# The Hazard Library
# Copyright (C) 2012-2014, 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/>.
"""
:mod:`openquake.hazardlib.calc.disagg` contains
:func:`disaggregation` as well as several aggregation functions for
extracting a specific PMF from the result of :func:`disaggregation`.
"""
from __future__ import division
from openquake.baselib.python3compat import range
import sys
import numpy
import warnings
import collections
from openquake.baselib.python3compat import raise_
from openquake.hazardlib.calc import filters
from openquake.hazardlib.geo.geodetic import npoints_between
from openquake.hazardlib.geo.utils import get_longitudinal_extent
from openquake.hazardlib.geo.utils import get_spherical_bounding_box, cross_idl
from openquake.hazardlib.site import SiteCollection
from openquake.hazardlib.gsim.base import ContextMaker
[docs]def disaggregation(
sources, site, imt, iml, gsims, truncation_level,
n_epsilons, mag_bin_width, dist_bin_width, coord_bin_width,
source_site_filter=filters.source_site_noop_filter,
rupture_site_filter=filters.rupture_site_noop_filter):
"""
Compute "Disaggregation" matrix representing conditional probability of an
intensity mesaure type ``imt`` exceeding, at least once, an intensity
measure level ``iml`` at a geographical location ``site``, given rupture
scenarios classified in terms of:
- rupture magnitude
- Joyner-Boore distance from rupture surface to site
- longitude and latitude of the surface projection of a rupture's point
closest to ``site``
- epsilon: number of standard deviations by which an intensity measure
level deviates from the median value predicted by a GSIM, given the
rupture parameters
- rupture tectonic region type
In other words, the disaggregation matrix allows to compute the probability
of each scenario with the specified properties (e.g., magnitude, or the
magnitude and distance) to cause one or more exceedences of a given hazard
level.
For more detailed information about the disaggregation, see for instance
"Disaggregation of Seismic Hazard", Paolo Bazzurro, C. Allin Cornell,
Bulletin of the Seismological Society of America, Vol. 89, pp. 501-520,
April 1999.
:param sources:
Seismic source model, as for
:mod:`PSHA <openquake.hazardlib.calc.hazard_curve>` calculator it
should be an iterator of seismic sources.
:param site:
:class:`~openquake.hazardlib.site.Site` of interest to calculate
disaggregation matrix for.
:param imt:
Instance of :mod:`intensity measure type <openquake.hazardlib.imt>`
class.
:param iml:
Intensity measure level. A float value in units of ``imt``.
:param gsims:
Tectonic region type to GSIM objects mapping.
:param truncation_level:
Float, number of standard deviations for truncation of the intensity
distribution.
:param n_epsilons:
Integer number of epsilon histogram bins in the result matrix.
:param mag_bin_width:
Magnitude discretization step, width of one magnitude histogram bin.
:param dist_bin_width:
Distance histogram discretization step, in km.
:param coord_bin_width:
Longitude and latitude histograms discretization step,
in decimal degrees.
:param source_site_filter:
Optional source-site filter function. See
:mod:`openquake.hazardlib.calc.filters`.
:param rupture_site_filter:
Optional rupture-site filter function. See
:mod:`openquake.hazardlib.calc.filters`.
:returns:
A tuple of two items. First is itself a tuple of bin edges information
for (in specified order) magnitude, distance, longitude, latitude,
epsilon and tectonic region types.
Second item is 6d-array representing the full disaggregation matrix.
Dimensions are in the same order as bin edges in the first item
of the result tuple. The matrix can be used directly by pmf-extractor
functions.
"""
bins_data = _collect_bins_data(sources, site, imt, iml, gsims,
truncation_level, n_epsilons,
source_site_filter, rupture_site_filter)
if all(len(x) == 0 for x in bins_data):
# No ruptures have contributed to the hazard level at this site.
warnings.warn(
'No ruptures have contributed to the hazard at site %s'
% site,
RuntimeWarning
)
return None, None
bin_edges = _define_bins(bins_data, mag_bin_width, dist_bin_width,
coord_bin_width, truncation_level, n_epsilons)
diss_matrix = _arrange_data_in_bins(bins_data, bin_edges)
return bin_edges, diss_matrix
def _collect_bins_data(sources, site, imt, iml, gsims,
truncation_level, n_epsilons,
source_site_filter, rupture_site_filter):
"""
Extract values of magnitude, distance, closest point, tectonic region
types and PoE distribution.
