Source code for openquake.hazardlib.gsim.frankel_1996

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2022 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.

"""
Module exports :class:`FrankelEtAl1996MblgAB1987NSHMP2008`,
:class:`FrankelEtAl1996MblgJ1996NSHMP2008`,
:class:`FrankelEtAl1996MwNSHMP2008`.
"""
import numpy as np
from scipy.interpolate import RectBivariateSpline

from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib.gsim.utils import (
    mblg_to_mw_atkinson_boore_87, mblg_to_mw_johnston_96, clip_mean)
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
from openquake.baselib.general import CallableDict


# magnitude values for lookup table from minimum magnitude 4.4 to maximum
# magnitude 8.2
MAGS = np.linspace(4.4, 8.2, 20)

# hypocentral distance values (log10) for lookup table
# from minimum distance 10 km to maximum distance 1000 km
DISTS = np.linspace(1., 3., 21)

# lookup table for PGA
PGA_TBL = np.array([
    [-0.71, -0.62, -0.53, -0.44, -0.36, -0.29, -0.21, -0.14, -0.07,  0.00,  0.06,  0.12,  0.19,  0.25,  0.31,  0.37,  0.43,  0.49,  0.54,  0.60],
    [-0.84, -0.75, -0.66, -0.57, -0.49, -0.41, -0.33, -0.26, -0.19, -0.12, -0.05,  0.01,  0.07,  0.14,  0.20,  0.26,  0.32,  0.38,  0.43,  0.49],
    [-0.98, -0.88, -0.79, -0.70, -0.62, -0.53, -0.46, -0.38, -0.31, -0.24, -0.17, -0.10, -0.04,  0.02,  0.08,  0.14,  0.20,  0.26,  0.32,  0.38],
    [-1.12, -1.02, -0.93, -0.84, -0.75, -0.66, -0.58, -0.51, -0.43, -0.36, -0.29, -0.22, -0.16, -0.10, -0.03,  0.03,  0.09,  0.15,  0.21,  0.27],
    [-1.27, -1.17, -1.07, -0.98, -0.89, -0.80, -0.72, -0.64, -0.56, -0.49, -0.42, -0.35, -0.28, -0.22, -0.15, -0.09, -0.03,  0.03,  0.09,  0.15],
    [-1.43, -1.32, -1.22, -1.13, -1.03, -0.94, -0.86, -0.78, -0.70, -0.62, -0.55, -0.48, -0.41, -0.34, -0.28, -0.22, -0.15, -0.09, -0.03,  0.03],
    [-1.59, -1.48, -1.38, -1.28, -1.19, -1.09, -1.01, -0.92, -0.84, -0.76, -0.69, -0.61, -0.54, -0.48, -0.41, -0.35, -0.28, -0.22, -0.16, -0.10],
    [-1.76, -1.65, -1.54, -1.44, -1.35, -1.25, -1.16, -1.07, -0.99, -0.91, -0.83, -0.76, -0.69, -0.62, -0.55, -0.48, -0.42, -0.35, -0.29, -0.23],
    [-1.93, -1.82, -1.72, -1.61, -1.51, -1.42, -1.33, -1.24, -1.15, -1.07, -0.99, -0.91, -0.83, -0.76, -0.69, -0.63, -0.56, -0.50, -0.43, -0.37],
    [-2.07, -1.95, -1.84, -1.74, -1.64, -1.54, -1.44, -1.35, -1.26, -1.18, -1.10, -1.02, -0.94, -0.86, -0.79, -0.72, -0.65, -0.59, -0.53, -0.46],
    [-2.17, -2.05, -1.94, -1.83, -1.73, -1.63, -1.53, -1.43, -1.34, -1.25, -1.17, -1.09, -1.01, -0.93, -0.86, -0.78, -0.71, -0.65, -0.58, -0.52],
