Source code for openquake.hazardlib.gsim.nath_2012

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"""
Module
:mod:`openquake.hazardlib.gsim.nath_2012`
exports
:class:`NathEtAl2012Lower`
:class:`NathEtAl2012Upper`
"""

from __future__ import division
import numpy as np

from openquake.hazardlib import const
from openquake.hazardlib.imt import SA, PGA, PGV
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable


[docs]class NathEtAl2012Lower(GMPE): # pylint: disable=too-few-public-methods, no-init """ Implements GMPE of Nath et. al (2012) for intraplate margin seismicity in the Shillong Plateau of India at 25-45 km deph. This model is based on stochastic simulation with a mean stress drop of 150 bars. Verification of mean value data was done by digitizing Figure 11 using http://arohatgi.info/WebPlotDigitizer/app/. Note that this independent verification did not include magnitude dependence or standard deviations. **Reference** Page number citations in this documentation refer to: Nath, S. K., Thingbaijam, K. K. S., Maiti, S. K., and Nayak, A. (2012). Ground-motion predictions in Shillong region, northeast India. *Journal of Seismology*, 16(3):475–488. """ #: "studies on micro-earthquakes indicated that reverse faulting is #: predominant in the region" (p. 476) DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE #: Set of :mod:`intensity measure types <openquake.hazardlib.imt>` #: this GSIM can calculate. A set should contain classes from #: module :mod:`openquake.hazardlib.imt`. DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([SA, PGA, PGV]) #: In simulations only the vertical component is estimated (see p. 479) #: and the stochastic dataset is what the GMPE is based on, so this model #: effectively predicts vertical motions. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.VERTICAL #: The only sigma is reported in the main coefficient table, Table 5 on #: p. 483, and must be the total standard deviation. DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL]) #: Required site parameter Vs30 is used to determing the NEHRP #: site class, and thus to choose site amplification coefficients #: and site amplification stanard error from Table 5 on p. 208. REQUIRES_SITES_PARAMETERS = set() #: Sole required rupture parameter is magnitude, since faulting #: style is not addressed. REQUIRES_RUPTURE_PARAMETERS = set(('mag',)) #: It is noted that "r_rup is the fault-rupture distance in kilometers" #: following equation (11) on p. 484. REQUIRES_DISTANCES = set(('rrup',))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types): # pylint: disable=too-many-arguments """ See :meth:`superclass method <.base.GroundShakingIntensityModel.get_mean_and_stddevs>` for specification of input and result values. Implements equation (11) on p. 484: ``ln(P) = c1 + c2*M + c3*(10 - M)^3 + c4*ln(R + c5*exp(c6*M)`` """ # obtain coefficients for required intensity measure type (IMT) coeffs = self.COEFFS_BEDROCK[imt].copy() # obtain IMT-independent coefficients coeffs.update(self.CONSTS) # compute bedrock motion, equation (11) ln_mean = self._compute_mean(rup, dists, coeffs) # obtain standard deviation ln_stddev = self._get_stddevs(coeffs, stddev_types) return ln_mean, [ln_stddev]
def _compute_mean(self, rup, dists, coeffs): """ Evaluate equation (11) on p. 484. """ ln_p = coeffs['c1'] + coeffs['c2']*rup.mag + \ coeffs['c3']*(self.CONSTS['ref_mag'] - rup.mag)**3 +\ coeffs['c4']*np.log(dists.rrup + coeffs['c5']*np.exp(coeffs['c6']*rup.mag)) return ln_p def _get_stddevs(self, coeffs, stddev_types): """ Look up values from Table 5 on p. 483 and convert to natural logarithm. Interpretation of "sigma_log(Y)" as the common logarithm is based on the order of magnitude of the values and consistent use of "log" and "ln" to denote common and natural logarithm elsewhere in the paper. """ for stddev_type in stddev_types: assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES log_stddev = coeffs['sigma'] ln_stddev = log_stddev*np.log(10) return ln_stddev #: Coefficients taken from Table 5, p. 483. COEFFS_BEDROCK = CoeffsTable(sa_damping=5., table="""\ IMT c1 c2 c3 c4 c5 c6 sigma pga 9.1430 0.2470 -0.0140 -2.6700 32.9458 0.0663 0.3300 pgv -8.1069 1.2225 -0.0072 -1.1962 0.0004 1.4474 0.3807 0.1 4.8183 0.3531 -0.0152 -1.7445 5.0087 0.2973 0.3441 0.2 4.0396 0.3376 -0.0148 -1.6820 3.9925 0.2764 0.3117 0.5 2.6536 0.5799 -0.0162 -1.8479 1.9570 0.3919 0.3384 1 2.9150 0.1758 -0.0235 -1.3546 7.1026 0.1700 0.3762 2 -0.8191 0.4950 -0.0247 -1.1763 1.4407 0.3910 0.4536 4 -6.9619 0.9977 -0.0270 -0.8393 0.0000 1.9613 0.4614 """) CONSTS = { 'ref_mag': 10., }
[docs]class NathEtAl2012Upper(NathEtAl2012Lower): # pylint: disable=too-few-public-methods, no-init """ Implements GMPE of Nath et. al (2012) for intraplate margin seismicity in the Shillong Plateau of India above 25 km deph. This model is based on stochastic simulation with a mean stress drop of 40 bars. """
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types): # pylint: disable=too-many-arguments """ See :meth:`superclass method <.base.GroundShakingIntensityModel.get_mean_and_stddevs>` for specification of input and result values. Implements the correction factor for the upper crust, equation (12) on p. 484: ``P' = P x Correction_factor`` """ parent = super(NathEtAl2012Upper, self) ln_mean, [ln_stddev] = parent.get_mean_and_stddevs( sites, rup, dists, imt, stddev_types) # compute site corrections, equation (9) coeffs = self.COEFFS_UPPER[imt] ln_mean += np.log(coeffs['correction']) return ln_mean, [ln_stddev]
#: Coefficients taken from Table 6, p. 485. COEFFS_UPPER = CoeffsTable(sa_damping=5., table="""\ IMT correction pga 0.6169 pgv 0.8781 0.1 0.6249 0.2 0.6584 0.5 0.8355 1 0.8704 2 0.9109 4 0.9292 """)