Source code for openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_bayes

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4

# Copyright (C) 2010-2019 GEM Foundation, G. Weatherill, M. Pagani, D. Monelli
# The Hazard Modeller's Toolkit (openquake.hmtk) 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.
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <>
# The software Hazard Modeller's Toolkit (openquake.hmtk) provided herein is
# released as a prototype implementation on behalf of scientists and engineers
# working within the GEM Foundation (Global Earthquake Model).
# It is distributed for the purpose of open collaboration and in the hope that
# it will be useful to the scientific, engineering, disaster risk and software
# design communities.
# The software is NOT distributed as part of GEM's OpenQuake suite
# ( and must be considered as a
# separate entity. The software provided herein is designed and implemented
# by scientific staff. It is not developed to the design standards, nor
# subject to same level of critical review by professional software developers,
# as GEM's OpenQuake software suite.
# Feedback and contribution to the software is welcome, and can be directed to
# the hazard scientific staff of the GEM Model Facility
# (
# The Hazard Modeller's Toolkit (openquake.hmtk) is therefore distributed WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
# The GEM Foundation, and the authors of the software, assume no liability for
# use of the software.

Module :mod:`openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_bayes`
implements the Kijko & Sellevol (1989) method for estimating maximum magnitude
from observed seismicity with uncertain b-value

import numpy as np
from math import fabs
from scipy.integrate import quadrature
from openquake.hmtk.seismicity.max_magnitude.base import (
    BaseMaximumMagnitude, MAX_MAGNITUDE_METHODS,
    _get_observed_mmax, _get_magnitude_vector_properties)

[docs]def check_config(config, data): '''Check config file inputs :param dict config: Configuration settings for the function ''' essential_keys = ['input_mmin', 'b-value', 'sigma-b'] for key in essential_keys: if not key in config.keys(): raise ValueError('For KijkoSellevolBayes the key %s needs to ' 'be set in the configuation' % key) if 'tolerance' not in config.keys() or not config['tolerance']: config['tolerance'] = 1E-5 if not config.get('maximum_iterations', False): config['maximum_iterations'] = 1000 if config['input_mmin'] < np.min(data['magnitude']): config['input_mmin'] = np.min(data['magnitude']) if fabs(config['sigma-b'] < 1E-15): raise ValueError('Sigma-b must be greater than zero!') return config
[docs]@MAX_MAGNITUDE_METHODS.add( "get_mmax", **{"input_mmin": lambda cat: np.min(['magnitude']), "input_mmax": lambda cat:['magnitude'][ np.argmax(['magnitude'])], "input_mmax_uncertainty": lambda cat: cat.get_observed_mmax_sigma(0.2), "b-value": np.float, "sigma-b": np.float, "maximum_iterations": 1000, "tolerance": 1E-5}) class KijkoSellevolBayes(BaseMaximumMagnitude): ''' Class to implement Kijko & Sellevol Bayesian estimator of Mmax, with uncertain b-value '''
[docs] def get_mmax(self, catalogue, config): '''Calculate maximum magnitude :returns: **mmax** Maximum magnitude and **mmax_sig** corresponding uncertainty :rtype: Float ''' # Check configuration file config = check_config(config, # Negative b-values will return nan - this simply skips the integral if config['b-value'] <= 0.0: return np.nan, np.nan obsmax, obsmaxsig = _get_observed_mmax(, config) beta = config['b-value'] * np.log(10.) sigbeta = config['sigma-b'] * np.log(10.) neq, mmin = _get_magnitude_vector_properties(, config) pval = beta / (sigbeta ** 2.) qval = (beta / sigbeta) ** 2. mmax = np.copy(obsmax) d_t = np.inf iterator = 0 while d_t > config['tolerance']: rval = pval / (pval + mmax - mmin) ldelt = (1. / (1. - (rval ** qval))) ** neq delta = ldelt * quadrature(self._ksb_intfunc, mmin, mmax, args=(neq, mmin, pval, qval))[0] tmmax = obsmax + delta d_t = np.abs(tmmax - mmax) mmax = np.copy(tmmax) iterator += 1 if iterator > config['maximum_iterations']: print('Kijko-Sellevol-Bayes estimator reached' 'maximum # of iterations') d_t = -np.inf return mmax.item(), np.sqrt(obsmaxsig ** 2. + delta ** 2.)
def _ksb_intfunc(self, mval, neq, mmin, pval, qval): ''' Integral function inside Kijko-Sellevol-Bayes estimator (part of Eq. 10 in Kijko, 2004 - section 3.2) :param float mval: Magnitude :param float neq: Number of Earthquakes :param float mmin: Minimum Magnitude :param float pval: p-value (see Kijko, 2004 - section 3.2) :param float qval: q-value (see Kijki, 2004 - section 3.2) :returns: Output of function integrand ''' func1 = (1. - ((pval / (pval + mval - mmin)) ** qval)) ** neq return func1