    [-2.28, -2.16, -2.04, -1.93, -1.83, -1.72, -1.62, -1.53, -1.43, -1.34, -1.25, -1.17, -1.09, -1.01, -0.93, -0.86, -0.78, -0.71, -0.65, -0.58],
    [-2.44, -2.32, -2.20, -2.09, -1.98, -1.87, -1.77, -1.67, -1.58, -1.48, -1.39, -1.30, -1.22, -1.14, -1.06, -0.98, -0.91, -0.83, -0.77, -0.70],
    [-2.63, -2.50, -2.38, -2.26, -2.15, -2.04, -1.94, -1.84, -1.74, -1.64, -1.55, -1.46, -1.37, -1.29, -1.20, -1.12, -1.05, -0.97, -0.90, -0.83],
    [-2.83, -2.70, -2.57, -2.45, -2.34, -2.23, -2.12, -2.01, -1.91, -1.81, -1.72, -1.62, -1.53, -1.45, -1.36, -1.28, -1.20, -1.12, -1.05, -0.98],
    [-3.05, -2.92, -2.78, -2.66, -2.54, -2.42, -2.31, -2.20, -2.10, -2.00, -1.90, -1.80, -1.71, -1.62, -1.53, -1.45, -1.36, -1.28, -1.21, -1.13],
    [-3.29, -3.15, -3.01, -2.88, -2.75, -2.63, -2.52, -2.41, -2.30, -2.19, -2.09, -1.99, -1.90, -1.80, -1.71, -1.62, -1.54, -1.46, -1.38, -1.30],
    [-3.55, -3.40, -3.25, -3.11, -2.98, -2.86, -2.74, -2.62, -2.51, -2.40, -2.30, -2.19, -2.09, -2.00, -1.90, -1.81, -1.72, -1.64, -1.56, -1.48],
    [-3.84, -3.67, -3.52, -3.37, -3.23, -3.10, -2.97, -2.85, -2.73, -2.62, -2.51, -2.41, -2.30, -2.20, -2.10, -2.01, -1.92, -1.83, -1.74, -1.66],
    [-4.15, -3.97, -3.80, -3.65, -3.50, -3.36, -3.22, -3.09, -2.97, -2.85, -2.74, -2.63, -2.52, -2.42, -2.31, -2.22, -2.12, -2.03, -1.94, -1.85],
    [-4.48, -4.29, -4.11, -3.94, -3.78, -3.63, -3.49, -3.35, -3.22, -3.10, -2.98, -2.86, -2.75, -2.64, -2.53, -2.43, -2.33, -2.23, -2.14, -2.05]
])

# lookup table for SA 0.1
SA01_TBL = np.array([
    [-0.43, -0.32, -0.23, -0.14, -0.05,  0.03,  0.11,  0.19,  0.26,  0.33,  0.40,  0.47,  0.54,  0.60,  0.66,  0.72,  0.78,  0.84,  0.90,  0.96],
    [-0.55, -0.44, -0.35, -0.26, -0.17, -0.08,  0.00,  0.07,  0.15,  0.22,  0.29,  0.36,  0.43,  0.49,  0.55,  0.62,  0.68,  0.74,  0.80,  0.86],
    [-0.67, -0.57, -0.47, -0.38, -0.29, -0.20, -0.12, -0.04,  0.03,  0.11,  0.18,  0.25,  0.31,  0.38,  0.44,  0.51,  0.57,  0.63,  0.69,  0.75],
    [-0.80, -0.69, -0.60, -0.50, -0.41, -0.33, -0.24, -0.16, -0.09, -0.01,  0.06,  0.13,  0.20,  0.27,  0.33,  0.39,  0.46,  0.52,  0.58,  0.64],
    [-0.93, -0.83, -0.73, -0.63, -0.54, -0.45, -0.37, -0.29, -0.21, -0.13, -0.06,  0.01,  0.08,  0.15,  0.21,  0.28,  0.34,  0.40,  0.46,  0.52],
    [-1.07, -0.97, -0.86, -0.77, -0.68, -0.59, -0.50, -0.42, -0.34, -0.26, -0.18, -0.11, -0.04,  0.03,  0.09,  0.16,  0.22,  0.28,  0.35,  0.41],
