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'''
Module :mod:`openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_bayes`
implements the Kijko & Sellevol (1989) method for estimating maximum magnitude
from observed seismicity with uncertain b-value
'''
import numpy as np
from math import fabs
from scipy.integrate import quadrature
from openquake.hmtk.seismicity.max_magnitude.base import (
BaseMaximumMagnitude, MAX_MAGNITUDE_METHODS,
_get_observed_mmax, _get_magnitude_vector_properties)
[docs]def check_config(config, data):
'''Check config file inputs
:param dict config:
Configuration settings for the function
'''
essential_keys = ['input_mmin', 'b-value', 'sigma-b']
for key in essential_keys:
if not key in config.keys():
raise ValueError('For KijkoSellevolBayes the key %s needs to '
'be set in the configuation' % key)
if 'tolerance' not in config.keys() or not config['tolerance']:
config['tolerance'] = 1E-5
if not config.get('maximum_iterations', False):
config['maximum_iterations'] = 1000
if config['input_mmin'] < np.min(data['magnitude']):
config['input_mmin'] = np.min(data['magnitude'])
if fabs(config['sigma-b'] < 1E-15):
raise ValueError('Sigma-b must be greater than zero!')
return config
[docs]@MAX_MAGNITUDE_METHODS.add(
"get_mmax",
**{"input_mmin": lambda cat: np.min(cat.data['magnitude']),
"input_mmax": lambda cat: cat.data['magnitude'][
np.argmax(cat.data['magnitude'])],
"input_mmax_uncertainty": lambda cat: cat.get_observed_mmax_sigma(0.2),
"b-value": np.float,
"sigma-b": np.float,
"maximum_iterations": 1000,
"tolerance": 1E-5})
class KijkoSellevolBayes(BaseMaximumMagnitude):
'''
Class to implement Kijko & Sellevol Bayesian estimator of Mmax, with
uncertain b-value
'''
[docs] def get_mmax(self, catalogue, config):
'''Calculate maximum magnitude
:returns: **mmax** Maximum magnitude and **mmax_sig** corresponding uncertainty
:rtype: Float
'''
# Check configuration file
config = check_config(config, catalogue.data)
# Negative b-values will return nan - this simply skips the integral
if config['b-value'] <= 0.0:
return np.nan, np.nan
obsmax, obsmaxsig = _get_observed_mmax(catalogue.data, config)
beta = config['b-value'] * np.log(10.)
sigbeta = config['sigma-b'] * np.log(10.)
neq, mmin = _get_magnitude_vector_properties(catalogue.data, config)
pval = beta / (sigbeta ** 2.)
qval = (beta / sigbeta) ** 2.
mmax = np.copy(obsmax)
d_t = np.inf
iterator = 0
while d_t > config['tolerance']:
rval = pval / (pval + mmax - mmin)
ldelt = (1. / (1. - (rval ** qval))) ** neq
delta = ldelt * quadrature(self._ksb_intfunc, mmin, mmax,
args=(neq, mmin, pval, qval))[0]
tmmax = obsmax + delta
d_t = np.abs(tmmax - mmax)
mmax = np.copy(tmmax)
iterator += 1
if iterator > config['maximum_iterations']:
print('Kijko-Sellevol-Bayes estimator reached'
'maximum # of iterations')
d_t = -np.inf
return mmax.item(), np.sqrt(obsmaxsig ** 2. + delta ** 2.)
def _ksb_intfunc(self, mval, neq, mmin, pval, qval):
'''
Integral function inside Kijko-Sellevol-Bayes estimator
(part of Eq. 10 in Kijko, 2004 - section 3.2)
:param float mval:
Magnitude
:param float neq:
Number of Earthquakes
:param float mmin:
Minimum Magnitude
:param float pval:
p-value (see Kijko, 2004 - section 3.2)
:param float qval:
q-value (see Kijki, 2004 - section 3.2)
:returns:
Output of function integrand
'''
func1 = (1. - ((pval / (pval + mval - mmin)) ** qval)) ** neq
return func1