Source code for openquake.hmtk.faults.mfd.characteristic
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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 * 1.0e9) * (area * 1.0e6) * (slip / 1000.0)
)
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 / 2.0),
self.lower_bound,
self.upper_bound,
loc=self.mmax,
scale=self.sigma,
)
- truncnorm.cdf(
mag_range - (self.bin_width / 2.0),
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