    [-1.22, -1.11, -1.01, -0.91, -0.82, -0.73, -0.64, -0.55, -0.47, -0.39, -0.32, -0.24, -0.17, -0.10, -0.03,  0.03,  0.10,  0.16,  0.22,  0.28],
    [-1.37, -1.26, -1.16, -1.06, -0.97, -0.87, -0.78, -0.70, -0.61, -0.53, -0.45, -0.38, -0.30, -0.23, -0.16, -0.10, -0.03,  0.03,  0.10,  0.16],
    [-1.53, -1.42, -1.32, -1.22, -1.12, -1.03, -0.94, -0.85, -0.76, -0.68, -0.60, -0.52, -0.45, -0.37, -0.30, -0.23, -0.17, -0.10, -0.04,  0.02],
    [-1.65, -1.54, -1.43, -1.33, -1.24, -1.14, -1.05, -0.96, -0.87, -0.79, -0.70, -0.62, -0.54, -0.47, -0.40, -0.33, -0.26, -0.19, -0.13, -0.06],
    [-1.73, -1.62, -1.51, -1.41, -1.31, -1.22, -1.12, -1.03, -0.94, -0.86, -0.77, -0.69, -0.61, -0.53, -0.46, -0.39, -0.32, -0.25, -0.18, -0.12],
    [-1.83, -1.72, -1.61, -1.51, -1.41, -1.31, -1.21, -1.12, -1.03, -0.94, -0.85, -0.77, -0.69, -0.61, -0.53, -0.46, -0.39, -0.32, -0.25, -0.18],
    [-1.98, -1.87, -1.76, -1.66, -1.56, -1.46, -1.36, -1.27, -1.18, -1.09, -1.00, -0.91, -0.83, -0.75, -0.67, -0.59, -0.52, -0.44, -0.37, -0.31],
    [-2.17, -2.05, -1.95, -1.84, -1.74, -1.64, -1.54, -1.45, -1.35, -1.26, -1.17, -1.08, -0.99, -0.91, -0.83, -0.75, -0.67, -0.60, -0.53, -0.46],
    [-2.38, -2.26, -2.15, -2.05, -1.94, -1.84, -1.74, -1.64, -1.55, -1.45, -1.36, -1.27, -1.18, -1.10, -1.01, -0.93, -0.85, -0.78, -0.70, -0.63],
    [-2.61, -2.50, -2.39, -2.28, -2.17, -2.07, -1.97, -1.87, -1.77, -1.68, -1.58, -1.49, -1.40, -1.31, -1.22, -1.14, -1.06, -0.98, -0.91, -0.83],
    [-2.89, -2.77, -2.66, -2.55, -2.44, -2.33, -2.23, -2.13, -2.03, -1.93, -1.83, -1.74, -1.64, -1.55, -1.46, -1.38, -1.29, -1.21, -1.13, -1.06],
    [-3.20, -3.08, -2.96, -2.85, -2.73, -2.62, -2.51, -2.41, -2.31, -2.20, -2.10, -2.01, -1.91, -1.82, -1.72, -1.63, -1.55, -1.46, -1.38, -1.30],
    [-3.56, -3.43, -3.30, -3.18, -3.06, -2.94, -2.82, -2.71, -2.60, -2.49, -2.39, -2.29, -2.19, -2.09, -1.99, -1.90, -1.81, -1.72, -1.64, -1.56],
    [-3.96, -3.81, -3.67, -3.53, -3.39, -3.26, -3.14, -3.02, -2.90, -2.78, -2.67, -2.57, -2.46, -2.36, -2.26, -2.16, -2.07, -1.97, -1.88, -1.80],
    [-4.37, -4.20, -4.04, -3.88, -3.73, -3.59, -3.45, -3.32, -3.19, -3.07, -2.95, -2.83, -2.72, -2.61, -2.51, -2.40, -2.31, -2.21, -2.12, -2.03]
])

# lookup table for SA 0.2
SA02_TBL = np.array([
    [-0.71, -0.57, -0.46, -0.35, -0.25, -0.15, -0.06,  0.02,  0.10,  0.18,  0.25,  0.32,  0.39,  0.46,  0.53,  0.59,  0.65,  0.72,  0.78,  0.84],
    [-0.82, -0.69, -0.57, -0.46, -0.36, -0.26, -0.17, -0.09, -0.01,  0.07,  0.14,  0.22,  0.29,  0.35,  0.42,  0.48,  0.55,  0.61,  0.67,  0.73],
