# The Hazard Library
# Copyright (C) 2012-2019 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 numpy
from openquake.baselib.slots import with_slots
from openquake.hazardlib.scalerel import PointMSR
from openquake.hazardlib.geo import Point, geodetic
from openquake.hazardlib.geo.surface.planar import PlanarSurface
from openquake.hazardlib.geo.nodalplane import NodalPlane
from openquake.hazardlib.source.base import ParametricSeismicSource
from openquake.hazardlib.source.rupture import ParametricProbabilisticRupture
from openquake.hazardlib.geo.utils import get_bounding_box
def _get_rupture_dimensions(src, mag, nodal_plane):
"""
Calculate and return the rupture length and width
for given magnitude ``mag`` and nodal plane.
:param src:
a PointSource, AreaSource or MultiPointSource
:param mag:
a magnitude
:param nodal_plane:
Instance of :class:`openquake.hazardlib.geo.nodalplane.NodalPlane`.
:returns:
Tuple of two items: rupture length in width in km.
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.
"""
area = src.magnitude_scaling_relationship.get_median_area(
mag, nodal_plane.rake)
rup_length = math.sqrt(area * src.rupture_aspect_ratio)
rup_width = area / rup_length
seismogenic_layer_width = (src.lower_seismogenic_depth
- src.upper_seismogenic_depth)
max_width = (seismogenic_layer_width
/ math.sin(math.radians(nodal_plane.dip)))
if rup_width > max_width:
rup_width = max_width
rup_length = area / rup_width
return rup_length, rup_width
[docs]@with_slots
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'
_slots_ = ParametricSeismicSource._slots_ + '''upper_seismogenic_depth
lower_seismogenic_depth location nodal_plane_distribution
hypocenter_distribution
'''.split()
MODIFICATIONS = set(())
RUPTURE_WEIGHT = 0.1
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
self.max_radius = 0
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 self.max_radius: # already computed
return self.max_radius
# extract maximum magnitude
max_mag, _rate = self.get_annual_occurrence_rates()[-1]
for (np_prob, np) in self.nodal_plane_distribution.data:
# compute rupture dimensions
rup_length, rup_width = _get_rupture_dimensions(self, max_mag, np)
# compute rupture width surface projection
rup_width = rup_width * math.cos(math.radians(np.dip))
# the projection radius is half of the rupture diagonal
radius = math.sqrt(rup_length ** 2 + rup_width ** 2) / 2.0
if radius > self.max_radius:
self.max_radius = radius
return self.max_radius
[docs] def iter_ruptures(self, hcdist=True, npdist=True):
"""
Generate one rupture for each combination of magnitude, nodal plane
and hypocenter depth.
"""
for mag, mag_occ_rate in self.get_annual_occurrence_rates():
for np_prob, np in self.nodal_plane_distribution.data:
for hc_prob, hc_depth in self.hypocenter_distribution.data:
hypocenter = Point(latitude=self.location.latitude,
longitude=self.location.longitude,
depth=hc_depth)
occurrence_rate = (mag_occ_rate *
(np_prob if npdist else 1) *
(hc_prob if hcdist else 1))
surface = self._get_rupture_surface(mag, np, hypocenter)
yield ParametricProbabilisticRupture(
mag, np.rake, self.tectonic_region_type, hypocenter,
surface, occurrence_rate,
self.temporal_occurrence_model)
if not hcdist:
break
if not npdist:
break
[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()
def _get_rupture_surface(self, mag, nodal_plane, hypocenter):
"""
Create and return rupture surface object with given properties.
:param mag:
Magnitude value, used to calculate rupture dimensions,
see :meth:`_get_rupture_dimensions`.
:param nodal_plane:
Instance of :class:`openquake.hazardlib.geo.nodalplane.NodalPlane`
describing the rupture orientation.
:param hypocenter:
Point representing rupture's hypocenter.
:returns:
Instance of :class:`~openquake.hazardlib.geo.surface.planar.PlanarSurface`.
