Source code for openquake.hazardlib.tom

# 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/>.
"""
Module :mod:`openquake.hazardlib.tom` contains implementations of probability
density functions for earthquake temporal occurrence modeling.
"""
import math

import numpy
import scipy.stats

from openquake.baselib.slots import with_slots


@with_slots
[docs]class PoissonTOM(object): """ Poissonian temporal occurrence model. :param time_span: The time interval of interest, in years. :raises ValueError: If ``time_span`` is not positive. """ _slots_ = ['time_span'] def __init__(self, time_span): if time_span <= 0: raise ValueError('time_span must be positive') self.time_span = time_span
[docs] def get_probability_one_or_more_occurrences(self, occurrence_rate): """ Calculate and return the probability of event to happen one or more times within the time range defined by constructor's ``time_span`` parameter value. Calculates probability as ``1 - e ** (-occurrence_rate*time_span)``. :param occurrence_rate: The average number of events per year. :return: Float value between 0 and 1 inclusive. """ return 1 - math.exp(- occurrence_rate * self.time_span)
[docs] def get_probability_one_occurrence(self, occurrence_rate): """ Calculate and return the probability of event to occur once within the time range defined by the constructor's ``time_span`` parameter value. """ return scipy.stats.poisson(occurrence_rate * self.time_span).pmf(1)
[docs] def sample_number_of_occurrences(self, occurrence_rate): """ Draw a random sample from the distribution and return a number of events to occur. Method uses numpy random generator, which needs to be seeded outside of this method in order to get reproducible results. :param occurrence_rate: The average number of events per year. :return: Sampled integer number of events to occur within model's time span. """ return numpy.random.poisson(occurrence_rate * self.time_span)
[docs] def get_probability_no_exceedance(self, occurrence_rate, poes): """ Compute and return, for a number of ground motion levels and sites, the probability that a rupture with annual occurrence rate given by ``occurrence_rate`` and able to cause ground motion values higher than a given level at a site with probability ``poes``, does not cause any exceedance in the time window specified by the ``time_span`` parameter given in the constructor. The probability is computed using the following formula :: (1 - e ** (-occurrence_rate * time_span)) ** poes :param occurrence_rate: The average number of events per year. :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>`. :return: 2D numpy array containing probabilities of no exceedance. First dimension represents sites, second dimensions intensity measure levels. """ p = self.get_probability_one_or_more_occurrences(occurrence_rate) return (1 - p) ** poes