    [-0.93, -0.80, -0.68, -0.57, -0.47, -0.38, -0.29, -0.20, -0.12, -0.04,  0.03,  0.11,  0.18,  0.25,  0.31,  0.38,  0.44,  0.50,  0.56,  0.63],
    [-1.05, -0.92, -0.80, -0.69, -0.59, -0.49, -0.40, -0.32, -0.23, -0.15, -0.08,  0.00,  0.07,  0.14,  0.20,  0.27,  0.33,  0.40,  0.46,  0.52],
    [-1.17, -1.04, -0.92, -0.81, -0.71, -0.61, -0.52, -0.44, -0.35, -0.27, -0.19, -0.12, -0.05,  0.02,  0.09,  0.16,  0.22,  0.29,  0.35,  0.41],
    [-1.30, -1.17, -1.05, -0.94, -0.84, -0.74, -0.65, -0.56, -0.47, -0.39, -0.31, -0.24, -0.16, -0.09, -0.02,  0.04,  0.11,  0.17,  0.24,  0.30],
    [-1.43, -1.30, -1.18, -1.07, -0.97, -0.87, -0.77, -0.69, -0.60, -0.52, -0.44, -0.36, -0.28, -0.21, -0.14, -0.07, -0.01,  0.06,  0.12,  0.18],
    [-1.57, -1.44, -1.32, -1.21, -1.10, -1.00, -0.91, -0.82, -0.73, -0.65, -0.56, -0.49, -0.41, -0.34, -0.27, -0.20, -0.13, -0.06,  0.00,  0.06],
    [-1.72, -1.58, -1.46, -1.35, -1.25, -1.15, -1.05, -0.96, -0.87, -0.78, -0.70, -0.62, -0.54, -0.47, -0.39, -0.32, -0.25, -0.19, -0.12, -0.06],
    [-1.82, -1.68, -1.56, -1.45, -1.34, -1.24, -1.14, -1.05, -0.96, -0.87, -0.79, -0.70, -0.63, -0.55, -0.47, -0.40, -0.33, -0.26, -0.20, -0.13],
    [-1.88, -1.74, -1.62, -1.51, -1.40, -1.30, -1.20, -1.10, -1.01, -0.92, -0.84, -0.75, -0.67, -0.59, -0.52, -0.44, -0.37, -0.30, -0.24, -0.17],
    [-1.95, -1.82, -1.69, -1.58, -1.47, -1.37, -1.27, -1.17, -1.08, -0.99, -0.90, -0.81, -0.73, -0.65, -0.57, -0.50, -0.42, -0.35, -0.28, -0.22],
    [-2.08, -1.94, -1.82, -1.70, -1.59, -1.49, -1.39, -1.29, -1.20, -1.11, -1.02, -0.93, -0.84, -0.76, -0.68, -0.60, -0.53, -0.45, -0.38, -0.32],
    [-2.23, -2.09, -1.97, -1.85, -1.74, -1.64, -1.53, -1.44, -1.34, -1.25, -1.15, -1.06, -0.98, -0.89, -0.81, -0.73, -0.65, -0.58, -0.51, -0.44],
    [-2.40, -2.26, -2.13, -2.01, -1.90, -1.80, -1.70, -1.60, -1.50, -1.40, -1.31, -1.22, -1.13, -1.04, -0.96, -0.88, -0.80, -0.72, -0.65, -0.58],
    [-2.58, -2.44, -2.32, -2.20, -2.09, -1.98, -1.88, -1.78, -1.68, -1.58, -1.49, -1.39, -1.30, -1.22, -1.13, -1.04, -0.96, -0.88, -0.81, -0.73],
    [-2.80, -2.66, -2.53, -2.41, -2.30, -2.19, -2.09, -1.98, -1.88, -1.79, -1.69, -1.60, -1.50, -1.41, -1.32, -1.24, -1.15, -1.07, -0.99, -0.92],
    [-3.04, -2.90, -2.77, -2.65, -2.54, -2.43, -2.32, -2.22, -2.12, -2.02, -1.92, -1.83, -1.73, -1.64, -1.55, -1.46, -1.37, -1.29, -1.21, -1.13],
    [-3.33, -3.19, -3.06, -2.93, -2.82, -2.71, -2.60, -2.49, -2.39, -2.29, -2.19, -2.09, -1.99, -1.90, -1.80, -1.71, -1.62, -1.54, -1.45, -1.37],
    [-3.66, -3.52, -3.38, -3.26, -3.14, -3.02, -2.91, -2.80, -2.69, -2.59, -2.48, -2.38, -2.28, -2.18, -2.09, -1.99, -1.90, -1.81, -1.73, -1.64],
