Source code for openquake.hmtk.seismicity.max_magnitude.cumulative_moment_release
#!/usr/bin/env python
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# Copyright (C) 2010-2018 GEM Foundation, G. Weatherill, M. Pagani, D. Monelli
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'''
Module :class: openquake.hmtk.seismicity.max_magnitude.cumulative_moment.CumulativeMoment
implements cumulative moment estimator of maximum magnitude from instrumental
seismicity
'''
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", number_bootstraps=np.int)
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(catalogue.data['sigmaMagnitude'], np.ndarray) or\
len(catalogue.data['sigmaMagnitude']) == 0 or\
np.all(np.isnan(catalogue.data['sigmaMagnitude']))
if cond:
return self.cumulative_moment(catalogue.data['year'],
catalogue.data['magnitude']), 0.0
neq = len(catalogue.data['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 = catalogue.data['magnitude'] + \
catalogue.data['sigmaMagnitude'] * np.random.normal(0., 1.,
neq)
mmax_samp[iloc] = self.cumulative_moment(catalogue.data['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