class TaperedGRMFD(BaseMFD):
"""
Tapered Gutenberg-Richter MFD is defined as a typical Truncated
Gutenberg-Richter MFD up to a ``corner_mag`` above which an exponential
taper is applied; see Kagan (2002a, Geophysical Journal International)
for details. This implementation is based on
the United States National Seismic Hazard Map Project code
(https://github.com/usgs/nshmp-haz).
:param min_mag:
The lowest possible magnitude for this MFD. The first bin in the
:meth:`result histogram <get_annual_occurrence_rates>` will be aligned
to make its left border match this value.
:param max_mag:
The highest possible magnitude. The same as for ``min_mag``: the last
bin in the histogram will correspond to the magnitude value equal to
``max_mag - bin_width / 2``.
:param corner_mag:
The magnitude above which the exponential tapering of the earthquake
frequency (rate) occurs. Rates below this magnitude are identical to
a Gutenberg-Richter with the same ``a`` and ``b`` values.
:param bin_width:
A positive float value -- the width of a single histogram bin.
Values for ``min_mag`` and ``max_mag`` don't have to be aligned with
respect to ``bin_width``. They get rounded accordingly anyway so that
both are divisible by ``bin_width`` just before converting a function
to a histogram. See :meth:`_get_min_mag_and_num_bins`.
"""
MODIFICATIONS = set(())
def __init__(self, min_mag: float, max_mag: float, corner_mag: float,
bin_width: float, a_val: float, b_val: float):
self.min_mag = min_mag
self.max_mag = max_mag
self.corner_mag = corner_mag
self.bin_width = bin_width
self.a_val = a_val
self.b_val = b_val
self.beta = 2. / 3. * self.b_val
# constants from Mfds.java
self.SMALL_MO_MAG: float = 4.
self.TAPERED_LARGE_MAG: float = 9.05
self.min_mo = mag_to_mo(self.SMALL_MO_MAG)
self.large_mo = mag_to_mo(self.TAPERED_LARGE_MAG)
self.corner_mo = mag_to_mo(corner_mag)
# This class uses a Double Truncated GR distribution, and the
# rates are modified per the tapering.
self._dt_gr = TruncatedGRMFD(self.min_mag, self.max_mag,
self.bin_width, self.a_val, self.b_val)
self._get_min_mag_and_num_bins = self._dt_gr._get_min_mag_and_num_bins
self.check_constraints()
def check_constraints(self):
"""
Checks the following constraints:
* Bin width is greater than 0.
* Minimum magnitude is positive.
* Maximum magnitude is greater than minimum magnitude
by at least one bin width (or equal to that value).
* Corner magnitude is greater than minimum magnitude
by at least one bin width (or equal to that value).
* ``b`` value is positive.
"""
if not self.bin_width > 0:
raise ValueError('bin width %g must be positive' % self.bin_width)
if not self.min_mag >= 0:
raise ValueError('minimum magnitude %g must be non-negative' %
self.min_mag)
if not self.max_mag >= self.min_mag + self.bin_width:
raise ValueError('maximum magnitude %g must be higher than '
'minimum magnitude %g by '
'bin width %g at least' %
(self.max_mag, self.min_mag, self.bin_width))
if not self.b_val > 0.:
raise ValueError('b-value %g must be non-negative' % self.b_val)
if not self.corner_mag >= self.min_mag + self.bin_width:
raise ValueError('corner magnitude %g must be higher than '
'minimum magnitude %g by '
'bin width %g at least' %
(self.corner_mag, self.min_mag, self.bin_width))
def _pareto(self, mo, corner_mo):
"""'pareto' function from nhsmp-haz
"""
return (self.min_mo / mo)**self.beta * math.exp(
(self.min_mo - mo) / corner_mo)
def _scale_mag_bin_rate(self, mag, rate):
"""
This function scales the TruncatedGRMFD rate for that bin using
a tapering scheme developed in the NSHM-HAZ function; see
Mfds.java in the nshmp-haz codebase.
"""
mag_mo_lo = mag_to_mo(mag - self.bin_width / 2.)
mag_mo_hi = mag_to_mo(mag + self.bin_width / 2.)
scale_num = (self._pareto(mag_mo_lo, self.corner_mo) -
self._pareto(mag_mo_hi, self.corner_mo))
scale_denom = (self._pareto(mag_mo_lo, self.large_mo) -
self._pareto(mag_mo_hi, self.large_mo))
scale = scale_num / scale_denom
return rate * scale
def _get_rate(self, mag):
"""
Calculate and return an annual occurrence rate for a specific bin.
:param mag:
Magnitude value corresponding to the center of the bin of interest.
:returns:
Float number, the annual occurrence rate
"""
gr_rate = self._dt_gr._get_rate(mag)
return self._scale_mag_bin_rate(mag, gr_rate)
def get_min_max_mag(self):
"""
Return the minimum and maximum magnitudes
"""
return self._dt_gr.get_min_max_mag()
def get_annual_occurrence_rates(self):
"""
Calculate and return the annual occurrence rates histogram.
The result histogram has only one bin if minimum and maximum magnitude
values appear equal after rounding.
:returns:
See :meth:
`openquake.hazardlib.mfd.base.BaseMFD.get_annual_occurrence_rates`.
"""
mag_rates = []
gr_rates = self._dt_gr.get_annual_occurrence_rates()
for mag, rate in gr_rates:
mag_rates.append((mag, self._scale_mag_bin_rate(mag, rate)))
return mag_rates
a_val = log10(4e4) # random number
N0 = 10**a_val
b_val = 1.2
beta = bval2beta(b_val)
bin_width = [0.1] #, 0.01]
fig = plt.figure(1, figsize=(12, 6))
# loop through bin width
for i, bw in enumerate(bin_width):
plt.subplot(1, 2, i + 1)
# get oq rates
gr = TruncatedGRMFD(min_mag, max_mag, bw, a_val, b_val)
oq_rates = gr.get_annual_occurrence_rates()
# get cum OQ ratescum_oq_rates = []
# get cummulative frisk rates (for OQ)
cum_inc_rates, frisk_mags = get_oq_incrementalMFD(beta, N0, min_mag,
max_mag, bw)
# get rates
inc_rates = []
for i in range(0, len(cum_inc_rates)):
if i < len(cum_inc_rates) - 1:
inc_rates.append(cum_inc_rates[i] - cum_inc_rates[i + 1])
else:
inc_rates.append(cum_inc_rates[i])
print 'IncrementalMFD'