2])
new.bottom_right_corner = None if iffs or ims or igs else (
new.lons[3], new.lats[3], new.depths[3])
return new
def __repr__(self):
return '<%s %d[%d]>' % (
self.__class__.__name__, self.serial, self.n_occ)