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(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(10.0) 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**2.0 + delta**2.0)
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 = 1.0 - np.exp(-beta * (mval - mmin)) if np.fabs(beta) > 1e-3: func1 = (func1 / (1.0 - np.exp(-beta * (mmax - mmin)))) ** neq else: warnings.warn("beta is lower or equal to 0", RuntimeWarning) return func1