Source code for openquake.hmtk.faults.mfd.characteristic

# -*- coding: utf-8 -*-
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Module :mod: openquake.hmtk.faults.mfd.characteristic implements
:class:Characteristic the simple characteristic earthquake calculator
of recurrence.

import numpy as np
from scipy.stats import truncnorm
from math import fabs
from openquake.hmtk.faults.mfd.base import _scale_moment, BaseMFDfromSlip

[docs]class Characteristic(BaseMFDfromSlip): ''' Class to implement the characteristic earthquake model assuming a truncated Gaussian distribution :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 lower_bound: Lower bound of Gaussian distribution (as number of standard deviations) :param float upper_bound: Upper bound of Gaussian distribution (as number of standard deviations) :param float sigma: Standard deviation (in magnitude units) of the Gaussian 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) * 'Maximum_Magnitude' - Characteristic magnituded (float) (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) * 'Lower_Bound' - Lower bound in terms of number of sigma (float) * 'Upper_Bound' - Upper bound in terms of number of sigma (float) * 'Sigma' - Standard deviation (in magnitude units) of distribution ''' self.mfd_model = 'Characteristic' self.mfd_weight = mfd_conf['Model_Weight'] self.bin_width = mfd_conf['MFD_spacing'] self.mmin = None self.mmax = None self.mmax_sigma = None self.lower_bound = mfd_conf['Lower_Bound'] self.upper_bound = mfd_conf['Upper_Bound'] self.sigma = mfd_conf['Sigma'] 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 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 fault_width: Width of the fault (km) :param float disp_length_ratio: Displacement to length ratio (dimensionless) :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) characteristic_rate = moment_rate / moment_mag if self.sigma and (fabs(self.sigma) > 1E-5): self.mmin = self.mmax + (self.lower_bound * self.sigma) mag_upper = self.mmax + (self.upper_bound * self.sigma) mag_range = np.arange(self.mmin, mag_upper + self.bin_width, self.bin_width) self.occurrence_rate = characteristic_rate * ( truncnorm.cdf(mag_range + (self.bin_width / 2.), self.lower_bound, self.upper_bound, loc=self.mmax, scale=self.sigma) - truncnorm.cdf(mag_range - (self.bin_width / 2.), self.lower_bound, self.upper_bound, loc=self.mmax, scale=self.sigma)) else: # Returns only a single rate self.mmin = self.mmax self.occurrence_rate = np.array([characteristic_rate], dtype=float) return self.mmin, self.bin_width, self.occurrence_rate