# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# LICENSE
#
# Copyright (C) 2010-2020 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
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# The software Hazard Modeller's Toolkit (openquake.hmtk) provided herein
# is released as a prototype implementation on behalf of
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# Earthquake Model).
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# hope that it will be useful to the scientific, engineering, disaster
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# (https://www.globalquakemodel.org/tools-products) and must be considered as a
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# developers, as GEM’s OpenQuake software suite.
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# Feedback and contribution to the software is welcome, and can be
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'''
Module :mod:`openquake.hmtk.seismicity.smoothing.utils` implements
utility functions for smoothed seismicity analysis
'''
import numpy as np
[docs]def hermann_adjustment_factors(bval, min_mag, mag_inc):
'''
Returns the adjustment factors (fval, fival) proposed by Hermann (1978)
:param float bval:
Gutenberg & Richter (1944) b-value
:param np.ndarray min_mag:
Minimum magnitude of completeness table
:param non-negative float mag_inc:
Magnitude increment of the completeness table
'''
fval = 10. ** (bval * min_mag)
fival = 10. ** (bval * (mag_inc / 2.)) - 10. ** (-bval * (mag_inc / 2.))
return fval, fival
[docs]def incremental_a_value(bval, min_mag, mag_inc):
'''
Incremental a-value from cumulative - using the version of the
Hermann (1979) formula described in Wesson et al. (2003)
:param float bval:
Gutenberg & Richter (1944) b-value
:param np.ndarray min_mag:
Minimum magnitude of completeness table
:param float mag_inc:
Magnitude increment of the completeness table
'''
a_cum = 10. ** (bval * min_mag)
a_inc = a_cum + np.log10((10. ** (bval * mag_inc)) -
(10. ** (-bval * mag_inc)))
return a_inc
[docs]def get_weichert_factor(beta, cmag, cyear, end_year):
'''
Gets the Weichert adjustment factor for each the magnitude bins
:param float beta:
Beta value of Gutenberg & Richter parameter (b * log(10.))
:param np.ndarray cmag:
Magnitude values of the completeness table
:param np.ndarray cyear:
Year values of the completeness table
:param float end_year:
Last year for consideration in the catalogue
:returns:
Weichert adjustment factor (float)
'''
if len(cmag) > 1:
# cval corresponds to the mid-point of the completeness bins
# In the original code it requires that the magnitude bins be
# equal sizedclass IsotropicGaussian(BaseSmoothingKernel):
dmag = (cmag[1:] + cmag[:-1]) / 2.
cval = np.hstack([dmag, cmag[-1] + (dmag[-1] - cmag[-2])])
else:
# Single completeness value so Weichert factor is unity
return 1.0 / (end_year - cyear[0] + 1), None
t_f = sum(np.exp(-beta * cval)) / sum((end_year - cyear + 1) *
np.exp(-beta * cval))
return t_f, cval
[docs]def check_completeness_table(completeness_table, catalogue):
'''
Check to ensure completeness table is in the correct format
`completeness_table = np.array([[year_, mag_i]]) for i in number of bins`
:param np.ndarray completeness_table:
Completeness table in format [[year, mag]]
:param catalogue:
Instance of openquake.hmtk.seismicity.catalogue.Catalogue class
:returns:
Correct completeness table
'''
if isinstance(completeness_table, np.ndarray):
assert np.shape(completeness_table)[1] == 2
return completeness_table
elif isinstance(completeness_table, list):
# Assuming list has only two elements
assert len(completeness_table) == 2
return np.array([[completeness_table[0], completeness_table[1]]])
else:
# Accepts the minimum magnitude and earliest year of the catalogue
return np.array([[np.min(catalogue.data['year']),
np.min(catalogue.data['magnitude'])]])
[docs]def get_even_magnitude_completeness(completeness_table, catalogue=None):
'''
To make the magnitudes evenly spaced, render to a constant 0.1
magnitude unit
:param np.ndarray completeness_table:
Completeness table in format [[year, mag]]
:param catalogue:
Instance of openquake.hmtk.seismicity.catalogue.Catalogue class
:returns:
Correct completeness table
'''
mmax = np.floor(10. * np.max(catalogue.data['magnitude'])) / 10.
check_completeness_table(completeness_table, catalogue)
cmag = np.hstack([completeness_table[:, 1], mmax + 0.1])
cyear = np.hstack([completeness_table[:, 0], completeness_table[-1, 0]])
if np.shape(completeness_table)[0] == 1:
# Simple single-valued table
return completeness_table, 0.1
for iloc in range(0, len(cmag) - 1):
mrange = np.arange(np.floor(10. * cmag[iloc]) / 10.,
(np.ceil(10. * cmag[iloc + 1]) / 10.),
0.1)
temp_table = np.column_stack([
cyear[iloc] * np.ones(len(mrange), dtype=float),
mrange])
if iloc == 0:
completeness_table = np.copy(temp_table)
else:
completeness_table = np.vstack([completeness_table,
temp_table])
# completeness_table = np.vstack([completeness_table,
# np.array([[cyear[-1], cmag[-1]]])])
return completeness_table, 0.1