Source code for shakelib.gmice.fm11

# third party imports
import numpy as np

# stdlib imports
from openquake.hazardlib.imt import PGA, PGV, SA
from shakelib.gmice.gmice import GMICE


[docs]class FM11(GMICE): """ Implements the ground motion intensity conversion equations (GMICE) of Faenza and Michelini (2010, 2011). References: Faenza and Michelini,(2010). Regression analysis of MCS intensity and ground motion parameters in Italy and its application in ShakeMap. GJI, 180, 1138-1152, doi: 10.1111/j.1365-246X.2009.04467.xself and Faenza and Michelini (2011). Regression analysis of MCS intensity and ground motion spectral accelerations (SAs) in Italy. GJI, 186, 1415-1430, doi: 10.1111/j.1365-246X.2011.05125.x """ # ----------------------------------------------------------------------- # MMI = C1 + C2 * log10 (Y) # # Limit the distance residuals to between 0 and 160 km. # Limit the magnitude residuals to between M3.0 and M6.9. # These are the default in the other gmice # Limit the distance residuals to between 10 and 300 km. # Limit the magnitude residuals to between M3.0 and M7.3. # # These are calcualted on the basis of the maximum horizontal component. # For psa 03, 10 and 30 the regression for the geometrical mean are # available but not implemented in this modeles since the one for PGA # and PGV are not available. # ----------------------------------------------------------------------- def __init__(self): super().__init__() self.min_max = (1.0, 10.0) self.name = "Faenza and Michelini (2010, 2011)" self.scale = "scale_fm11.ps" self._constants = { self._pga: {"C1": 1.68, "C2": 2.58, "SMMI": 0.18, "SPGM": 0.31}, self._pgv: {"C1": 5.11, "C2": 2.35, "SMMI": 0.14, "SPGM": 0.22}, self._sa03: {"C1": 1.24, "C2": 2.47, "SMMI": 0.30, "SPGM": 0.42}, self._sa10: {"C1": 3.12, "C2": 2.05, "SMMI": 0.21, "SPGM": 0.31}, self._sa30: {"C1": 4.31, "C2": 2.00, "SMMI": 0.14, "SPGM": 0.26}, } self.DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA]) self.DEFINED_FOR_SA_PERIODS = set([0.3, 1.0, 3.0])
[docs] def getMIfromGM(self, amps, imt, dists=None, mag=None): """ Function to compute macroseismic intensity from ground-motion intensity. Supported ground-motion IMTs are PGA, PGV and PSA at 0.3, 1.0, and 3.0 sec periods. Args: amps (ndarray): Ground motion amplitude; natural log units; g for PGA and PSA, cm/s for PGV. imt (OpenQuake IMT): Type the input amps (must be one of PGA, PGV, or SA). Supported SA periods are 0.3, 1.0, and 3.0 sec. `[link] <http://docs.openquake.org/oq-hazardlib/master/imt.html>` dists (ndarray): Not used mag (float): Not used Returns: ndarray of Modified Mercalli Intensity and ndarray of dMMI / dln(amp) (i.e., the slope of the relationship at the point in question). """ # noqa lfact = np.log10(np.e) c = self._getConsts(imt) # # Convert (for accelerations) from ln(g) to cm/s^2 # then take the log10 # if imt != self._pgv: units = 981.0 else: units = 1.0 # # Math: log10(981 * exp(amps)) = log10(981) + log10(exp(amps)) # = log10(981) + amps * log10(e) # For PGV, just convert ln(amp) to log10(amp) by multiplying # by log10(e) # lamps = np.log10(units) + amps * lfact mmi = c["C1"] + c["C2"] * lamps dmmi_damp = np.full_like(lamps, c["C2"] * lfact) mmi = np.clip(mmi, 1.0, 10.0) mmi[np.isnan(amps)] = np.nan return mmi, dmmi_damp
[docs] def getGMfromMI(self, mmi, imt, dists=None, mag=None): """ Function to tcompute ground-motion intensity from macroseismic intensity. Supported IMTs are PGA, PGV and PSA for 0.3, 1.0, and 3.0 sec periods. Args: mmi (ndarray): Macroseismic intensity. imt (OpenQuake IMT): IMT of the requested ground-motions intensities (must be one of PGA, PGV, or SA). `[link] <http://docs.openquake.org/oq-hazardlib/master/imt.html>` dists (ndarray): Not used mag (float): Not used Returns: Ndarray of ground motion intensity in natural log of g for PGA and PSA, and natural log cm/s for PGV; ndarray of dln(amp) / dMMI (i.e., the slope of the relationship at the point in question). """ # noqa lfact = np.log10(np.e) c = self._getConsts(imt) mmi = mmi.copy() # Set nan values to 1 ix_nan = np.isnan(mmi) mmi[ix_nan] = 1.0 pgm = np.zeros_like(mmi) dpgm_dmmi = np.zeros_like(mmi) dummy_variable = np.ones(len(mmi)) # # MMI to PGM # pgm = np.power(10, (mmi - c["C1"]) / c["C2"]) dpgm_dmmi = 1.0 / (c["C2"] * lfact) * dummy_variable if imt != self._pgv: units = 981.0 else: units = 1.0 # Return a ln(amp) value. Convert PGA to from cm/s^2 to g pgm /= units pgm = np.log(pgm) # Set nan values back from 1 to nan pgm[ix_nan] = np.nan dpgm_dmmi[ix_nan] = np.nan return pgm, dpgm_dmmi
[docs] def getGM2MIsd(self): """ Return a dictionary of standard deviations for the ground-motion to MMI conversion. The keys are the ground motion types. Returns: Dictionary of GM to MI sigmas (in MMI units). """ return { self._pga: self._constants[self._pga]["SMMI"], self._pgv: self._constants[self._pgv]["SMMI"], self._sa03: self._constants[self._sa03]["SMMI"], self._sa10: self._constants[self._sa10]["SMMI"], self._sa30: self._constants[self._sa30]["SMMI"], }
[docs] def getMI2GMsd(self): """ Return a dictionary of standard deviations for the MMI to ground-motion conversion. The keys are the ground motion types. Returns: Dictionary of MI to GM sigmas (ln(PGM) units). """ # # Need to convert log10 to ln units # lfact = np.log(10.0) return { self._pga: lfact * self._constants[self._pga]["SPGM"], self._pgv: lfact * self._constants[self._pgv]["SPGM"], self._sa03: lfact * self._constants[self._sa03]["SPGM"], self._sa10: lfact * self._constants[self._sa10]["SPGM"], self._sa30: lfact * self._constants[self._sa30]["SPGM"], }
def _getConsts(self, imt): """ Helper function to get the constants. """ if ( imt != self._pga and imt != self._pgv and imt != self._sa03 and imt != self._sa10 and imt != self._sa30 ): raise ValueError("Invalid IMT " + str(imt)) c = self._constants[imt] return c