# The Hazard Library
# Copyright (C) 2012-2022 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.point` defines :class:`PointSource`.
"""
import math
import copy
import numpy
from openquake.baselib.general import AccumDict, groupby_grid
from openquake.baselib.performance import Monitor
from openquake.hazardlib.geo import Point, geodetic
from openquake.hazardlib.geo.nodalplane import NodalPlane
from openquake.hazardlib.geo.surface.planar import (
build_planar, PlanarSurface, planin_dt)
from openquake.hazardlib.pmf import PMF
from openquake.hazardlib.scalerel.point import PointMSR
from openquake.hazardlib.source.base import ParametricSeismicSource
from openquake.hazardlib.source.rupture import (
ParametricProbabilisticRupture, PointRupture)
from openquake.hazardlib.geo.utils import get_bounding_box, angular_distance
# this is fast
[docs]def get_rupdims(areas, dip, width, rar):
"""
Calculate and return the rupture length and width
for given magnitude surface parameters.
:returns:
array of shape (M, 3) with rupture lengths, widths and heights
The rupture area is calculated using method
:meth:`~openquake.hazardlib.scalerel.base.BaseMSR.get_median_area`
of source's
magnitude-scaling relationship. In any case the returned
dimensions multiplication is equal to that value. Than
the area is decomposed to length and width with respect
to source's rupture aspect ratio.
If calculated rupture width being inclined by nodal plane's
dip angle would not fit in between upper and lower seismogenic
depth, the rupture width is shrunken to a maximum possible
and rupture length is extended to preserve the same area.
"""
out = numpy.zeros((len(areas), 3))
rup_length = numpy.sqrt(areas * rar)
rup_width = areas / rup_length
rdip = math.radians(dip)
max_width = width / math.sin(rdip)
big = rup_width > max_width
rup_width[big] = max_width
rup_length[big] = areas[big] / rup_width[big]
out[:, 0] = rup_length
out[:, 1] = rup_width * math.cos(rdip)
out[:, 2] = rup_width * math.sin(rdip)
return out
[docs]def msr_name(src):
"""
:returns: string representation of the MSR or "Undefined" if not applicable
"""
try:
return str(src.magnitude_scaling_relationship)
except AttributeError: # no MSR for nonparametric sources
return 'Undefined'
[docs]def calc_average(pointsources):
"""
:returns:
a dict with average strike, dip, rake, lon, lat, dep,
upper_seismogenic_depth, lower_seismogenic_depth
"""
acc = dict(lon=[], lat=[], dep=[], strike=[], dip=[], rake=[],
upper_seismogenic_depth=[], lower_seismogenic_depth=[],
rupture_aspect_ratio=[])
rates = []
trt = pointsources[0].tectonic_region_type
msr = msr_name(pointsources[0])
for src in pointsources:
assert src.tectonic_region_type == trt
assert msr_name(src) == msr
rates.append(sum(r for m, r in src.get_annual_occurrence_rates()))
ws, ds = zip(*src.nodal_plane_distribution.data)
strike = numpy.average([np.strike for np in ds], weights=ws)
dip = numpy.average([np.dip for np in ds], weights=ws)
rake = numpy.average([np.rake for np in ds], weights=ws)
ws, deps = zip(*src.hypocenter_distribution.data)
dep = numpy.average(deps, weights=ws)
acc['lon'].append(src.location.x)
acc['lat'].append(src.location.y)
acc['dep'].append(dep)
acc['strike'].append(strike)
acc['dip'].append(dip)
acc['rake'].append(rake)
acc['upper_seismogenic_depth'].append(src.upper_seismogenic_depth)
acc['lower_seismogenic_depth'].append(src.lower_seismogenic_depth)
acc['rupture_aspect_ratio'].append(src.rupture_aspect_ratio)
dic = {key: numpy.average(acc[key], weights=rates) for key in acc}
dic['lon'] = numpy.round(dic['lon'], 6)
dic['lat'] = numpy.round(dic['lat'], 6)
return dic
[docs]class PointSource(ParametricSeismicSource):
"""
Point source typology represents seismicity on a single geographical
location.
:param upper_seismogenic_depth:
Minimum depth an earthquake rupture can reach, in km.
:param lower_seismogenic_depth:
Maximum depth an earthquake rupture can reach, in km.
