def test_sample_number_of_occurrences(self):
time_span = 40
rate = 0.05
num_samples = 8000
tom = PoissonTOM(time_span)
numpy.random.seed(31)
mean = sum(tom.sample_number_of_occurrences(rate)
for i in xrange(num_samples)) / float(num_samples)
self.assertAlmostEqual(mean, rate * time_span, delta=1e-3)
def test_sample_number_of_occurrences(self):
time_span = 40
rate = 0.05
num_samples = 8000
tom = PoissonTOM(time_span)
numpy.random.seed(31)
mean = sum(tom.sample_number_of_occurrences(rate)
for i in xrange(num_samples)) / float(num_samples)
self.assertAlmostEqual(mean, rate * time_span, delta=1e-3)
def test_get_probability_one_or_more_occurrences(self):
pdf = PoissonTOM(time_span=50)
self.assertEqual(pdf.get_probability_one_or_more_occurrences(10), 1)
aae = self.assertAlmostEqual
aae(pdf.get_probability_one_or_more_occurrences(0.1), 0.9932621)
aae(pdf.get_probability_one_or_more_occurrences(0.01), 0.39346934)
pdf = PoissonTOM(time_span=5)
self.assertEqual(pdf.get_probability_one_or_more_occurrences(8), 1)
aae = self.assertAlmostEqual
aae(pdf.get_probability_one_or_more_occurrences(0.1), 0.3934693)
aae(pdf.get_probability_one_or_more_occurrences(0.01), 0.0487706)
def test_implied_point_sources(self):
source = self.make_area_source(Polygon(
[Point(-2, -2),
Point(0, -2),
Point(0, 0),
Point(-2, 0)]),
discretization=66.7,
rupture_mesh_spacing=5)
ruptures = list(source.iter_ruptures(PoissonTOM(50)))
self.assertEqual(len(ruptures), 9 * 2)
# resulting 3x3 mesh has points in these coordinates:
lons = [-1.4, -0.8, -0.2]
lats = [-0.6, -1.2, -1.8]
ruptures_iter = iter(ruptures)
for lat in lats:
for lon in lons:
r1 = next(ruptures_iter)
r2 = next(ruptures_iter)
for rupture in [r1, r2]:
self.assertAlmostEqual(rupture.hypocenter.longitude,
lon,
delta=1e-3)
self.assertAlmostEqual(rupture.hypocenter.latitude,
lat,
delta=1e-3)
self.assertEqual(rupture.surface.mesh_spacing, 5)
self.assertIs(rupture.source_typology, AreaSource)
self.assertEqual(r1.mag, 5.5)
self.assertEqual(r2.mag, 6.5)
self.assertEqual(len(ruptures), 9 * 2)
def stochastic_event_set_poissonian(sources, time_span):
"""
The Poissonian Stochastic Event Set calculator generates a 'Stochastic
Event Set' (that is a collection of earthquake ruptures) by randomly
sampling a source model whose rupture follow a Poissonian temporal
occurrence model. The Stochastic Event Set represent a possible
*realization* of the seismicity as described by the source model,
in the given time span.
The calculator assumes :class:`Poissonian <nhlib.tom.PoissonTOM>`
temporal occurrence model.
:param sources:
An iterator of seismic sources objects (instances of subclasses
of :class:`~nhlib.source.base.SeismicSource`).
:param time_span:
An investigation period for Poissonian temporal occurrence model,
floating point number in years.
:returns:
Generator of :class:`~nhlib.source.rupture.Rupture` objects that
are contained in an event set. Some ruptures can be missing from
it, others can appear one or more times in a row.