    [-4.05, -3.90, -3.76, -3.63, -3.50, -3.38, -3.26, -3.14, -3.03, -2.92, -2.81, -2.70, -2.59, -2.49, -2.39, -2.29, -2.19, -2.10, -2.01, -1.92]
])

# lookup table for SA 0.3
SA03_TBL = np.array([
    [-0.97, -0.81, -0.66, -0.53, -0.42, -0.31, -0.21, -0.12, -0.03,  0.05,  0.13,  0.20,  0.28,  0.35,  0.41,  0.48,  0.54,  0.61,  0.67,  0.73],
    [-1.08, -0.91, -0.77, -0.64, -0.53, -0.42, -0.32, -0.23, -0.14, -0.06,  0.02,  0.10,  0.17,  0.24,  0.31,  0.38,  0.44,  0.50,  0.57,  0.63],
    [-1.19, -1.02, -0.88, -0.75, -0.64, -0.53, -0.43, -0.34, -0.25, -0.17, -0.09, -0.01,  0.06,  0.13,  0.20,  0.27,  0.33,  0.40,  0.46,  0.52],
    [-1.30, -1.14, -0.99, -0.86, -0.75, -0.64, -0.54, -0.45, -0.36, -0.28, -0.20, -0.12, -0.05,  0.03,  0.09,  0.16,  0.23,  0.29,  0.36,  0.42],
    [-1.41, -1.25, -1.11, -0.98, -0.86, -0.76, -0.66, -0.57, -0.48, -0.39, -0.31, -0.23, -0.16, -0.09, -0.02,  0.05,  0.12,  0.18,  0.25,  0.31],
    [-1.53, -1.37, -1.23, -1.10, -0.98, -0.88, -0.78, -0.68, -0.59, -0.51, -0.43, -0.35, -0.27, -0.20, -0.13, -0.06,  0.01,  0.07,  0.14,  0.20],
    [-1.66, -1.50, -1.35, -1.23, -1.11, -1.00, -0.90, -0.81, -0.72, -0.63, -0.55, -0.47, -0.39, -0.31, -0.24, -0.17, -0.11, -0.04,  0.02,  0.09],
    [-1.79, -1.63, -1.48, -1.36, -1.24, -1.13, -1.03, -0.93, -0.84, -0.75, -0.67, -0.59, -0.51, -0.44, -0.36, -0.29, -0.22, -0.16, -0.09, -0.03],
    [-1.93, -1.77, -1.62, -1.49, -1.37, -1.26, -1.16, -1.07, -0.97, -0.88, -0.80, -0.72, -0.64, -0.56, -0.49, -0.41, -0.34, -0.28, -0.21, -0.15],
    [-2.02, -1.85, -1.71, -1.58, -1.46, -1.35, -1.25, -1.15, -1.06, -0.97, -0.88, -0.80, -0.71, -0.64, -0.56, -0.49, -0.42, -0.35, -0.28, -0.21],
    [-2.07, -1.91, -1.76, -1.63, -1.51, -1.40, -1.30, -1.20, -1.10, -1.01, -0.92, -0.84, -0.75, -0.67, -0.60, -0.52, -0.45, -0.38, -0.31, -0.24],
    [-2.13, -1.97, -1.82, -1.69, -1.57, -1.46, -1.35, -1.25, -1.16, -1.06, -0.97, -0.89, -0.80, -0.72, -0.64, -0.56, -0.49, -0.42, -0.35, -0.28],
    [-2.25, -2.08, -1.93, -1.80, -1.68, -1.57, -1.46, -1.36, -1.26, -1.17, -1.08, -0.99, -0.90, -0.82, -0.74, -0.66, -0.58, -0.51, -0.44, -0.37],
    [-2.38, -2.21, -2.06, -1.93, -1.81, -1.70, -1.59, -1.49, -1.39, -1.29, -1.20, -1.11, -1.02, -0.94, -0.85, -0.77, -0.70, -0.62, -0.55, -0.48],
    [-2.53, -2.36, -2.21, -2.08, -1.96, -1.84, -1.73, -1.63, -1.53, -1.43, -1.34, -1.25, -1.16, -1.07, -0.99, -0.90, -0.82, -0.75, -0.67, -0.60],