:param location:
:class:`~openquake.hazardlib.geo.point.Point` object
representing the location of the seismic source.
:param nodal_plane_distribution:
:class:`~openquake.hazardlib.pmf.PMF` object with values
that are instances
of :class:`openquake.hazardlib.geo.nodalplane.NodalPlane`.
Shows the distribution
of probability for rupture to have the certain nodal plane.
:param hypocenter_distribution:
:class:`~openquake.hazardlib.pmf.PMF` with values being float
numbers in km representing the depth of the hypocenter. Latitude
and longitude of the hypocenter is always set to ones of ``location``.
See also :class:`openquake.hazardlib.source.base.ParametricSeismicSource`
for description of other parameters.
:raises ValueError:
If upper seismogenic depth is below lower seismogenic
depth, if one or more of hypocenter depth values is shallower
than upper seismogenic depth or deeper than lower seismogenic depth.
"""
code = b'P'
MODIFICATIONS = set()
ps_grid_spacing = 0 # updated in CollapsedPointSource
def __init__(self, source_id, name, tectonic_region_type,
mfd, rupture_mesh_spacing,
magnitude_scaling_relationship, rupture_aspect_ratio,
temporal_occurrence_model,
# point-specific parameters
upper_seismogenic_depth, lower_seismogenic_depth,
location, nodal_plane_distribution, hypocenter_distribution):
super().__init__(
source_id, name, tectonic_region_type, mfd, rupture_mesh_spacing,
magnitude_scaling_relationship, rupture_aspect_ratio,
temporal_occurrence_model)
if not lower_seismogenic_depth > upper_seismogenic_depth:
raise ValueError('lower seismogenic depth must be below '
'upper seismogenic depth')
if not all(upper_seismogenic_depth <= depth <= lower_seismogenic_depth
for (prob, depth) in hypocenter_distribution.data):
raise ValueError('depths of all hypocenters must be in between '
'lower and upper seismogenic depths')
if not upper_seismogenic_depth > geodetic.EARTH_ELEVATION:
raise ValueError(
"Upper seismogenic depth must be greater than the "
"maximum elevation on Earth's surface (-8.848 km)")
self.location = location
self.nodal_plane_distribution = nodal_plane_distribution
self.hypocenter_distribution = hypocenter_distribution
self.upper_seismogenic_depth = upper_seismogenic_depth
self.lower_seismogenic_depth = lower_seismogenic_depth
[docs] def restrict(self, nodalplane, depth):
"""
:returns: source restricted to a single nodal plane and depth
"""
new = copy.copy(self)
new.nodal_plane_distribution = PMF([(1., nodalplane)])
new.hypocenter_distribution = PMF([(1., depth)])
return new
[docs] def get_planin(self, magd, npd):
"""
:return: array of dtype planin_dt of shape (#mags, #planes, #depths)
"""
msr = self.magnitude_scaling_relationship
width = self.lower_seismogenic_depth - self.upper_seismogenic_depth
rar = self.rupture_aspect_ratio
planin = numpy.zeros((len(magd), len(npd)), planin_dt).view(
numpy.recarray)
mrate, mags = numpy.array(magd).T # shape (2, M)
nrate = numpy.array([nrate for nrate, np in npd])
planin['rate'] = mrate[:, None] * nrate
for n, (nrate, np) in enumerate(npd):
arr = planin[:, n]
areas = msr.get_median_area(mags, np.rake)
arr['mag'] = mags
arr['strike'] = np.strike
arr['dip'] = np.dip
arr['rake'] = np.rake
arr['dims'] = get_rupdims(areas, np.dip, width, rar)
return planin
[docs] def max_radius(self):
"""
:returns: max radius + ps_grid_spacing * sqrt(2)/2
"""
max_rp_radius = self._get_max_rupture_projection_radius()
return self.ps_grid_spacing * .707 + max_rp_radius
def _get_max_rupture_projection_radius(self):
"""
Find a maximum radius of a circle on Earth surface enveloping a rupture
produced by this source.
:returns:
Half of maximum rupture's diagonal surface projection.
