Source code for openquake.hmtk.strain.strain_utils
# -*- coding: utf-8 -*-
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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))