"""
assert self.upper_seismogenic_depth <= hypocenter.depth \
and self.lower_seismogenic_depth >= hypocenter.depth
rdip = math.radians(nodal_plane.dip)
# precalculated azimuth values for horizontal-only and vertical-only
# moves from one point to another on the plane defined by strike
# and dip:
azimuth_right = nodal_plane.strike
azimuth_down = (azimuth_right + 90) % 360
azimuth_left = (azimuth_down + 90) % 360
azimuth_up = (azimuth_left + 90) % 360
rup_length, rup_width = _get_rupture_dimensions(self, mag, nodal_plane)
# calculate the height of the rupture being projected
# on the vertical plane:
rup_proj_height = rup_width * math.sin(rdip)
# and it's width being projected on the horizontal one:
rup_proj_width = rup_width * math.cos(rdip)
# half height of the vertical component of rupture width
# is the vertical distance between the rupture geometrical
# center and it's upper and lower borders:
hheight = rup_proj_height / 2.
# calculate how much shallower the upper border of the rupture
# is than the upper seismogenic depth:
vshift = self.upper_seismogenic_depth - hypocenter.depth + hheight
# if it is shallower (vshift > 0) than we need to move the rupture
# by that value vertically.
if vshift < 0:
# the top edge is below upper seismogenic depth. now we need
# to check that we do not cross the lower border.
vshift = self.lower_seismogenic_depth - hypocenter.depth - hheight
if vshift > 0:
# the bottom edge of the rupture is above the lower sesmogenic
# depth. that means that we don't need to move the rupture
# as it fits inside seismogenic layer.
vshift = 0
# if vshift < 0 than we need to move the rupture up by that value.
# now we need to find the position of rupture's geometrical center.
# in any case the hypocenter point must lie on the surface, however
# the rupture center might be off (below or above) along the dip.
rupture_center = hypocenter
if vshift != 0:
# we need to move the rupture center to make the rupture fit
# inside the seismogenic layer.
hshift = abs(vshift / math.tan(rdip))
rupture_center = rupture_center.point_at(
horizontal_distance=hshift, vertical_increment=vshift,
azimuth=(azimuth_up if vshift < 0 else azimuth_down))
# from the rupture center we can now compute the coordinates of the
# four coorners by moving along the diagonals of the plane. This seems
# to be better then moving along the perimeter, because in this case
# errors are accumulated that induce distorsions in the shape with
# consequent raise of exceptions when creating PlanarSurface objects
# theta is the angle between the diagonal of the surface projection
# and the line passing through the rupture center and parallel to the
# top and bottom edges. Theta is zero for vertical ruptures (because
# rup_proj_width is zero)
theta = math.degrees(
math.atan((rup_proj_width / 2.) / (rup_length / 2.)))
hor_dist = math.sqrt(
(rup_length / 2.) ** 2 + (rup_proj_width / 2.) ** 2)
left_top = rupture_center.point_at(
horizontal_distance=hor_dist,
vertical_increment=-rup_proj_height / 2.,
azimuth=(nodal_plane.strike + 180 + theta) % 360)
right_top = rupture_center.point_at(
horizontal_distance=hor_dist,
vertical_increment=-rup_proj_height / 2.,
azimuth=(nodal_plane.strike - theta) % 360)
left_bottom = rupture_center.point_at(
horizontal_distance=hor_dist,
vertical_increment=rup_proj_height / 2.,
azimuth=(nodal_plane.strike + 180 - theta) % 360)
right_bottom = rupture_center.point_at(
horizontal_distance=hor_dist,
vertical_increment=rup_proj_height / 2.,
azimuth=(nodal_plane.strike + theta) % 360)
surface = PlanarSurface(
nodal_plane.strike, nodal_plane.dip, left_top, right_top,
right_bottom, left_bottom)
return surface
@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
"""
radius = self._get_max_rupture_projection_radius()
return get_bounding_box([self.location], maxdist + radius)
[docs] def geom(self):
"""
:returns: the geometry as an array of shape (1, 3)
"""
loc = self.location
return numpy.array([[loc.x, loc.y, loc.z]], numpy.float32)
[docs]def make_rupture(trt, mag, msr=PointMSR(), aspect_ratio=1.0, seismo=(10, 30),
nodal_plane_tup=(0, 90, 0), hc_tup=(0, 0, 20),
occurrence_rate=1, tom=None):
hc = Point(*hc_tup)
np = NodalPlane(*nodal_plane_tup)
ps = object.__new__(PointSource)
ps.magnitude_scaling_relationship = msr
ps.upper_seismogenic_depth = seismo[0]
ps.lower_seismogenic_depth = seismo[1]
ps.rupture_aspect_ratio = aspect_ratio
surface = ps._get_rupture_surface(mag, np, hc)
rup = ParametricProbabilisticRupture(
mag, np.rake, trt, hc, surface, occurrence_rate, tom)
return rup