This method processes the source model (generates ruptures) and collects
all needed parameters to arrays. It also defines tectonic region type
bins sequence.
"""
mags = []
dists = []
lons = []
lats = []
tect_reg_types = []
probs_no_exceed = []
sitecol = SiteCollection([site])
sitemesh = sitecol.mesh
_next_trt_num = 0
trt_nums = {}
sources_sites = ((source, sitecol) for source in sources)
# here we ignore filtered site collection because either it is the same
# as the original one (with one site), or the source/rupture is filtered
# out and doesn't show up in the filter's output
for src_idx, (source, s_sites) in \
enumerate(source_site_filter(sources_sites)):
try:
tect_reg = source.tectonic_region_type
gsim = gsims[tect_reg]
cmaker = ContextMaker([gsim])
if tect_reg not in trt_nums:
trt_nums[tect_reg] = _next_trt_num
_next_trt_num += 1
tect_reg = trt_nums[tect_reg]
ruptures_sites = ((rupture, s_sites)
for rupture in source.iter_ruptures())
for rupture, r_sites in rupture_site_filter(ruptures_sites):
# extract rupture parameters of interest
mags.append(rupture.mag)
[jb_dist] = rupture.surface.get_joyner_boore_distance(sitemesh)
dists.append(jb_dist)
[closest_point] = rupture.surface.get_closest_points(sitemesh)
lons.append(closest_point.longitude)
lats.append(closest_point.latitude)
tect_reg_types.append(tect_reg)
# compute conditional probability of exceeding iml given
# the current rupture, and different epsilon level, that is
# ``P(IMT >= iml | rup, epsilon_bin)`` for each of epsilon bins
sctx, rctx, dctx = cmaker.make_contexts(sitecol, rupture)
[poes_given_rup_eps] = gsim.disaggregate_poe(
sctx, rctx, dctx, imt, iml, truncation_level, n_epsilons
)
# collect probability of a rupture causing no exceedances
probs_no_exceed.append(
rupture.get_probability_no_exceedance(poes_given_rup_eps)
)
except Exception as err:
etype, err, tb = sys.exc_info()
msg = 'An error occurred with source id=%s. Error: %s'
msg %= (source.source_id, str(err))
raise_(etype, msg, tb)
mags = numpy.array(mags, float)
dists = numpy.array(dists, float)
lons = numpy.array(lons, float)
lats = numpy.array(lats, float)
tect_reg_types = numpy.array(tect_reg_types, int)
probs_no_exceed = numpy.array(probs_no_exceed, float)
trt_bins = [
trt for (num, trt) in sorted((num, trt)
for (trt, num) in trt_nums.items())
]
return (mags, dists, lons, lats, tect_reg_types, trt_bins, probs_no_exceed)
def _define_bins(bins_data, mag_bin_width, dist_bin_width,
coord_bin_width, truncation_level, n_epsilons):
"""
Define bin edges for disaggregation histograms.
Given bins data as provided by :func:`_collect_bins_data`, this function
finds edges of histograms, taking into account maximum and minimum values
of magnitude, distance and coordinates as well as requested sizes/numbers
of bins.
"""
mags, dists, lons, lats, tect_reg_types, trt_bins, _ = bins_data
mag_bins = mag_bin_width * numpy.arange(
int(numpy.floor(mags.min() / mag_bin_width)),
int(numpy.ceil(mags.max() / mag_bin_width) + 1)
)
dist_bins = dist_bin_width * numpy.arange(
int(numpy.floor(dists.min() / dist_bin_width)),
int(numpy.ceil(dists.max() / dist_bin_width) + 1)
)
west, east, north, south = get_spherical_bounding_box(lons, lats)
west = numpy.floor(west / coord_bin_width) * coord_bin_width
east = numpy.ceil(east / coord_bin_width) * coord_bin_width
lon_extent = get_longitudinal_extent(west, east)
lon_bins, _, _ = npoints_between(
west, 0, 0, east, 0, 0,
numpy.round(lon_extent / coord_bin_width + 1)
)
lat_bins = coord_bin_width * numpy.arange(
int(numpy.floor(south / coord_bin_width)),
int(numpy.ceil(north / coord_bin_width) + 1)
)
eps_bins = numpy.linspace(-truncation_level, truncation_level,
n_epsilons + 1)
return mag_bins, dist_bins, lon_bins, lat_bins, eps_bins, trt_bins
def _arrange_data_in_bins(bins_data, bin_edges):
"""
Given bins data, as it comes from :func:`_collect_bins_data`, and bin edges
from :func:`_define_bins`, create a normalized 6d disaggregation matrix.