    [-2.69, -2.52, -2.37, -2.24, -2.12, -2.00, -1.89, -1.79, -1.69, -1.59, -1.50, -1.40, -1.31, -1.22, -1.13, -1.05, -0.97, -0.89, -0.81, -0.74],
    [-2.88, -2.71, -2.56, -2.42, -2.30, -2.18, -2.08, -1.97, -1.87, -1.77, -1.67, -1.58, -1.48, -1.39, -1.30, -1.22, -1.13, -1.05, -0.97, -0.90],
    [-3.09, -2.92, -2.77, -2.63, -2.51, -2.39, -2.28, -2.18, -2.07, -1.97, -1.87, -1.78, -1.68, -1.59, -1.50, -1.41, -1.32, -1.24, -1.16, -1.08],
    [-3.33, -3.16, -3.01, -2.87, -2.75, -2.63, -2.52, -2.41, -2.31, -2.20, -2.11, -2.01, -1.91, -1.82, -1.72, -1.63, -1.54, -1.46, -1.37, -1.29],
    [-3.61, -3.44, -3.29, -3.15, -3.02, -2.91, -2.79, -2.68, -2.58, -2.47, -2.37, -2.27, -2.17, -2.08, -1.98, -1.89, -1.80, -1.71, -1.62, -1.54],
    [-3.95, -3.77, -3.62, -3.48, -3.35, -3.22, -3.11, -3.00, -2.89, -2.78, -2.67, -2.57, -2.47, -2.37, -2.27, -2.17, -2.08, -1.99, -1.90, -1.81]
])

# lookup table for SA 0.5
SA05_TBL = np.array([
    [-1.44, -1.23, -1.03, -0.87, -0.72, -0.58, -0.46, -0.35, -0.25, -0.16, -0.07,  0.01,  0.09,  0.16,  0.23,  0.30,  0.37,  0.44,  0.50,  0.57],
    [-1.54, -1.33, -1.14, -0.97, -0.82, -0.69, -0.57, -0.46, -0.36, -0.27, -0.18, -0.10, -0.02,  0.06,  0.13,  0.20,  0.27,  0.34,  0.40,  0.46],
    [-1.64, -1.43, -1.24, -1.07, -0.92, -0.79, -0.67, -0.57, -0.47, -0.37, -0.29, -0.20, -0.12, -0.05,  0.03,  0.10,  0.16,  0.23,  0.30,  0.36],
    [-1.74, -1.53, -1.35, -1.18, -1.03, -0.90, -0.78, -0.67, -0.57, -0.48, -0.39, -0.31, -0.23, -0.15, -0.08, -0.01,  0.06,  0.13,  0.19,  0.26],
    [-1.85, -1.64, -1.46, -1.29, -1.14, -1.01, -0.89, -0.79, -0.69, -0.59, -0.50, -0.42, -0.34, -0.26, -0.19, -0.12, -0.05,  0.02,  0.09,  0.15],
    [-1.96, -1.75, -1.57, -1.40, -1.25, -1.12, -1.01, -0.90, -0.80, -0.70, -0.62, -0.53, -0.45, -0.37, -0.30, -0.23, -0.16, -0.09, -0.02,  0.04],
    [-2.08, -1.87, -1.68, -1.52, -1.37, -1.24, -1.12, -1.02, -0.91, -0.82, -0.73, -0.65, -0.56, -0.49, -0.41, -0.34, -0.27, -0.20, -0.13, -0.07],
    [-2.20, -1.99, -1.81, -1.64, -1.49, -1.36, -1.24, -1.14, -1.03, -0.94, -0.85, -0.76, -0.68, -0.60, -0.53, -0.45, -0.38, -0.31, -0.24, -0.18],
    [-2.33, -2.12, -1.93, -1.77, -1.62, -1.49, -1.37, -1.26, -1.16, -1.06, -0.97, -0.89, -0.80, -0.72, -0.64, -0.57, -0.50, -0.43, -0.36, -0.29],
    [-2.41, -2.20, -2.01, -1.84, -1.70, -1.56, -1.45, -1.34, -1.23, -1.14, -1.04, -0.96, -0.87, -0.79, -0.71, -0.64, -0.56, -0.49, -0.42, -0.36],
    [-2.45, -2.24, -2.05, -1.88, -1.73, -1.60, -1.48, -1.37, -1.27, -1.17, -1.08, -0.99, -0.90, -0.82, -0.74, -0.66, -0.59, -0.52, -0.45, -0.38],
