Source code for openquake.hmtk.strain.strain_utils

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

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# D. Monelli.
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'''
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))