# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# LICENSE
#
# Copyright (C) 2010-2021 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.
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# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>
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# DISCLAIMER
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# 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.
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# 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
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# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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import warnings
import numpy as np
from openquake.hmtk.seismicity.occurrence.base import (
SeismicityOccurrence, OCCURRENCE_METHODS)
from openquake.hmtk.seismicity.occurrence.utils import (input_checks,
get_completeness_counts)
[docs]@OCCURRENCE_METHODS.add(
'calculate',
completeness=True,
reference_magnitude=0.0,
magnitude_interval=0.1,
bvalue=1.0,
itstab=1E-5,
maxiter=1000)
class Weichert(SeismicityOccurrence):
'''Class to Implement Weichert Algorithm'''
[docs] def calculate(self, catalogue, config, completeness=None):
'''Calculates recurrence using the Weichert (1980) method'''
# Input checks
cmag, ctime, ref_mag, _, config = input_checks(catalogue,
config,
completeness)
if not "dtime" in catalogue.data.keys() or not\
len(catalogue.data["dtime"]):
catalogue.data["dtime"] = catalogue.get_decimal_time()
if not catalogue.end_year:
catalogue.update_end_year()
if completeness is None:
start_year = float(np.min(catalogue.data["year"]))
completeness = np.column_stack([ctime, cmag])
# Apply Weichert preparation
cent_mag, t_per, n_obs = get_completeness_counts(
catalogue, completeness, config["magnitude_interval"])
# A few more Weichert checks
key_list = config.keys()
if (not 'bvalue' in key_list) or (not config['bvalue']):
config['bvalue'] = 1.0
if (not 'itstab' in key_list) or (not config['itstab']):
config['itstab'] = 1E-5
if (not 'maxiter' in key_list) or (not config['maxiter']):
config['maxiter'] = 1000
bval, sigma_b, rate, sigma_rate, aval, sigma_a = \
self.weichert_algorithm(t_per, cent_mag, n_obs, ref_mag,
config['bvalue'], config['itstab'], config['maxiter'])
if not config['reference_magnitude']:
rate = np.log10(aval)
sigma_rate = np.log10(aval + sigma_a) - np.log10(aval)
return bval, sigma_b, rate, sigma_rate
[docs] def weichert_algorithm(self, tper, fmag, nobs, mrate=0.0, bval=1.0,
itstab=1E-5, maxiter=1000):
"""
Weichert algorithm
:param tper: length of observation period corresponding to magnitude
:type tper: numpy.ndarray (float)
:param fmag: central magnitude
:type fmag: numpy.ndarray (float)
:param nobs: number of events in magnitude increment
:type nobs: numpy.ndarray (int)
:keyword mrate: reference magnitude
:type mrate: float
:keyword bval: initial value for b-value
:type beta: float
:keyword itstab: stabilisation tolerance
:type itstab: float
:keyword maxiter: Maximum number of iterations
:type maxiter: Int
:returns: b-value, sigma_b, a-value, sigma_a
:rtype: float
"""
beta = bval * np.log(10.)
d_m = fmag[1] - fmag[0]
itbreak = 0
snm = np.sum(nobs * fmag)
nkount = np.sum(nobs)
iteration = 1
while (itbreak != 1):
beta_exp = np.exp(-beta * fmag)
tjexp = tper * beta_exp
tmexp = tjexp * fmag
sumexp = np.sum(beta_exp)
stmex = np.sum(tmexp)
sumtex = np.sum(tjexp)
stm2x = np.sum(fmag * tmexp)
dldb = stmex / sumtex
if np.isnan(stmex) or np.isnan(sumtex):
warnings.warn('NaN occurs in Weichert iteration')
return np.nan, np.nan, np.nan, np.nan, np.nan, np.nan
#raise ValueError('NaN occers in Weichert iteration')
d2ldb2 = nkount * ((dldb ** 2.0) - (stm2x / sumtex))
dldb = (dldb * nkount) - snm
betl = np.copy(beta)
beta = beta - (dldb / d2ldb2)
sigbeta = np.sqrt(-1. / d2ldb2)
if np.abs(beta - betl) <= itstab:
# Iteration has reached convergence
bval = beta / np.log(10.0)
sigb = sigbeta / np.log(10.)
fngtm0 = nkount * (sumexp / sumtex)
fn0 = fngtm0 * np.exp((beta) * (fmag[0] - (d_m / 2.0)))
stdfn0 = fn0 / np.sqrt(nkount)
a_m = fngtm0 * np.exp((-beta) * (mrate -
(fmag[0] - (d_m / 2.0))))
siga_m = a_m / np.sqrt(nkount)
itbreak = 1
else:
iteration += 1
if iteration > maxiter:
warnings.warn('Maximum Number of Iterations reached')
return np.nan, np.nan, np.nan, np.nan, np.nan, np.nan
return bval, sigb, a_m, siga_m, fn0, stdfn0