"""
tom = PoissonTOM(time_span)
for source in sources:
for rupture in source.iter_ruptures(tom):
for i in xrange(rupture.sample_number_of_occurrences()):
yield rupture
def test_get_probability(self):
pdf = PoissonTOM(time_span=50)
self.assertEqual(pdf.get_probability(occurrence_rate=10), 1)
aae = self.assertAlmostEqual
aae(pdf.get_probability(occurrence_rate=0.1), 0.9932621)
aae(pdf.get_probability(occurrence_rate=0.01), 0.39346934)
pdf = PoissonTOM(time_span=5)
self.assertEqual(pdf.get_probability(occurrence_rate=8), 1)
aae = self.assertAlmostEqual
aae(pdf.get_probability(occurrence_rate=0.1), 0.3934693)
aae(pdf.get_probability(occurrence_rate=0.01), 0.0487706)
def test_sample_number_of_occurrences(self):
time_span = 20
rate = 0.01
num_samples = 2000
tom = PoissonTOM(time_span)
rupture = make_rupture(ProbabilisticRupture,
occurrence_rate=rate,
temporal_occurrence_model=tom)
numpy.random.seed(37)
mean = sum(rupture.sample_number_of_occurrences()
for i in xrange(num_samples)) / float(num_samples)
self.assertAlmostEqual(mean, rate * time_span, delta=2e-3)
def test_occurrence_rate_rescaling(self):
mfd = EvenlyDiscretizedMFD(min_mag=4,
bin_width=1,
occurrence_rates=[3])
polygon = Polygon([
Point(0, 0),
Point(0, -0.2248),
Point(-0.2248, -0.2248),
Point(-0.2248, 0)
])
source = self.make_area_source(polygon, discretization=10, mfd=mfd)
self.assertIs(source.mfd, mfd)
ruptures = list(source.iter_ruptures(PoissonTOM(1)))
self.assertEqual(len(ruptures), 4)
for rupture in ruptures:
self.assertNotEqual(rupture.occurrence_rate, 3)
self.assertEqual(rupture.occurrence_rate, 3.0 / 4.0)
def _make_rupture(self, width, length, dip):
mid_left = self.hypocenter.point_at(length / 2.0, 0, azimuth=270)
mid_right = self.hypocenter.point_at(length / 2.0, 0, azimuth=90)
hwidth = width * numpy.cos(numpy.radians(dip)) / 2.0
vwidth = width * numpy.sin(numpy.radians(dip)) / 2.0
top_left = mid_left.point_at(hwidth, -vwidth, azimuth=0)
bottom_left = mid_left.point_at(hwidth, vwidth, azimuth=180)
top_right = mid_right.point_at(hwidth, -vwidth, azimuth=0)
bottom_right = mid_right.point_at(hwidth, vwidth, azimuth=180)
surface = PlanarSurface(1, 2, dip, top_left, top_right, bottom_right,
bottom_left)
rupture = ProbabilisticRupture(mag=1,
rake=2,
tectonic_region_type=TRT.VOLCANIC,
hypocenter=self.hypocenter,
surface=surface,
source_typology=PointSource,
occurrence_rate=3,
temporal_occurrence_model=PoissonTOM(1))
return rupture
def _get_rupture(self,
min_mag,
max_mag,
hypocenter_depth,
aspect_ratio,
dip,
rupture_mesh_spacing,
upper_seismogenic_depth=2,
lower_seismogenic_depth=16):
source_id = name = 'test-source'
trt = TRT.ACTIVE_SHALLOW_CRUST
mfd = TruncatedGRMFD(a_val=2,
b_val=1,
min_mag=min_mag,
max_mag=max_mag,
bin_width=1)
location = Point(0, 0)
nodal_plane = NodalPlane(strike=45, dip=dip, rake=-123.23)
nodal_plane_distribution = PMF([(1, nodal_plane)])
hypocenter_distribution = PMF([(1, hypocenter_depth)])
magnitude_scaling_relationship = PeerMSR()
rupture_aspect_ratio = aspect_ratio
point_source = PointSource(
source_id, name, trt, mfd, rupture_mesh_spacing,
magnitude_scaling_relationship, rupture_aspect_ratio,
upper_seismogenic_depth, lower_seismogenic_depth, location,
nodal_plane_distribution, hypocenter_distribution)
tom = PoissonTOM(time_span=50)
ruptures = list(point_source.iter_ruptures(tom))
self.assertEqual(len(ruptures), 1)
[rupture] = ruptures
