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 = 10.0 ** (bval * min_mag) fival = 10.0 ** (bval * (mag_inc / 2.0)) - 10.0 ** ( -bval * (mag_inc / 2.0) ) 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 = 10.0 ** (bval * min_mag) a_inc = a_cum + np.log10( (10.0 ** (bval * mag_inc)) - (10.0 ** (-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]) / 2.0 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(10.0 * np.max(catalogue.data["magnitude"])) / 10.0 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(10.0 * cmag[iloc]) / 10.0, (np.ceil(10.0 * cmag[iloc + 1]) / 10.0), 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