# -*- coding: utf-8 -*-
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# Copyright (C) 2010-2023 GEM Foundation, G. Weatherill, M. Pagani,
# D. Monelli.
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# The Hazard Modeller's Toolkit is free software: you can redistribute
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"""
Module :mod: openquake.hmtk.faults.mfd.youngs_coppersmith implements class
YoungsCoppersmithExponential and YoungsCoppersmithCharacteristic, the
exponential and characteristic forms of the Youngs & Coppersmith (1985)
models for calculating earthquake recurrence from slip rate
Youngs, R. R., and Coppersmith, K., J. (1985) "Implications of Fault Slip Rates
and Earthquake Recurrence Models to Probabilistic Seismic Hazard Estimates"
Bull. Seis. Soc. Am. 75(4) 939 - 964
"""
import numpy as np
from math import exp, log
from openquake.hmtk.faults.mfd.base import _scale_moment, BaseMFDfromSlip
from openquake.hazardlib.mfd.youngs_coppersmith_1985 import \
YoungsCoppersmith1985MFD
C_VALUE = 16.05
D_VALUE = 1.5
[docs]class YoungsCoppersmithExponential(BaseMFDfromSlip):
'''
Calculates the activity rate on a fault with a given slip assuming the
exponential model described in Youngs & Coppersmith (1985) Eq. 11
:param str mfd_model:
Type of magnitude frequency distribution
:param float mfd_weight:
Weight of the mfd distribution (for subsequent logic tree processing)
:param float bin_width:
Width of the magnitude bin (rates are given for the centre point)
:param float mmin:
Minimum magnitude
:param float mmax:
Maximum magnitude
:param float mmax_sigma:
Uncertainty on maximum magnitude
:param float b_value:
Exponent (b-value) for the magnitude frequency distribution
:param float b_value_sigma:
Uncertainty on exponent (b-value) for the magnitude frequency
distribution
:param numpy.ndarray occurrence_rate:
Activity rates for magnitude in the range mmin to mmax in steps of
bin_width
'''
[docs] def setUp(self, mfd_conf):
'''
Input core configuration parameters as specified in the
configuration file
:param dict mfd_conf:
Configuration file containing the following attributes:
* 'Model_Weight' - Logic tree weight of model type (float)
* 'MFD_spacing' - Width of MFD bin (float)
* 'Minimum_Magnitude' - Minimum magnitude of activity rates (float)
* 'b_value' - Tuple of (b-value, b-value uncertainty)
* 'Maximum_Magnitude' - Maximum magnitude on fault (if not defined
will use scaling relation)
* 'Maximum_Magnitude_Uncertainty' - Uncertainty on
maximum magnitude
(If not defined and the MSR has a sigma term then this will be
taken from sigma)
'''
self.mfd_model = 'Youngs & Coppersmith Exponential'
self.mfd_weight = mfd_conf['Model_Weight']
self.bin_width = mfd_conf['MFD_spacing']
self.mmin = mfd_conf['Minimum_Magnitude']
self.mmax = None
self.mmax_sigma = None
self.b_value = mfd_conf['b_value'][0]
self.b_value_sigma = mfd_conf['b_value'][1]
self.occurrence_rate = None
[docs] def get_mmax(self, mfd_conf, msr, rake, area):
'''
Gets the mmax for the fault - reading directly from the config file
or using the msr otherwise
:param dict mfd_config:
Configuration file (see setUp for parameters)
:param msr:
Instance of :class: nhlib.scalerel
:param float rake:
Rake of the fault (in range -180 to 180)
:param float area:
Area of the fault surface (km^2)
'''
if mfd_conf['Maximum_Magnitude']:
self.mmax = mfd_conf['Maximum_Magnitude']
else:
self.mmax = msr.get_median_mag(area, rake)
self.mmax_sigma = (mfd_conf.get('Maximum_Magnitude_Uncertainty', None)
or msr.get_std_dev_mag(None, rake))
[docs] def get_mfd(self, slip, area, shear_modulus=30.0):
'''
Calculates activity rate on the fault
:param float slip:
Slip rate in mm/yr
:param area:
Width of the fault (km)
:param float shear_modulus:
Shear modulus of the fault (GPa)
:returns:
* Minimum Magnitude (float)
* Bin width (float)
* Occurrence Rates (numpy.ndarray)
'''
# Working in Nm so convert: shear_modulus - GPa -> Nm
# area - km ** 2. -> m ** 2.
# slip - mm/yr -> m/yr
moment_rate = (shear_modulus * 1.E9) * (area * 1.E6) * (slip / 1000.)
moment_mag = _scale_moment(self.mmax, in_nm=True)
beta = self.b_value * log(10.)