self.assertIs(rupture.temporal_occurrence_model, tom)
self.assertIs(rupture.tectonic_region_type, trt)
self.assertEqual(rupture.rake, nodal_plane.rake)
self.assertIsInstance(rupture.surface, PlanarSurface)
self.assertEqual(rupture.surface.mesh_spacing, rupture_mesh_spacing)
return rupture
def test_7_many_ruptures(self):
source_id = name = 'test7-source'
trt = TRT.VOLCANIC
mag1 = 4.5
mag2 = 5.5
mag1_rate = 9e-3
mag2_rate = 9e-4
hypocenter1 = 9.0
hypocenter2 = 10.0
hypocenter1_weight = Decimal('0.8')
hypocenter2_weight = Decimal('0.2')
nodalplane1 = NodalPlane(strike=45, dip=90, rake=0)
nodalplane2 = NodalPlane(strike=0, dip=45, rake=10)
nodalplane1_weight = Decimal('0.3')
nodalplane2_weight = Decimal('0.7')
upper_seismogenic_depth = 2
lower_seismogenic_depth = 16
rupture_aspect_ratio = 2
rupture_mesh_spacing = 0.5
location = Point(0, 0)
magnitude_scaling_relationship = PeerMSR()
tom = PoissonTOM(time_span=50)
mfd = EvenlyDiscretizedMFD(min_mag=mag1,
bin_width=(mag2 - mag1),
occurrence_rates=[mag1_rate, mag2_rate])
nodal_plane_distribution = PMF([(nodalplane1_weight, nodalplane1),
(nodalplane2_weight, nodalplane2)])
hypocenter_distribution = PMF([(hypocenter1_weight, hypocenter1),
(hypocenter2_weight, hypocenter2)])
point_source = PointSource(
source_id, name, trt, mfd, rupture_mesh_spacing,
magnitude_scaling_relationship, rupture_aspect_ratio,
upper_seismogenic_depth, lower_seismogenic_depth, location,
nodal_plane_distribution, hypocenter_distribution)
actual_ruptures = list(point_source.iter_ruptures(tom))
self.assertEqual(len(actual_ruptures), 8)
expected_ruptures = {
(mag1, nodalplane1.rake, hypocenter1): (
# probabilistic rupture's occurrence rate
9e-3 * 0.3 * 0.8,
# rupture surface corners
planar_surface_test_data.TEST_7_RUPTURE_1_CORNERS),
(mag2, nodalplane1.rake, hypocenter1):
(9e-4 * 0.3 * 0.8,
planar_surface_test_data.TEST_7_RUPTURE_2_CORNERS),
(mag1, nodalplane2.rake, hypocenter1):
(9e-3 * 0.7 * 0.8,
planar_surface_test_data.TEST_7_RUPTURE_3_CORNERS),
(mag2, nodalplane2.rake, hypocenter1):
(9e-4 * 0.7 * 0.8,
planar_surface_test_data.TEST_7_RUPTURE_4_CORNERS),
(mag1, nodalplane1.rake, hypocenter2):
(9e-3 * 0.3 * 0.2,
planar_surface_test_data.TEST_7_RUPTURE_5_CORNERS),
(mag2, nodalplane1.rake, hypocenter2):
(9e-4 * 0.3 * 0.2,
planar_surface_test_data.TEST_7_RUPTURE_6_CORNERS),
(mag1, nodalplane2.rake, hypocenter2):
(9e-3 * 0.7 * 0.2,
planar_surface_test_data.TEST_7_RUPTURE_7_CORNERS),
(mag2, nodalplane2.rake, hypocenter2):
(9e-4 * 0.7 * 0.2,
planar_surface_test_data.TEST_7_RUPTURE_8_CORNERS)
}
for actual_rupture in actual_ruptures:
expected_occurrence_rate, expected_corners = expected_ruptures[(
actual_rupture.mag, actual_rupture.rake,
actual_rupture.hypocenter.depth)]
self.assertTrue(isinstance(actual_rupture, ProbabilisticRupture))
self.assertEqual(actual_rupture.occurrence_rate,
expected_occurrence_rate)
self.assertIs(actual_rupture.temporal_occurrence_model, tom)
self.assertEqual(actual_rupture.tectonic_region_type, trt)
surface = actual_rupture.surface
tl, tr, br, bl = expected_corners
self.assertEqual(tl, surface.top_left)
self.assertEqual(tr, surface.top_right)
self.assertEqual(bl, surface.bottom_left)
self.assertEqual(br, surface.bottom_right)
def test_areasource(self):
nodalplane = NodalPlane(strike=0.0, dip=90.0, rake=0.0)
src = AreaSource(source_id='src_1',
name='area source',
tectonic_region_type='Active Shallow Crust',
mfd=TruncatedGRMFD(a_val=3.5,