"""
if hasattr(self, 'radius'):
return self.radius[-1] # max radius
if isinstance(self.magnitude_scaling_relationship, PointMSR):
M = len(self.get_annual_occurrence_rates())
self.radius = numpy.zeros(M)
return self.radius[-1]
magd = [(r, mag) for mag, r in self.get_annual_occurrence_rates()]
npd = self.nodal_plane_distribution.data
self.radius = numpy.zeros(len(magd))
for m, planin in enumerate(self.get_planin(magd, npd)):
rup_length, rup_width, _ = planin.dims.max(axis=0) # (N, 3) => 3
# the projection radius is half of the rupture diagonal
self.radius[m] = math.sqrt(rup_length ** 2 + rup_width ** 2) / 2.0
return self.radius[-1] # max radius
[docs] def get_planar(self, shift_hypo=False, iruptures=False):
"""
:returns: a dictionary mag -> list of arrays of shape (U, 3)
"""
magd = [(r, mag) for mag, r in self.get_annual_occurrence_rates()]
if isinstance(self, CollapsedPointSource) and not iruptures:
out = AccumDict(accum=[])
for src in self.pointsources:
out += src.get_planar(shift_hypo)
return out
npd = self.nodal_plane_distribution.data
hdd = numpy.array(self.hypocenter_distribution.data)
clon, clat = self.location.x, self.location.y
usd = self.upper_seismogenic_depth
lsd = self.lower_seismogenic_depth
planin = self.get_planin(magd, npd)
planar = build_planar(planin, hdd, clon, clat, usd, lsd) # MND3
if not shift_hypo: # use the original hypocenter
planar.hypo[:, :, :, 0] = clon
planar.hypo[:, :, :, 1] = clat
for d, (drate, dep) in enumerate(hdd):
planar.hypo[:, :, d, 2] = dep
dic = {mag: [pla.reshape(-1, 3)]
for (_rate, mag), pla in zip(magd, planar)}
return dic
def _gen_ruptures(self, shift_hypo=False, step=1, iruptures=False):
magd = [(r, mag) for mag, r in self.get_annual_occurrence_rates()]
npd = self.nodal_plane_distribution.data
hdd = self.hypocenter_distribution.data
clon, clat = self.location.x, self.location.y
if step == 1:
# return full ruptures (one per magnitude)
planardict = self.get_planar(shift_hypo, iruptures)
for mag, [planar] in planardict.items():
for pla in planar.reshape(-1, 3):
surface = PlanarSurface.from_(pla)
strike, dip, rake = pla.sdr
rate = pla.wlr[2]
yield ParametricProbabilisticRupture(
mag, rake, self.tectonic_region_type,
Point(*pla.hypo), surface, rate,
self.temporal_occurrence_model)
else:
# return point ruptures (fast)
magd_ = list(enumerate(magd))
npd_ = list(enumerate(npd))
hdd_ = list(enumerate(hdd))
for m, (mrate, mag) in magd_[::step]:
for n, (nrate, np) in npd_[::step]:
for d, (drate, cdep) in hdd_[::step]:
rate = mrate * nrate * drate
yield PointRupture(
mag, np.rake, self.tectonic_region_type,
Point(clon, clat, cdep), np.strike, np.dip, rate,
self.temporal_occurrence_model,
self.lower_seismogenic_depth)
[docs] def iter_ruptures(self, **kwargs):
"""
Generate one rupture for each combination of magnitude, nodal plane
and hypocenter depth.
"""
return self._gen_ruptures(
shift_hypo=kwargs.get('shift_hypo'),
step=kwargs.get('step', 1))
# PointSource
[docs] def iruptures(self):
"""
Generate one rupture for each magnitude, called only if nphc > 1
"""
avg = calc_average([self]) # over nodal planes and hypocenters
np = NodalPlane(avg['strike'], avg['dip'], avg['rake'])
yield from self.restrict(np, avg['dep'])._gen_ruptures(iruptures=True)
[docs] def count_nphc(self):
"""
:returns: the number of nodal planes times the number of hypocenters
"""
return len(self.nodal_plane_distribution.data) * len(
self.hypocenter_distribution.data)
[docs] def count_ruptures(self):
"""
See :meth:
`openquake.hazardlib.source.base.BaseSeismicSource.count_ruptures`.
