def test_cumulative_value(self):
'''
Tests the calculation of the cumulative rate M > Mref
Data and tests taken from Bungum (2007). Current parameters should
reproduce Model 4 line in Figure 1 of Bungum (2007)
'''
self.model = YoungsCoppersmithExponential()
self.config = {'MFD_spacing': 0.1,
'Maximum_Magnitude': 8.0,
'Maximum_Magnitude_Uncertainty': None,
'Minimum_Magnitude': 5.0,
'Model_Weight': 1.0,
'b_value': [1.0, 0.1]}
# Test case 1 - Fault of 120 km length and 60 km width (7200 km ** 2 area)
# b-value 1, slip = 1 mm/yr
self.model.setUp(self.config)
self.model.get_mmax(self.config, self.msr, 0., 7200.)
moment_rate = (30. * 1E9) * (7200. * 1E6) * (1.0 / 1000.)
momax = _scale_moment(self.model.mmax, in_nm=True)
beta = log(10.)
expected_result = YC_EXP_DATA[:, 1]
mags = np.arange(5.0, 8.1, 0.1)
for iloc, mag in enumerate(mags):
self.assertAlmostEqual(
expected_result[iloc],
self.model.cumulative_value(mag, moment_rate, beta, momax))
def test_cumulative_value(self):
'''
Tests the calculation of the cumulative rate M > Mref
Data and tests taken from Bungum (2007). Current parameters should
reproduce Model 4 line in Figure 1 of Bungum (2007)
'''
self.model = YoungsCoppersmithExponential()
self.config = {'MFD_spacing': 0.1,
'Maximum_Magnitude': 8.0,
'Maximum_Magnitude_Uncertainty': None,
'Minimum_Magnitude': 5.0,
'Model_Weight': 1.0,
'b_value': [1.0, 0.1]}
# Test case 1 - Fault of 120 km length and 60 km width (7200 km ** 2 area)
# b-value 1, slip = 1 mm/yr
self.model.setUp(self.config)
self.model.get_mmax(self.config, self.msr, 0., 7200.)
moment_rate = (30. * 1E9) * (7200. * 1E6) * (1.0 / 1000.)
momax = _scale_moment(self.model.mmax, in_nm=True)
beta = log(10.)
expected_result = YC_EXP_DATA[:, 1]
mags = np.arange(5.0, 8.1, 0.1)
for iloc, mag in enumerate(mags):
self.assertAlmostEqual(
expected_result[iloc],
self.model.cumulative_value(mag, moment_rate, beta, momax))
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
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
def cumulative_value(self, slip_moment, mmax, mag_value, bbar, dbar):
'''
Returns the rate of events with M > mag_value
:param float slip_moment:
:param float slip_moment:
Product of slip (cm/yr) * Area (cm ^ 2) * shear_modulus (dyne-cm)
:param float mmax:
Maximum magnitude
:param float mag_value:
Magnitude value
:param float bbar:
\bar{b} parameter (effectively = b * log(10.))
:param float dbar:
\bar{d} parameter
'''
moment_ratio = slip_moment / _scale_moment(mmax)
delta_m = mmax - mag_value
return ((dbar - bbar) / dbar) * moment_ratio * np.exp(bbar * (delta_m))
def cumulative_value(self, slip_moment, mmax, mag_value, bbar, dbar):
'''
Returns the rate of events with M > mag_value
:param float slip_moment:
:param float slip_moment:
Product of slip (cm/yr) * Area (cm ^ 2) * shear_modulus (dyne-cm)
:param float mmax:
Maximum magnitude
:param float mag_value:
Magnitude value
:param float bbar:
\bar{b} parameter (effectively = b * log(10.))
:param float dbar:
\bar{d} parameter
'''
moment_ratio = slip_moment / _scale_moment(mmax)
delta_m = mmax - mag_value
return ((dbar - bbar) / dbar) * moment_ratio * np.exp(bbar * (delta_m))
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
def _get_a3(bbar, dbar, slip_moment, mmax):
"""
Returns the A3 term (III.4 in Table 4)
"""
return ((dbar * (dbar - bbar)) /
(bbar**2.)) * (slip_moment / _scale_moment(mmax))
def _get_a2(bbar, dbar, slip_moment, mmax):
"""
Returns the A2 value defined in II.4 of Table 2
"""
return ((dbar - bbar) / bbar) * (slip_moment / _scale_moment(mmax))
def _get_a1(bbar, dbar, slip_moment, mmax):
"""
Returns the A1 term (I.4 of Table 2 in Anderson & Luco)
"""
return ((dbar - bbar) / dbar) * (slip_moment / _scale_moment(mmax))
def _get_a3(bbar, dbar, slip_moment, mmax):
"""
Returns the A3 term (III.4 in Table 4)
"""
return ((dbar * (dbar - bbar)) / (bbar ** 2.)) * (slip_moment /
_scale_moment(mmax))
def _get_a2(bbar, dbar, slip_moment, mmax):
"""
Returns the A2 value defined in II.4 of Table 2
"""
return ((dbar - bbar) / bbar) * (slip_moment / _scale_moment(mmax))
def _get_a1(bbar, dbar, slip_moment, mmax):
"""
Returns the A1 term (I.4 of Table 2 in Anderson & Luco)
"""
return ((dbar - bbar) / dbar) * (slip_moment / _scale_moment(mmax))