    [-2.49, -2.28, -2.10, -1.93, -1.78, -1.65, -1.53, -1.42, -1.31, -1.21, -1.12, -1.03, -0.94, -0.86, -0.78, -0.70, -0.62, -0.55, -0.48, -0.41],
    [-2.59, -2.38, -2.19, -2.03, -1.88, -1.74, -1.62, -1.51, -1.41, -1.31, -1.21, -1.12, -1.03, -0.94, -0.86, -0.78, -0.70, -0.63, -0.56, -0.49],
    [-2.71, -2.50, -2.31, -2.14, -1.99, -1.86, -1.74, -1.62, -1.52, -1.42, -1.32, -1.23, -1.14, -1.05, -0.96, -0.88, -0.80, -0.73, -0.65, -0.58],
    [-2.84, -2.63, -2.44, -2.27, -2.12, -1.98, -1.86, -1.75, -1.64, -1.54, -1.44, -1.34, -1.25, -1.16, -1.08, -0.99, -0.91, -0.83, -0.76, -0.68],
    [-2.98, -2.77, -2.58, -2.41, -2.26, -2.12, -2.00, -1.88, -1.77, -1.67, -1.57, -1.48, -1.38, -1.29, -1.20, -1.12, -1.04, -0.96, -0.88, -0.80],
    [-3.14, -2.92, -2.73, -2.56, -2.41, -2.27, -2.15, -2.04, -1.93, -1.82, -1.72, -1.63, -1.53, -1.44, -1.35, -1.26, -1.18, -1.09, -1.01, -0.94],
    [-3.32, -3.10, -2.91, -2.74, -2.59, -2.45, -2.32, -2.21, -2.10, -1.99, -1.89, -1.79, -1.70, -1.60, -1.51, -1.42, -1.34, -1.25, -1.17, -1.09],
    [-3.52, -3.30, -3.11, -2.94, -2.78, -2.65, -2.52, -2.40, -2.29, -2.19, -2.08, -1.98, -1.89, -1.79, -1.70, -1.61, -1.52, -1.43, -1.35, -1.26],
    [-3.75, -3.53, -3.34, -3.17, -3.01, -2.87, -2.75, -2.63, -2.52, -2.41, -2.31, -2.20, -2.11, -2.01, -1.91, -1.82, -1.73, -1.64, -1.55, -1.47],
    [-4.02, -3.80, -3.60, -3.43, -3.27, -3.13, -3.01, -2.89, -2.77, -2.67, -2.56, -2.46, -2.36, -2.26, -2.16, -2.07, -1.97, -1.88, -1.79, -1.70],
])

# lookup table for SA 1.0
SA1_TBL = np.array([
    [-2.22, -1.98, -1.75, -1.52, -1.31, -1.12, -0.95, -0.80, -0.66, -0.54, -0.43, -0.33, -0.24, -0.15, -0.07,  0.01,  0.08,  0.16,  0.23,  0.29],
    [-2.32, -2.08, -1.85, -1.62, -1.41, -1.22, -1.05, -0.90, -0.77, -0.64, -0.54, -0.43, -0.34, -0.25, -0.17, -0.09, -0.02,  0.05,  0.12,  0.19],
    [-2.43, -2.18, -1.95, -1.72, -1.51, -1.32, -1.15, -1.00, -0.87, -0.75, -0.64, -0.54, -0.45, -0.36, -0.28, -0.20, -0.12, -0.05,  0.02,  0.09],
    [-2.53, -2.29, -2.05, -1.82, -1.61, -1.42, -1.25, -1.11, -0.97, -0.85, -0.74, -0.64, -0.55, -0.46, -0.38, -0.30, -0.23, -0.15, -0.08, -0.01],
    [-2.63, -2.39, -2.15, -1.92, -1.71, -1.53, -1.36, -1.21, -1.08, -0.96, -0.85, -0.75, -0.66, -0.57, -0.49, -0.41, -0.33, -0.26, -0.19, -0.12],
    [-2.74, -2.49, -2.25, -2.03, -1.82, -1.63, -1.46, -1.32, -1.18, -1.06, -0.96, -0.86, -0.76, -0.68, -0.59, -0.51, -0.44, -0.36, -0.29, -0.22],
    [-2.84, -2.60, -2.36, -2.13, -1.92, -1.74, -1.57, -1.42, -1.29, -1.17, -1.07, -0.97, -0.87, -0.78, -0.70, -0.62, -0.54, -0.47, -0.40, -0.33],