mag = np.arange(self.mmin - (self.bin_width / 2.),
self.mmax + self.bin_width,
self.bin_width)
if self.b_value > 1.5:
print('b-value larger than 1.5 will produce invalid results in '
'Anderson & Luco models')
self.occurrence_rate = np.nan * np.ones(len(mag) - 1)
return self.mmin, self.bin_width, self.occurrence_rate
self.occurrence_rate = np.zeros(len(mag) - 1, dtype=float)
for ival in range(0, len(mag) - 1):
self.occurrence_rate[ival] = (
self.cumulative_value(mag[ival], moment_rate, beta, moment_mag)
- self.cumulative_value(
mag[ival + 1], moment_rate, beta, moment_mag))
return self.mmin, self.bin_width, self.occurrence_rate
[docs] def cumulative_value(self, mag_val, moment_rate, beta, moment_mag):
'''
Calculates the cumulative rate of events with M > m0 using
equation 11 of Youngs & Coppersmith (1985)
:param float mag_val:
Magnitude
:param float moment_rate:
Moment rate on fault (in Nm) from slip rate
:param float beta:
Exponent (b log(10)
:param float moment_mag:
Moment of the upper bound magnitude
'''
exponent = exp(-beta * (self.mmax - mag_val))
return (moment_rate * (D_VALUE - self.b_value) * (1. - exponent)) /\
(self.b_value * moment_mag * exponent)
[docs]class YoungsCoppersmithCharacteristic(BaseMFDfromSlip):
'''
Calculates the activity rate on a fault with a given slip assuming the
characteristic model described in Youngs & Coppersmith (1985)
Eqs. 16 and 17
:param str mfd_type:
Type of magnitude frequency distribution
:param float mfd_weight:
Weight of the mfd distribution (for subsequent logic tree processing)
:param float bin_width:
Width of the magnitude bin (rates are given for the centre point)
:param float mmin:
Minimum magnitude
:param float mmax:
Maximum magnitude
:param float mmax_sigma:
Uncertainty on maximum magnitude
:param float b_value:
Exponent (b-value) for the exponential magnitude frequency distribution
:param float b_value_sigma:
Uncertainty on exponent (b-value) for the magnitude frequency
distribution
:param numpy.ndarray occurrence_rate:
Activity rates for magnitude in the range mmin to mmax in steps of
bin_width
:param model:
Maintains present instance of :class: YoungsCoppersmith1985MFD
'''
[docs] def setUp(self, mfd_conf):
'''
Input core configuration parameters as specified in the
configuration file
:param dict mfd_conf:
Configuration file containing the following attributes:
* 'Model_Weight' - Logic tree weight of model type (float)
* 'MFD_spacing' - Width of MFD bin (float)
* 'Minimum_Magnitude' - Minimum magnitude of activity rates (float)
* 'b_value' - Tuple of (b-value, b-value uncertainty)
* 'Maximum_Magnitude' - Characteristic magnitude on fault
(if not defined, will use scaling relation)
* 'Maximum_Magnitude_Uncertainty' - Uncertainty on
maximum magnitude
(If not defined and the MSR has a sigma term then this will be
taken from sigma)
'''
self.mfd_type = 'Youngs & Coppersmith (1985) Characteristic'
self.mfd_weight = mfd_conf['Model_Weight']
self.bin_width = mfd_conf['MFD_spacing']
self.mmin = mfd_conf['Minimum_Magnitude']
self.mmax = None
self.mmax_sigma = None
self.b_value = mfd_conf['b_value'][0]
self.b_value_sigma = mfd_conf['b_value'][1]
self.occurrence_rate = None
self.model = None
[docs] def get_mmax(self, mfd_conf, msr, rake, area):
'''
Gets the mmax for the fault - reading directly from the config file
or using the msr otherwise
:param dict mfd_config:
Configuration file (see setUp for paramters)
:param msr:
Instance of :class: nhlib.scalerel
:param float rake:
Rake of the fault (in range -180 to 180)
:param float area:
Area of the fault surface (km^2)
'''
if mfd_conf['Maximum_Magnitude']:
self.mmax = mfd_conf['Maximum_Magnitude']
else:
self.mmax = msr.get_median_mag(area, rake)
self.mmax_sigma = (mfd_conf.get('Maximum_Magnitude_Uncertainty', None)
or msr.get_std_dev_mag(None, rake))
[docs] def get_mfd(self, slip, area, shear_modulus=30.0):
'''
Calculates activity rate on the fault
:param float slip:
Slip rate in mm/yr
:param area:
Area of the fault (km)
:param float shear_modulus:
Shear modulus of the fault (GPa)
:returns:
* Minimum Magnitude (float)
* Bin width (float)
* Occurrence Rates (numpy.ndarray)
Behavioural Notes: To use the openquake.hazardlib implementation the
magnitudes returned will be the mid_point of the bins and not the
original edge points. The minimum magnitude is update to reflect this!
'''
# Calculate moment rate in N-m / year
moment_rate = (shear_modulus * 1.E9) * (area * 1.E6) * (slip / 1000.)
# Get Youngs & Coppersmith rate from
# youngs_coppersmith.YoungsCoppersmith1985MFD.from_total_moment_rate
self.model = YoungsCoppersmith1985MFD.from_total_moment_rate(
self.mmin - (self.bin_width / 2.),
self.b_value,
self.mmax - 0.25,
moment_rate,
self.bin_width)
temp_data = self.model.get_annual_occurrence_rates()
self.occurrence_rate = np.array([value[1] for value in temp_data])
self.mmin = np.min(np.array([value[0] for value in temp_data]))
return self.mmin, self.bin_width, self.occurrence_rate