Source code for openquake.hmtk.seismicity.smoothing.utils

# -*- coding: utf-8 -*-
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'''
Module :mod:`openquake.hmtk.seismicity.smoothing.utils` implements
utility functions for smoothed seismicity analysis
'''

import numpy as np


[docs]def hermann_adjustment_factors(bval, min_mag, mag_inc): ''' Returns the adjustment factors (fval, fival) proposed by Hermann (1978) :param float bval: Gutenberg & Richter (1944) b-value :param np.ndarray min_mag: Minimum magnitude of completeness table :param non-negative float mag_inc: Magnitude increment of the completeness table ''' fval = 10. ** (bval * min_mag) fival = 10. ** (bval * (mag_inc / 2.)) - 10. ** (-bval * (mag_inc / 2.)) return fval, fival
[docs]def incremental_a_value(bval, min_mag, mag_inc): ''' Incremental a-value from cumulative - using the version of the Hermann (1979) formula described in Wesson et al. (2003) :param float bval: Gutenberg & Richter (1944) b-value :param np.ndarray min_mag: Minimum magnitude of completeness table :param float mag_inc: Magnitude increment of the completeness table ''' a_cum = 10. ** (bval * min_mag) a_inc = a_cum + np.log10((10. ** (bval * mag_inc)) - (10. ** (-bval * mag_inc))) return a_inc
[docs]def get_weichert_factor(beta, cmag, cyear, end_year): ''' Gets the Weichert adjustment factor for each the magnitude bins :param float beta: Beta value of Gutenberg & Richter parameter (b * log(10.)) :param np.ndarray cmag: Magnitude values of the completeness table :param np.ndarray cyear: Year values of the completeness table :param float end_year: Last year for consideration in the catalogue :returns: Weichert adjustment factor (float) ''' if len(cmag) > 1: # cval corresponds to the mid-point of the completeness bins # In the original code it requires that the magnitude bins be # equal sizedclass IsotropicGaussian(BaseSmoothingKernel): dmag = (cmag[1:] + cmag[:-1]) / 2. cval = np.hstack([dmag, cmag[-1] + (dmag[-1] - cmag[-2])]) else: # Single completeness value so Weichert factor is unity return 1.0 / (end_year - cyear[0] + 1), None t_f = sum(np.exp(-beta * cval)) / sum((end_year - cyear + 1) * np.exp(-beta * cval)) return t_f, cval
[docs]def check_completeness_table(completeness_table, catalogue): ''' Check to ensure completeness table is in the correct format `completeness_table = np.array([[year_, mag_i]]) for i in number of bins` :param np.ndarray completeness_table: Completeness table in format [[year, mag]] :param catalogue: Instance of openquake.hmtk.seismicity.catalogue.Catalogue class :returns: Correct completeness table ''' if isinstance(completeness_table, np.ndarray): assert np.shape(completeness_table)[1] == 2 return completeness_table elif isinstance(completeness_table, list): # Assuming list has only two elements assert len(completeness_table) == 2 return np.array([[completeness_table[0], completeness_table[1]]]) else: # Accepts the minimum magnitude and earliest year of the catalogue return np.array([[np.min(catalogue.data['year']), np.min(catalogue.data['magnitude'])]])
[docs]def get_even_magnitude_completeness(completeness_table, catalogue=None): ''' To make the magnitudes evenly spaced, render to a constant 0.1 magnitude unit :param np.ndarray completeness_table: Completeness table in format [[year, mag]] :param catalogue: Instance of openquake.hmtk.seismicity.catalogue.Catalogue class :returns: Correct completeness table ''' mmax = np.floor(10. * np.max(catalogue.data['magnitude'])) / 10. check_completeness_table(completeness_table, catalogue) cmag = np.hstack([completeness_table[:, 1], mmax + 0.1]) cyear = np.hstack([completeness_table[:, 0], completeness_table[-1, 0]]) if np.shape(completeness_table)[0] == 1: # Simple single-valued table return completeness_table, 0.1 for iloc in range(0, len(cmag) - 1): mrange = np.arange(np.floor(10. * cmag[iloc]) / 10., (np.ceil(10. * cmag[iloc + 1]) / 10.), 0.1) temp_table = np.column_stack([ cyear[iloc] * np.ones(len(mrange), dtype=float), mrange]) if iloc == 0: completeness_table = np.copy(temp_table) else: completeness_table = np.vstack([completeness_table, temp_table]) # completeness_table = np.vstack([completeness_table, # np.array([[cyear[-1], cmag[-1]]])]) return completeness_table, 0.1