Source code for openquake.hmtk.seismicity.occurrence.aki_maximum_likelihood

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4

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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 recurrence_table, input_checks

[docs]@OCCURRENCE_METHODS.add('calculate', completeness=True) class AkiMaxLikelihood(SeismicityOccurrence):
[docs] def calculate(self, catalogue, config=None, completeness=None): """ Calculation of b-value and its uncertainty for a given catalogue, using the maximum likelihood method of Aki (1965), with a correction for discrete bin width (Bender, 1983). :param catalogue: See :class:`` for further explanation :param config: The configuration in this case do not contains specific information :keyword float completeness: Completeness magnitude :return float bval: b-value of the Gutenberg-Richter relationship :return float sigma_b: Standard deviation of the GR b-value """ # Input checks _cmag, _ctime, _ref_mag, dmag, config = input_checks(catalogue, config, completeness) rt = recurrence_table(['magnitude'], dmag,['year']) bval, sigma_b = self._aki_ml(rt[:, 0], rt[:, 1]) return bval, sigma_b
def _aki_ml(self, mval, number_obs, dmag=0.1, m_c=0.0): """ :param numpy.ndarray mval: array of reference magnitudes (column 0 from recurrence table) :param numpy.ndarray number_obs: number of observations in magnitude bin (column 1 from recurrence table) :keyword float dmag: magnitude interval :keyword float m_c: completeness magnitude :return float bval: b-value of the Gutenberg-Richter relationship :return float sigma_b: Standard deviation of the GR b-value """ # Exclude data below Mc id0 = mval >= m_c mval = mval[id0] number_obs = number_obs[id0] # Get Number of events, minimum magnitude and mean magnitude neq = np.sum(number_obs) if neq <= 1: # Cannot determine b-value (too few event) return NaNs warnings.warn('Too few events (<= 1) to calculate b-value') return np.nan, np.nan m_min = np.min(mval) m_ave = np.sum(mval * number_obs) / neq # Calculate b-value bval = np.log10(np.exp(1.0)) / (m_ave - m_min + (dmag / 2.)) # Calculate sigma b from Bender estimator sigma_b = np.sum(number_obs * ((mval - m_ave) ** 2.0)) /\ (neq * (neq - 1)) sigma_b = np.log(10.) * (bval ** 2.0) * np.sqrt(sigma_b) return bval, sigma_b