# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# LICENSE
#
# Copyright (C) 2010-2023 GEM Foundation, G. Weatherill, M. Pagani,
# D. Monelli.
#
# The Hazard Modeller's Toolkit is free software: you can redistribute
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# Earthquake Model).
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import numpy as np
from openquake.hmtk.seismicity.occurrence.base import (
SeismicityOccurrence, OCCURRENCE_METHODS)
from openquake.hmtk.seismicity.occurrence.utils import input_checks, recurrence_table
from openquake.hmtk.seismicity.occurrence.aki_maximum_likelihood import AkiMaxLikelihood
[docs]@OCCURRENCE_METHODS.add(
'calculate',
completeness=True,
reference_magnitude=0.0,
magnitude_interval=0.1)
class KijkoSmit(SeismicityOccurrence):
"""
Class to Implement the Kijko & Smit (2012) algorithm for estimation
of a- and b-value
"""
[docs] def calculate(self, catalogue, config, completeness=None):
"""
Main function to calculate the a- and b-value
"""
# Input checks
cmag, ctime, ref_mag, dmag, config = input_checks(catalogue,
config,
completeness)
ival = 0
tolerance = 1E-7
number_intervals = np.shape(ctime)[0]
b_est = np.zeros(number_intervals, dtype=float)
neq = np.zeros(number_intervals, dtype=float)
nyr = np.zeros(number_intervals, dtype=float)
for ival in range(0, number_intervals):
id0 = np.abs(ctime - ctime[ival]) < tolerance
m_c = np.min(cmag[id0])
if ival == 0:
id1 = np.logical_and(
catalogue.data['year'] >= (ctime[ival] - tolerance),
catalogue.data['magnitude'] >= (m_c - tolerance))
nyr[ival] = float(catalogue.end_year) - ctime[ival] + 1.
elif ival == number_intervals - 1:
id1 = np.logical_and(
catalogue.data['year'] < (ctime[ival - 1] - tolerance),
catalogue.data['magnitude'] >= (m_c - tolerance))
nyr[ival] = ctime[ival - 1] - ctime[ival]
else:
id1 = np.logical_and(
catalogue.data['year'] >= (ctime[ival] - tolerance),
catalogue.data['year'] < (ctime[ival - 1] - tolerance))
id1 = np.logical_and(
id1, catalogue.data['magnitude'] > (m_c - tolerance))
nyr[ival] = ctime[ival - 1] - ctime[ival]
neq[ival] = np.sum(id1)
# Get a- and b- value for the selected events
temp_rec_table = recurrence_table(catalogue.data['magnitude'][id1],
dmag,
catalogue.data['year'][id1])
aki_ml = AkiMaxLikelihood()
b_est[ival] = aki_ml._aki_ml(temp_rec_table[:, 0],
temp_rec_table[:, 1],
dmag, m_c)[0]
ival += 1
total_neq = float(np.sum(neq))
bval = self._harmonic_mean(b_est, neq)
sigma_b = bval / np.sqrt(total_neq)
aval = self._calculate_a_value(bval, total_neq, nyr, cmag, ref_mag)
sigma_a = self._calculate_a_value(bval + sigma_b, total_neq, nyr,
cmag, ref_mag)
if not config['reference_magnitude']:
aval = np.log10(aval)
sigma_a = np.log10(sigma_a) - aval
else:
sigma_a = sigma_a - aval
return bval, sigma_b, aval, sigma_a
def _harmonic_mean(self, parameters, neq):
"""
Calculates the Harmonic mean of a vector of parameters
"""
weight = neq.astype(float) / np.sum(neq)
if np.shape(parameters)[0] != np.shape(weight)[0]:
raise ValueError('Parameter vector not same shape as weights')
else:
average_value = np.zeros(np.shape(parameters)[0], dtype=float)
id0 = np.logical_not(np.isnan(parameters))
average_value = 1. / np.sum(weight[id0] / parameters[id0])
return average_value
def _calculate_a_value(self, bval, nvalue, nyr, cmag, ref_mag):
"""
Calculates the rate of events >= ref_mag using the b-value estimator
and Eq. 10 of Kijko & Smit
"""
denominator = np.sum(nyr * np.exp(-bval * (cmag - ref_mag)))
return nvalue / denominator