"""
(mags, dists, lons, lats, tect_reg_types, trt_bins, probs_no_exceed) = \
bins_data
mag_bins, dist_bins, lon_bins, lat_bins, eps_bins, trt_bins = bin_edges
dim1 = len(mag_bins) - 1
dim2 = len(dist_bins) - 1
dim3 = len(lon_bins) - 1
dim4 = len(lat_bins) - 1
shape = (dim1, dim2, dim3, dim4, len(eps_bins) - 1, len(trt_bins))
diss_matrix = numpy.ones(shape)
# find bin indexes of rupture attributes; bins are assumed closed
# on the lower bound, and open on the upper bound, that is [ )
# longitude values need an ad-hoc method to take into account
# the 'international date line' issue
# the 'minus 1' is needed because the digitize method returns the index
# of the upper bound of the bin
mags_idx = numpy.digitize(mags, mag_bins) - 1
dists_idx = numpy.digitize(dists, dist_bins) - 1
lons_idx = _digitize_lons(lons, lon_bins)
lats_idx = numpy.digitize(lats, lat_bins) - 1
# because of the way numpy.digitize works, values equal to the last bin
# edge are associated to an index equal to len(bins) which is not a valid
# index for the disaggregation matrix. Such values are assumed to fall
# in the last bin.
mags_idx[mags_idx == dim1] = dim1 - 1
dists_idx[dists_idx == dim2] = dim2 - 1
lons_idx[lons_idx == dim3] = dim3 - 1
lats_idx[lats_idx == dim4] = dim4 - 1
for i, (i_mag, i_dist, i_lon, i_lat, i_trt) in \
enumerate(
zip(mags_idx, dists_idx, lons_idx, lats_idx, tect_reg_types)):
diss_matrix[i_mag, i_dist, i_lon, i_lat, :, i_trt] *= \
probs_no_exceed[i, :]
return 1 - diss_matrix
def _digitize_lons(lons, lon_bins):
"""
Return indices of the bins to which each value in lons belongs.
Takes into account the case in which longitude values cross the
international date line.
:parameter lons:
An instance of `numpy.ndarray`.
:parameter lons_bins:
An instance of `numpy.ndarray`.
"""
if cross_idl(lon_bins[0], lon_bins[-1]):
idx = numpy.zeros_like(lons, dtype=numpy.int)
for i_lon in range(len(lon_bins) - 1):
extents = get_longitudinal_extent(lons, lon_bins[i_lon + 1])
lon_idx = extents > 0
if i_lon != 0:
extents = get_longitudinal_extent(lon_bins[i_lon], lons)
lon_idx &= extents >= 0
idx[lon_idx] = i_lon
return numpy.array(idx)
else:
return numpy.digitize(lons, lon_bins) - 1
[docs]def mag_pmf(matrix):
"""
Fold full disaggregation matrix to magnitude PMF.
:returns:
1d array, a histogram representing magnitude PMF.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
mag_pmf = numpy.zeros(nmags)
for i in range(nmags):
mag_pmf[i] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for j in range(ndists)
for k in range(nlons)
for l in range(nlats)
for m in range(neps)
for n in range(ntrts)]
)
return 1 - mag_pmf
[docs]def dist_pmf(matrix):
"""
Fold full disaggregation matrix to distance PMF.
:returns:
1d array, a histogram representing distance PMF.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
dist_pmf = numpy.zeros(ndists)
for j in range(ndists):
dist_pmf[j] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for i in range(nmags)
for k in range(nlons)
for l in range(nlats)
for m in range(neps)
for n in range(ntrts)]
)
return 1 - dist_pmf
[docs]def trt_pmf(matrix):
"""
Fold full disaggregation matrix to tectonic region type PMF.