b_val=1.0,
min_mag=5.0,
max_mag=6.5,
bin_width=0.1),
nodal_plane_distribution=PMF([(1.0, nodalplane)]),
hypocenter_distribution=PMF([(1.0, 5.0)]),
upper_seismogenic_depth=0.0,
lower_seismogenic_depth=10.0,
magnitude_scaling_relationship=WC1994(),
rupture_aspect_ratio=1.0,
polygon=Polygon([
Point(-0.5, -0.5),
Point(-0.5, 0.5),
Point(0.5, 0.5),
Point(0.5, -0.5)
]),
area_discretization=9.0,
rupture_mesh_spacing=1.0)
site = Site(location=Point(0.0, 0.0),
vs30=800.0,
vs30measured=True,
z1pt0=500.0,
z2pt5=2.0)
gsims = {'Active Shallow Crust': BooreAtkinson2008()}
imt = SA(period=0.1, damping=5.0)
iml = 0.2
time_span = 50.0
truncation_level = 3.0
tom = PoissonTOM(time_span)
n_epsilons = 3
mag_bin_width = 0.2
# in km
dist_bin_width = 10.0
# in decimal degree
coord_bin_width = 0.2
# compute disaggregation
bin_edges, diss_matrix = disagg.disaggregation(
[src], site, imt, iml, gsims, tom, truncation_level, n_epsilons,
mag_bin_width, dist_bin_width, coord_bin_width)
mag_bins, dist_bins, lon_bins, lat_bins, eps_bins, trt_bins = bin_edges
numpy.testing.assert_almost_equal(
mag_bins, [5., 5.2, 5.4, 5.6, 5.8, 6., 6.2, 6.4, 6.6])
numpy.testing.assert_almost_equal(
dist_bins, [0., 10., 20., 30., 40., 50., 60., 70., 80.])
numpy.testing.assert_almost_equal(
lat_bins, [-0.6, -0.4, -0.2, 0., 0.2, 0.4, 0.6])
numpy.testing.assert_almost_equal(
lon_bins, [-0.6, -0.4, -0.2, 0., 0.2, 0.4, 0.6])
numpy.testing.assert_almost_equal(eps_bins, [-3., -1., 1., 3.])
self.assertEqual(trt_bins, ['Active Shallow Crust'])
expected_matrix = numpy.fromstring("""\
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iHrOSeiLS3vhyvH+mtHok9WUT0Jrc0pEKH4BxLwXa1IWMcTWcjwfAAAAAAAAAAAAAAAAAGA8bbA8
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EqfFpCzLIur5SuyhF3H9ERyv84Gf51nvtQhHC8qCBJ0kthHzjizdtLj0cDRK2cirVOgXD30HAAAA
AAAAAAAAAAAAYEKqv7BXVsPcA7UbnLfOmJSDnBSyJaoGo4j73oopnalR2vHMuC/H7oeXiaUvOdJK
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fbm7l5oUBHQ3MuNuHLtf19E72FLBSMXyAWAi8tGR62423IFSFcvVz7QnEvX8s1Hr4b+Fbka3/Rv8
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b74p2UDk0yu35YfWHGfsHKHydrdbxFDQ70rL+FtHfMY9f4rDjYwBDy+kz8getukLJ8YXWiBh5WZq
iZ2n+l1xcqsi57LtnM0nPRaM4DfB8rlOo2eXr1VE38o6AgAAAAAAAAAAAAAwnna4nbSYdMIZSRdk
5lYMJyKBwbhcsc2rkZKrhrLVlrsU/SLXekPfSMT/Ke7Asftjp4wlyBTuBCKfz3HhhtupB+ghHM8H
AFYMP67reqqTiYQiav33UaKJuqXl2dspr4lFgp/igRyr53KFLMUPSjHYvDwaIV4mJmFY3wHwZ4a3
K3fWGZhidaKZ9EItKFuNbfvzbhGfoFkH5JGYH3fYkWEKMb7bSOsrG1Iwc97R/9Pr6LBHx+ORF5Zn
uB4tZabgSrbVec60O14CqgFYf6GI6EgZewfs+kgFppeWetuyLZ/gaO85VFs3LB/B42T+YtEl0O/f
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tkmFv6ewa10AAAAAAAAAAAAwdo7KlYFD4sbofGDcb5Q3/siJq1zhkbg5mrldVKTfyoYZX8+Mr+TY
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x/dcTd/kaufB3H8cod85TEN70/1ny2WxOrHr9f9eVtUYW5d7Wpe/402zR9VCedPrA0ef19Oy4k3L
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OI936gUrbJ9JVGXcml/pgJ37Wbz6Ax1G+LoDzhgprkmlTeLB+kVOcu/p3q5BypfxIP/+cONbDRSf
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P6/L6OfCvHOGsvSv3aN8GSe7qK1wqvzI8vUEAAAAAAAA/P9bdpfPPs9dFSV16KnXm6xAz6IHKv32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=\
""".decode('base64').decode('zip')).reshape((8, 8, 6, 6, 3, 1))
numpy.testing.assert_almost_equal(diss_matrix, expected_matrix)
def test_get_probability_one_occurrence(self):
pdf = PoissonTOM(time_span=30)
aae = self.assertAlmostEqual
aae(pdf.get_probability_one_occurrence(10), 0)
