def _b_ml(self, catalogue, config, cmag, ctime, ref_mag, dmag):
end_year = float(catalogue.end_year)
catalogue = catalogue.data
ival = 0
mag_eq_tolerance = 1E-5
aki_ml = AkiMaxLikelihood()
while ival < np.shape(ctime)[0]:
id0 = np.abs(ctime - ctime[ival]) < mag_eq_tolerance
m_c = np.min(cmag[id0])
print('--- ctime', ctime[ival], ' m_c', m_c)
# Find events later than cut-off year, and with magnitude
# greater than or equal to the corresponding completeness
# magnitude. m_c - mag_eq_tolerance is required to correct
# floating point differences.
id1 = np.logical_and(
catalogue['year'] >= ctime[ival], catalogue['magnitude'] >=
(m_c - mag_eq_tolerance))
# Get a- and b- value for the selected events
temp_rec_table = recurrence_table(catalogue['magnitude'][id1],
dmag, catalogue['year'][id1],
end_year - ctime[ival] + 1)
bval, sigma_b = aki_ml._aki_ml(temp_rec_table[:, 0],
temp_rec_table[:, 1], dmag, m_c)
if ival == 0:
gr_pars = np.array([np.hstack([bval, sigma_b])])
neq = np.sum(id1) # Number of events
else:
gr_pars = np.vstack([gr_pars, np.hstack([bval, sigma_b])])
neq = np.hstack([neq, np.sum(id1)])
ival = ival + np.sum(id0)
# Get average GR parameters
bval, sigma_b = self._average_parameters(gr_pars, neq,
config['Average Type'])
aval = self._calculate_a_value(bval, np.float(np.sum(neq)), cmag,
ctime, catalogue['magnitude'], end_year,
dmag)
sigma_a = self._calculate_a_value(bval + sigma_b,
np.float(np.sum(neq)), cmag, ctime,
catalogue['magnitude'], end_year,
dmag)
if not config['reference_magnitude']:
return bval,\
sigma_b,\
aval,\
sigma_a - aval
else:
rate = 10.**(aval - bval * config['reference_magnitude'])
sigma_rate = 10.**(sigma_a -
bval * config['reference_magnitude']) - rate
return bval,\
sigma_b,\
rate,\
sigma_rate
def calculate(self, catalogue, config, completeness=None):
"""
Main function to calculate the a- and b-value
"""
# Input checks
cmag, ctime, ref_mag, dmag, config = input_checks(catalogue,
config,
completeness)
ival = 0
tolerance = 1E-7
number_intervals = np.shape(ctime)[0]
b_est = np.zeros(number_intervals, dtype=float)
neq = np.zeros(number_intervals, dtype=float)
nyr = np.zeros(number_intervals, dtype=float)
for ival in range(0, number_intervals):
id0 = np.abs(ctime - ctime[ival]) < tolerance
m_c = np.min(cmag[id0])
if ival == 0:
id1 = np.logical_and(
catalogue.data['year'] >= (ctime[ival] - tolerance),
catalogue.data['magnitude'] >= (m_c - tolerance))
nyr[ival] = float(catalogue.end_year) - ctime[ival] + 1.
elif ival == number_intervals - 1:
id1 = np.logical_and(
catalogue.data['year'] < (ctime[ival - 1] - tolerance),
catalogue.data['magnitude'] >= (m_c - tolerance))
nyr[ival] = ctime[ival - 1] - ctime[ival]
else:
id1 = np.logical_and(
catalogue.data['year'] >= (ctime[ival] - tolerance),
catalogue.data['year'] < (ctime[ival - 1] - tolerance))
id1 = np.logical_and(
id1, catalogue.data['magnitude'] > (m_c - tolerance))
nyr[ival] = ctime[ival - 1] - ctime[ival]
neq[ival] = np.sum(id1)
# Get a- and b- value for the selected events
temp_rec_table = recurrence_table(catalogue.data['magnitude'][id1],
dmag,
catalogue.data['year'][id1])
aki_ml = AkiMaxLikelihood()
b_est[ival] = aki_ml._aki_ml(temp_rec_table[:, 0],
temp_rec_table[:, 1],
dmag, m_c)[0]
ival += 1
total_neq = np.float(np.sum(neq))
bval = self._harmonic_mean(b_est, neq)
sigma_b = bval / np.sqrt(total_neq)
aval = self._calculate_a_value(bval, total_neq, nyr, cmag, ref_mag)
sigma_a = self._calculate_a_value(bval + sigma_b, total_neq, nyr,
cmag, ref_mag)
if not config['reference_magnitude']:
aval = np.log10(aval)
sigma_a = np.log10(sigma_a) - aval
else:
sigma_a = sigma_a - aval
return bval, sigma_b, aval, sigma_a
class AkiMaximumLikelihoodTestCase(unittest.TestCase):
def setUp(self):
"""
This generates a minimum data-set to be used for the regression.
