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'''
Module :mod:`openquake.hmtk.seismicity.max_magnitude.kijko_sellevol` defines
the Kijko & Sellevol algorithm for maximum magnitude
'''
import warnings
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):
'''Checks that the config file contains all required parameters
:param dict config:
Configuration file
:returns:
Configuration file with all correct parameters
'''
if 'tolerance' not in config.keys() or not config['tolerance']:
config['tolerance'] = 1E-5
if not config.get('maximum_iterations', None):
config['maximum_iterations'] = 1000
mmin_obs = np.min(data['magnitude'])
if config.get('input_mmin', 0) < mmin_obs:
config['input_mmin'] = mmin_obs
if fabs(config['b-value']) < 1E-7:
config['b-value'] = 1E-7
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": 1E-7,
"maximum_iterations": 1000,
"tolerance": 1E-5})
class KijkoSellevolFixedb(BaseMaximumMagnitude):
'''
Implements Kijko and Sellevol estimator for maximim magnitude assuming
a fixed b-value. Coded from description in Kijko (2004):
Kijko, A. (2004), ..., Pure & Applied Geophysics,
'''
[docs] def get_mmax(self, catalogue, config):
'''
Calculates Maximum magnitude
:param catalogue:
Earthquake catalogue as instance of :class:
openquake.hmtk.seismicity.catalogue.Catalogue
:param dict config:
Configuration file for algorithm, contains the attributes:
* 'b-value': b-value (positive float)
* 'input_mmin': Minimum magnitude for integral (if less than
minimum observed magnitude, will be overwritten by
minimum observed magnitude)
* 'tolerance': Tolerance of stabilising of iterator
* 'maximum_interations': Maximum number of iterations
:returns: **mmax** Maximum magnitude and **mmax_sig** corresponding
uncertainty
'''
config = check_config(config, catalogue.data)
obsmax, obsmaxsig = _get_observed_mmax(catalogue.data, config)
mmin = config['input_mmin']
beta = config['b-value'] * np.log(10.)
neq, mmin = _get_magnitude_vector_properties(catalogue.data, config)
mmax = np.copy(obsmax)
d_t = np.inf
iterator = 0
print(mmin, mmax, neq, beta)
while d_t > config['tolerance']:
delta = quadrature(self._ks_intfunc, mmin, mmax,
args=(neq, mmax, mmin, beta))[0]
tmmax = obsmax + delta
d_t = np.abs(tmmax - mmax)
mmax = np.copy(tmmax)
iterator += 1
if iterator > config['maximum_iterations']:
print('Kijko-Sellevol estimator reached '
'maximum # of iterations')
d_t = -np.inf
return mmax.item(), np.sqrt(obsmaxsig ** 2. + delta ** 2.)
def _ks_intfunc(self, mval, neq, mmax, mmin, beta):
'''Integral function inside Kijko-Sellevol estimator
(Eq. 6 in Kijko, 2004)
:param float mval:
Magnitude value
:param float neq:
Number of earthquakes
:param float mmax:
Maximum Magnitude
:param float mmin:
Minimum Magnitude
:param float beta:
Beta-value of the distribution
:returns:
Integrand of Kijko-Sellevol estimator
'''
if mmin >= mmax:
raise ValueError('Maximum magnitude smaller than minimum magnitude'
' in Kijko & Sellevol (Fixed-b) integral')
func1 = 1. - np.exp(-beta * (mval - mmin))
if np.fabs(beta) > 1e-3:
func1 = (func1 / (1. - np.exp(-beta * (mmax - mmin)))) ** neq
else:
warnings.warn('beta is lower or equal to 0', RuntimeWarning)
return func1