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

# -*- coding: utf-8 -*-
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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:`openquake.hmtk.seismicity.occurrence.base.py`
            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(
            catalogue.data["magnitude"], dmag, catalogue.data["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 / 2.0))
        # Calculate sigma b from Bender estimator
        sigma_b = np.sum(number_obs * ((mval - m_ave) ** 2.0)) / (
            neq * (neq - 1)
        )
        sigma_b = np.log(10.0) * (bval**2.0) * np.sqrt(sigma_b)
        return bval, sigma_b