:returns:
1d array, a histogram representing tectonic region type PMF.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
trt_pmf = numpy.zeros(ntrts)
for n in range(ntrts):
trt_pmf[n] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for i in range(nmags)
for j in range(ndists)
for k in range(nlons)
for l in range(nlats)
for m in range(neps)]
)
return 1 - trt_pmf
[docs]def mag_dist_pmf(matrix):
"""
Fold full disaggregation matrix to magnitude / distance PMF.
:returns:
2d array. First dimension represents magnitude histogram bins,
second one -- distance histogram bins.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
mag_dist_pmf = numpy.zeros((nmags, ndists))
for i in range(nmags):
for j in range(ndists):
mag_dist_pmf[i][j] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for k in range(nlons)
for l in range(nlats)
for m in range(neps)
for n in range(ntrts)]
)
return 1 - mag_dist_pmf
[docs]def mag_dist_eps_pmf(matrix):
"""
Fold full disaggregation matrix to magnitude / distance / epsilon PMF.
:returns:
3d array. First dimension represents magnitude histogram bins,
second one -- distance histogram bins, third one -- epsilon
histogram bins.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
mag_dist_eps_pmf = numpy.zeros((nmags, ndists, neps))
for i in range(nmags):
for j in range(ndists):
for m in range(neps):
mag_dist_eps_pmf[i][j][m] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for k in range(nlons)
for l in range(nlats)
for n in range(ntrts)]
)
return 1 - mag_dist_eps_pmf
[docs]def lon_lat_pmf(matrix):
"""
Fold full disaggregation matrix to longitude / latitude PMF.
:returns:
2d array. First dimension represents longitude histogram bins,
second one -- latitude histogram bins.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
lon_lat_pmf = numpy.zeros((nlons, nlats))
for k in range(nlons):
for l in range(nlats):
lon_lat_pmf[k][l] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for i in range(nmags)
for j in range(ndists)
for m in range(neps)
for n in range(ntrts)]
)
return 1 - lon_lat_pmf
[docs]def mag_lon_lat_pmf(matrix):
"""
Fold full disaggregation matrix to magnitude / longitude / latitude PMF.
:returns:
3d array. First dimension represents magnitude histogram bins,
second one -- longitude histogram bins, third one -- latitude
histogram bins.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
mag_lon_lat_pmf = numpy.zeros((nmags, nlons, nlats))
for i in range(nmags):
for k in range(nlons):
for l in range(nlats):
mag_lon_lat_pmf[i][k][l] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for j in range(ndists)
for m in range(neps)
for n in range(ntrts)]
)
return 1 - mag_lon_lat_pmf
[docs]def lon_lat_trt_pmf(matrix):
"""
Fold full disaggregation matrix to longitude / latitude / tectonic region
type PMF.
:returns:
3d array. Dimension represent longitude, latitude and tectonic region
type histogram bins respectively.
"""
nmags, ndists, nlons, nlats, neps, ntrts = matrix.shape
lon_lat_trt_pmf = numpy.zeros((nlons, nlats, ntrts))
for k in range(nlons):
for l in range(nlats):
for n in range(ntrts):
lon_lat_trt_pmf[k][l][n] = numpy.prod(
[1 - matrix[i][j][k][l][m][n]
for i in range(nmags)
for j in range(ndists)
for m in range(neps)]
)
return 1 - lon_lat_trt_pmf
# this dictionary is useful to extract a fixed set of
# submatrices from the full disaggregation matrix
pmf_map = collections.OrderedDict([
(('Mag', ), mag_pmf),
(('Dist', ), dist_pmf),
(('TRT', ), trt_pmf),
(('Mag', 'Dist'), mag_dist_pmf),
(('Mag', 'Dist', 'Eps'), mag_dist_eps_pmf),
(('Lon', 'Lat'), lon_lat_pmf),
(('Mag', 'Lon', 'Lat'), mag_lon_lat_pmf),
(('Lon', 'Lat', 'TRT'), lon_lat_trt_pmf),
])