"""
# Test A: Generates a data set assuming b=1 and N(m=4.0)=10.0 events
self.dmag = 0.1
mext = np.arange(4.0, 7.01, 0.1)
self.mval = mext[0:-1] + self.dmag / 2.0
self.bval = 1.0
self.numobs = np.flipud(
np.diff(np.flipud(10.0**(-self.bval * mext + 8.0))))
# Test B: Generate a completely artificial catalogue using the
# Gutenberg-Richter distribution defined above
numobs = np.around(self.numobs)
size = int(np.sum(self.numobs))
magnitude = np.zeros(size)
lidx = 0
for mag, nobs in zip(self.mval, numobs):
uidx = int(lidx + nobs)
magnitude[lidx:uidx] = mag + 0.01
lidx = uidx
year = np.ones(size) * 1999
self.catalogue = Catalogue.make_from_dict({
'magnitude': magnitude,
'year': year
})
# Create the seismicity occurrence calculator
self.aki_ml = AkiMaxLikelihood()
def test_aki_maximum_likelihood_A(self):
"""
Tests that the computed b value corresponds to the same value
used to generate the test data set
"""
bval, sigma_b = self.aki_ml._aki_ml(self.mval, self.numobs)
self.assertAlmostEqual(self.bval, bval, 2)
def test_aki_maximum_likelihood_B(self):
"""
Tests that the computed b value corresponds to the same value
used to generate the test data set
"""
bval, sigma_b = self.aki_ml.calculate(self.catalogue)
self.assertAlmostEqual(self.bval, bval, 2)
class AkiMaximumLikelihoodTestCase(unittest.TestCase):
def setUp(self):
"""
This generates a minimum data-set to be used for the regression.
"""
# Test A: Generates a data set assuming b=1 and N(m=4.0)=10.0 events
self.dmag = 0.1
mext = np.arange(4.0, 7.01, 0.1)
self.mval = mext[0:-1] + self.dmag / 2.0
self.bval = 1.0
self.numobs = np.flipud(
np.diff(np.flipud(10.0 ** (-self.bval * mext + 8.0))))
# Test B: Generate a completely artificial catalogue using the
# Gutenberg-Richter distribution defined above
numobs = np.around(self.numobs)
size = int(np.sum(self.numobs))
magnitude = np.zeros(size)
lidx = 0
for mag, nobs in zip(self.mval, numobs):
uidx = int(lidx + nobs)
magnitude[lidx:uidx] = mag + 0.01
lidx = uidx
year = np.ones(size) * 1999
self.catalogue = Catalogue.make_from_dict(
{'magnitude': magnitude, 'year': year})
# Create the seismicity occurrence calculator
self.aki_ml = AkiMaxLikelihood()
def test_aki_maximum_likelihood_A(self):
"""
Tests that the computed b value corresponds to the same value
used to generate the test data set
"""
bval, sigma_b = self.aki_ml._aki_ml(self.mval, self.numobs)
self.assertAlmostEqual(self.bval, bval, 2)
def test_aki_maximum_likelihood_B(self):
"""
Tests that the computed b value corresponds to the same value
used to generate the test data set
"""
bval, sigma_b = self.aki_ml.calculate(self.catalogue)
self.assertAlmostEqual(self.bval, bval, 2)
def _b_ml(self, catalogue, config, cmag, ctime, ref_mag, dmag):
end_year = float(catalogue.end_year)
catalogue = catalogue.data
ival = 0
mag_eq_tolerance = 1E-5
aki_ml = AkiMaxLikelihood()
while ival < np.shape(ctime)[0]:
id0 = np.abs(ctime - ctime[ival]) < mag_eq_tolerance
m_c = np.min(cmag[id0])
print('--- ctime', ctime[ival], ' m_c', m_c)
# Find events later than cut-off year, and with magnitude
# greater than or equal to the corresponding completeness
# magnitude. m_c - mag_eq_tolerance is required to correct
# floating point differences.
id1 = np.logical_and(
catalogue['year'] >= ctime[ival],
catalogue['magnitude'] >= (m_c - mag_eq_tolerance))
# Get a- and b- value for the selected events
temp_rec_table = recurrence_table(catalogue['magnitude'][id1],
dmag,
catalogue['year'][id1],
end_year-ctime[ival]+1)
bval, sigma_b = aki_ml._aki_ml(temp_rec_table[:, 0],
temp_rec_table[:, 1], dmag, m_c)
if ival == 0:
gr_pars = np.array([np.hstack([bval, sigma_b])])
neq = np.sum(id1) # Number of events
else:
gr_pars = np.vstack([gr_pars, np.hstack([bval, sigma_b])])
neq = np.hstack([neq, np.sum(id1)])
ival = ival + np.sum(id0)
# Get average GR parameters
bval, sigma_b = self._average_parameters(
gr_pars, neq, config['Average Type'])
aval = self._calculate_a_value(bval,
np.float(np.sum(neq)),
cmag,
ctime,
catalogue['magnitude'],
end_year,
dmag)
sigma_a = self._calculate_a_value(bval + sigma_b,
np.float(np.sum(neq)),
cmag,
ctime,
catalogue['magnitude'],
end_year,
dmag)
if not config['reference_magnitude']:
return bval,\
sigma_b,\
aval,\
sigma_a - aval
else:
rate = 10. ** (aval - bval * config['reference_magnitude'])
sigma_rate = 10. ** (sigma_a -
bval * config['reference_magnitude']) - rate
return bval,\
sigma_b,\
rate,\
sigma_rate