aae(pdf.get_probability_one_occurrence(0.1), 0.1493612)
aae(pdf.get_probability_one_occurrence(0.01), 0.2222455)
def test_get_probability_one_occurrence(self):
rupture = make_rupture(ProbabilisticRupture,
occurrence_rate=0.4,
temporal_occurrence_model=PoissonTOM(10))
self.assertAlmostEqual(rupture.get_probability_one_occurrence(),
0.0732626)
def test_probabilistic_rupture_zero_occurrence_rate(self):
self.assert_failed_creation(ProbabilisticRupture,
ValueError,
'occurrence rate must be positive',
occurrence_rate=0,
temporal_occurrence_model=PoissonTOM(10))
def hazard_curves_poissonian(
sources,
sites,
imts,
time_span,
gsims,
truncation_level,
source_site_filter=filters.source_site_noop_filter,
rupture_site_filter=filters.rupture_site_noop_filter):
"""
Compute hazard curves on a list of sites, given a set of seismic sources
and a set of ground shaking intensity models (one per tectonic region type
considered in the seismic sources).
The calculator assumes :class:`Poissonian <nhlib.tom.PoissonTOM>`
temporal occurrence model.
The calculator computes probability of ground motion exceedance according
to the equation as described in pag. 419 of "OpenSHA: A Developing
Community-modeling Environment for Seismic Hazard Analysis, Edward
H. Field, Thomas H. Jordan and C. Allin Cornell. Seismological Research
Letters July/August 2003 v. 74 no. 4 p. 406-419".
:param sources:
An iterator of seismic sources objects (instances of subclasses
of :class:`~nhlib.source.base.SeismicSource`).
:param sites:
Instance of :class:`~nhlib.site.SiteCollection` object, representing
sites of interest.
:param imts:
Dictionary mapping intensity measure type objects (see
:mod:`nhlib.imt`) to lists of intensity measure levels.
:param time_span:
An investigation period for Poissonian temporal occurrence model,
floating point number in years.
:param gsims:
Dictionary mapping tectonic region types (members
of :class:`nhlib.const.TRT`) to :class:`~nhlib.gsim.base.GMPE`
or :class:`~nhlib.gsim.base.IPE` objects.
:param trunctation_level:
Float, number of standard deviations for truncation of the intensity
distribution.
:param source_site_filter:
Optional source-site filter function. See :mod:`nhlib.calc.filters`.
:param rupture_site_filter:
Optional rupture-site filter function. See :mod:`nhlib.calc.filters`.
:returns:
Dictionary mapping intensity measure type objects (same keys
as in parameter ``imts``) to 2d numpy arrays of float, where
first dimension differentiates sites (the order and length
are the same as in ``sites`` parameter) and the second one
differentiates IMLs (the order and length are the same as
corresponding value in ``imts`` dict).
"""
curves = dict(
(imt, numpy.ones([len(sites), len(imts[imt])])) for imt in imts)
tom = PoissonTOM(time_span)
total_sites = len(sites)
sources_sites = ((source, sites) for source in sources)
for source, s_sites in source_site_filter(sources_sites):
ruptures_sites = ((rupture, s_sites)
for rupture in source.iter_ruptures(tom))
for rupture, r_sites in rupture_site_filter(ruptures_sites):
prob = rupture.get_probability_one_or_more_occurrences()
gsim = gsims[rupture.tectonic_region_type]
sctx, rctx, dctx = gsim.make_contexts(r_sites, rupture)
for imt in imts:
poes = gsim.get_poes(sctx, rctx, dctx, imt, imts[imt],
truncation_level)
curves[imt] *= r_sites.expand((1 - prob)**poes,
total_sites,
placeholder=1)
for imt in imts:
curves[imt] = 1 - curves[imt]
return curves