"""
return len(self.get_annual_occurrence_rates()) * self.count_nphc()
@property
def polygon(self):
"""
Polygon corresponding to the max_rupture_projection_radius
"""
radius = self._get_max_rupture_projection_radius()
return self.location.to_polygon(radius)
[docs] def get_bounding_box(self, maxdist):
"""
Bounding box of the point, enlarged by the maximum distance
"""
return get_bounding_box([self.location], maxdist + self.max_radius())
[docs] def wkt(self):
"""
:returns: the geometry as a WKT string
"""
loc = self.location
return 'POINT(%s %s)' % (loc.x, loc.y)
[docs]class CollapsedPointSource(PointSource):
"""
Source typology representing a cluster of point sources around a
specific location. The underlying sources must all have the same
tectonic region type, magnitude_scaling_relationship and
temporal_occurrence_model.
"""
code = b'p'
MODIFICATIONS = set()
def __init__(self, source_id, pointsources):
self.source_id = source_id
self.pointsources = pointsources
self.tectonic_region_type = pointsources[0].tectonic_region_type
self.magnitude_scaling_relationship = (
pointsources[0].magnitude_scaling_relationship)
self.temporal_occurrence_model = (
pointsources[0].temporal_occurrence_model)
vars(self).update(calc_average(pointsources))
self.location = Point(self.lon, self.lat, self.dep)
self.nodal_plane_distribution = PMF(
[(1., NodalPlane(self.strike, self.dip, self.rake))])
self.hypocenter_distribution = PMF([(1., self.dep)])
[docs] def get_annual_occurrence_rates(self):
"""
:returns: a list of pairs [(mag, mag_occur_rate), ...]
"""
acc = AccumDict(accum=0)
for psource in self.pointsources:
acc += dict(psource.get_annual_occurrence_rates())
return sorted(acc.items())
[docs] def count_nphc(self):
"""
:returns: the total number of nodal planes and hypocenters
"""
return sum(src.count_nphc() for src in self.pointsources)
[docs] def iter_ruptures(self, **kwargs):
"""
:returns: an iterator over the underlying ruptures
"""
step = kwargs.get('step', 1)
for src in self.pointsources[::step]:
yield from src.iter_ruptures(**kwargs)
# CollapsedPointSource
[docs] def iruptures(self):
"""
:yields: the underlying ruptures with mean nodal plane and hypocenter
"""
np = NodalPlane(self.strike, self.dip, self.rake)
yield from self.restrict(np, self.location.z)._gen_ruptures(
iruptures=True)
[docs] def count_ruptures(self):
"""
:returns: the total number of underlying ruptures
"""
return sum(src.count_ruptures() for src in self.pointsources)
[docs]def grid_point_sources(sources, ps_grid_spacing, monitor=Monitor()):
"""
:param sources:
a list of sources with the same grp_id (point sources and not)
:param ps_grid_spacing:
value of the point source grid spacing in km; if None, do nothing
:returns:
a dict grp_id -> list of non-point sources and collapsed point sources
"""
grp_id = sources[0].grp_id
for src in sources[1:]:
assert src.grp_id == grp_id, (src.grp_id, grp_id)
if not ps_grid_spacing:
return {grp_id: sources}
out = [src for src in sources if not hasattr(src, 'location')]
ps = numpy.array([src for src in sources if hasattr(src, 'location')])
if len(ps) < 2: # nothing to collapse
return {grp_id: out + list(ps)}
coords = numpy.zeros((len(ps), 3))
for p, psource in enumerate(ps):
coords[p, 0] = psource.location.x
coords[p, 1] = psource.location.y
coords[p, 2] = psource.location.z
if (len(numpy.unique(coords[:, 0])) == 1 or
len(numpy.unique(coords[:, 1])) == 1):
# degenerated rectangle, there is no grid, do not collapse
return {grp_id: out + list(ps)}
deltax = angular_distance(ps_grid_spacing, lat=coords[:, 1].mean())
deltay = angular_distance(ps_grid_spacing)
grid = groupby_grid(coords[:, 0], coords[:, 1], deltax, deltay)
task_no = getattr(monitor, 'task_no', 0)
for i, idxs in enumerate(grid.values()):
if len(idxs) > 1:
cps = CollapsedPointSource('cps-%d-%d' % (task_no, i), ps[idxs])
cps.grp_id = ps[0].grp_id
cps.trt_smr = ps[0].trt_smr
cps.ps_grid_spacing = ps_grid_spacing
out.append(cps)
else: # there is a single source
out.append(ps[idxs[0]])
return {grp_id: out}