Source code for openquake.hmtk.strain.strain_utils

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

#
# LICENSE
#
# Copyright (C) 2010-2019 GEM Foundation, G. Weatherill, M. Pagani,
# D. Monelli.
#
# The Hazard Modeller's Toolkit 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 <http://www.gnu.org/licenses/>
#
# DISCLAIMER
#
# 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
# (https://www.globalquakemodel.org/tools-products) 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
# (hazard@globalquakemodel.org).
#
# 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.strain.utils` holds a set of useful
utility functions for the strain rate model calculations
'''

import numpy as np
from math import exp


[docs]def moment_function(magnitude): ''' Get moment (in Nm) from magnitude using Hanks & Kanamori (1979) :param float (or numpy.ndarray) magnitude: Magnitude of event :returns: Seismic Moment in Nm ''' return 10. ** ((1.5 * magnitude) + 9.05)
[docs]def moment_magnitude_function(moment): ''' For a given moment, get the moment magnitude using the formula of Hanks & Kanamori (1979) :param float or numpy.ndarray magnitude Seismic moment in Nm ''' return (2. / 3.) * (np.log10(moment) - 9.05)
[docs]def calculate_taper_function(obs_threshold_moment, sel_threshold_moment, corner_moment, beta): ''' Calculates the tapering function of the tapered Gutenberg & Richter model: as described in Bird & Liu (2007):: taper_function = (M_0(M_T) / M_0(M_T^{CMT}))^-beta x exp((M_0(m_T^CMT) - M_0(m_T)) / M_0(m_c)) :param numpy.ndarray obs_threshold_moment: Moment of the threshold magnitude of the observed earthquake catalogue :param numpy.ndarray sel_threshold_moment: Moment of the target magnitude :param float corner_momnet: Corner moment of the Tapered Gutenberg-Richter Function :param float beta: Beta value (b * ln(10.)) of the Tapered Gutenberg-Richter Function :returns: Relative moment rate ''' argument = (obs_threshold_moment - sel_threshold_moment) /\ corner_moment if argument < -100.0: g_function = 0.0 else: g_function = ((sel_threshold_moment / obs_threshold_moment) ** -beta) * exp(argument) return g_function
[docs]def tapered_gutenberg_richter_cdf(moment, moment_threshold, beta, corner_moment): ''' Tapered Gutenberg Richter Cumulative Density Function :param float or numpy.ndarray moment: Moment for calculation of rate :param float or numpy.ndarray moment_threshold: Threshold Moment of the distribution (moment rate essentially!) :param float beta: Beta value (b * ln(10.)) of the Tapered Gutenberg-Richter Function :param float corner_momnet: Corner moment of the Tapered Gutenberg-Richter Function :returns: Cumulative probability of moment release > moment ''' cdf = np.exp((moment_threshold - moment) / corner_moment) return ((moment / moment_threshold) ** (-beta)) * cdf
[docs]def tapered_gutenberg_richter_pdf(moment, moment_threshold, beta, corner_moment): ''' Tapered Gutenberg-Richter Probability Density Function :param float or numpy.ndarray moment: Moment for calculation of rate :param float or numpy.ndarray moment_threshold: Threshold Moment of the distribution (moment rate essentially!) :param float beta: Beta value (b * ln(10.)) of the Tapered Gutenberg-Richter Function :param float corner_momnet: Corner moment of the Tapered Gutenberg-Richter Function :returns: Absolute probability of moment release > moment ''' return ((beta / moment + 1. / corner_moment) * tapered_gutenberg_richter_cdf(moment, moment_threshold, beta, corner_moment))