Source code for openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_fixed_b

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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(['magnitude']), "input_mmax": lambda cat:['magnitude'][ np.argmax(['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, obsmax, obsmaxsig = _get_observed_mmax(, config) mmin = config['input_mmin'] beta = config['b-value'] * np.log(10.) neq, mmin = _get_magnitude_vector_properties(, 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