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

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

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Module :class: openquake.hmtk.seismicity.max_magnitude.cumulative_moment.CumulativeMoment
implements cumulative moment estimator of maximum magnitude from instrumental
from math import fabs
import numpy as np
from openquake.hmtk.seismicity.max_magnitude.base import (
    BaseMaximumMagnitude, MAX_MAGNITUDE_METHODS)

[docs]@MAX_MAGNITUDE_METHODS.add("get_mmax", class CumulativeMoment(BaseMaximumMagnitude): '''Class to implement the bootstrapped cumulative moment estimator of maximum magnitude. Adapted by G. Weatherill from the Cumulative Strain Energy approach originally suggested by Makropoulos & Burton (1983)'''
[docs] def get_mmax(self, catalogue, config): ''' Calculates Maximum magnitude and its uncertainty :param catalogue: Instance of openquake.hmtk.seismicity.catalogue.Catalogue class Earthquake calatalogue data as dictionary containing - * 'year' - Year of event * 'magnitude' - Magnitude of event * 'sigmaMagnitude' - Uncertainty on magnitude (optional) :param dict config: Configuration file for algorithm, containing thw following - * 'number_bootstraps' - Number of bootstraps for uncertainty :param int seed: Seed for random number generator (must be positive) :returns: * Maximum magnitude (float) * Uncertainty on maximum magnituse (float) ''' # If no bootstraps no uncertainty on magnitudes then simply calculate # Mmax without uncertainty self.check_config(config) cond = config['number_bootstraps'] == 1 or\ not isinstance(['sigmaMagnitude'], np.ndarray) or\ len(['sigmaMagnitude']) == 0 or\ np.all(np.isnan(['sigmaMagnitude'])) if cond: return self.cumulative_moment(['year'],['magnitude']), 0.0 neq = len(['magnitude']) mmax_samp = np.zeros(config['number_bootstraps'], dtype=float) # Sample magnitudes from catalogue and calculate MMax from sample for iloc in range(0, config['number_bootstraps']): mw_sample =['magnitude'] + \['sigmaMagnitude'] * np.random.normal(0., 1., neq) mmax_samp[iloc] = self.cumulative_moment(['year'], mw_sample) # Return mean and standard deviation of samples return np.mean(mmax_samp), np.std(mmax_samp, ddof=1)
[docs] def check_config(self, config): ''' Checks the configuration file for the number of bootstraps. Returns 1 if not found or invalid (i.e. < 0) ''' nb = config['number_bootstraps'] or 0 if nb < 1: config['number_bootstraps'] = 1 return config
[docs] def cumulative_moment(self, year, mag): '''Calculation of Mmax using aCumulative Moment approach, adapted from the cumulative strain energy method of Makropoulos & Burton (1983) :param year: Year of Earthquake :type year: numpy.ndarray :param mag: Magnitude of Earthquake :type mag: numpy.ndarray :keyword iplot: Include cumulative moment plot :type iplot: Boolean :return mmax: Returns Maximum Magnitude :rtype mmax: Float ''' # Calculate seismic moment m_o = 10. ** (9.05 + 1.5 * mag) year_range = np.arange(np.min(year), np.max(year) + 1, 1) nyr = np.shape(year_range)[0] morate = np.zeros(nyr, dtype=float) # Get moment release per year for loc, tyr in enumerate(year_range): idx = np.abs(year - tyr) < 1E-5 if np.sum(idx) > 0: # Some moment release in that year morate[loc] = np.sum(m_o[idx]) ave_morate = np.sum(morate) / nyr # Average moment rate vector exp_morate = np.cumsum(ave_morate * np.ones(nyr)) modiff = (np.abs(np.max(np.cumsum(morate) - exp_morate)) + np.abs(np.min(np.cumsum(morate) - exp_morate))) # Return back to Mw if fabs(modiff) < 1E-20: return -np.inf mmax = (2. / 3.) * (np.log10(modiff) - 9.05) return mmax