    [-2.95, -2.70, -2.47, -2.24, -2.03, -1.85, -1.68, -1.53, -1.40, -1.29, -1.18, -1.08, -0.98, -0.90, -0.81, -0.73, -0.65, -0.58, -0.51, -0.44],
    [-3.07, -2.82, -2.58, -2.35, -2.15, -1.96, -1.80, -1.65, -1.52, -1.40, -1.29, -1.19, -1.10, -1.01, -0.92, -0.84, -0.77, -0.69, -0.62, -0.55],
    [-3.14, -2.88, -2.64, -2.42, -2.21, -2.02, -1.86, -1.71, -1.58, -1.46, -1.36, -1.26, -1.16, -1.07, -0.99, -0.90, -0.83, -0.75, -0.68, -0.61],
    [-3.16, -2.91, -2.67, -2.44, -2.24, -2.05, -1.88, -1.74, -1.61, -1.49, -1.38, -1.28, -1.18, -1.09, -1.01, -0.92, -0.84, -0.77, -0.69, -0.62],
    [-3.20, -2.94, -2.70, -2.47, -2.27, -2.08, -1.91, -1.77, -1.63, -1.52, -1.41, -1.31, -1.21, -1.12, -1.03, -0.95, -0.87, -0.79, -0.71, -0.64],
    [-3.28, -3.03, -2.78, -2.55, -2.35, -2.16, -1.99, -1.84, -1.71, -1.59, -1.48, -1.38, -1.29, -1.19, -1.10, -1.02, -0.94, -0.86, -0.78, -0.71],
    [-3.38, -3.12, -2.88, -2.65, -2.44, -2.25, -2.09, -1.94, -1.81, -1.69, -1.58, -1.47, -1.37, -1.28, -1.19, -1.11, -1.02, -0.94, -0.87, -0.79],
    [-3.49, -3.23, -2.98, -2.75, -2.55, -2.36, -2.19, -2.04, -1.91, -1.79, -1.68, -1.57, -1.47, -1.38, -1.29, -1.20, -1.12, -1.03, -0.96, -0.88],
    [-3.61, -3.35, -3.10, -2.87, -2.66, -2.47, -2.30, -2.15, -2.02, -1.90, -1.79, -1.68, -1.58, -1.49, -1.39, -1.30, -1.22, -1.14, -1.05, -0.98],
    [-3.74, -3.48, -3.23, -3.00, -2.79, -2.60, -2.43, -2.28, -2.14, -2.02, -1.91, -1.80, -1.70, -1.60, -1.51, -1.42, -1.33, -1.25, -1.16, -1.09],
    [-3.88, -3.62, -3.37, -3.14, -2.93, -2.74, -2.57, -2.41, -2.28, -2.16, -2.04, -1.94, -1.83, -1.74, -1.64, -1.55, -1.46, -1.37, -1.29, -1.21],
    [-4.04, -3.78, -3.53, -3.30, -3.08, -2.89, -2.72, -2.57, -2.43, -2.31, -2.20, -2.09, -1.98, -1.88, -1.79, -1.69, -1.60, -1.51, -1.43, -1.35],
    [-4.22, -3.96, -3.71, -3.47, -3.26, -3.07, -2.90, -2.74, -2.61, -2.48, -2.37, -2.26, -2.15, -2.05, -1.96, -1.86, -1.77, -1.68, -1.59, -1.50],
    [-4.43, -4.16, -3.91, -3.68, -3.46, -3.27, -3.10, -2.94, -2.81, -2.68, -2.56, -2.45, -2.35, -2.25, -2.15, -2.05, -1.95, -1.86, -1.77, -1.69]
])

# lookup table for SA 2.0
SA2_TBL = np.array([
    [-2.87, -2.66, -2.45, -2.24, -2.03, -1.81, -1.60, -1.39, -1.20, -1.02, -0.87, -0.73, -0.61, -0.50, -0.40, -0.30, -0.21, -0.13, -0.05,  0.02],
    [-3.00, -2.78, -2.57, -2.36, -2.14, -1.92, -1.70, -1.49, -1.30, -1.12, -0.97, -0.83, -0.71, -0.60, -0.50, -0.40, -0.32, -0.23, -0.16, -0.08],
    [-3.14, -2.91, -2.69, -2.47, -2.24, -2.02, -1.80, -1.59, -1.40, -1.22, -1.07, -0.93, -0.81, -0.70, -0.60, -0.51, -0.42, -0.34, -0.26, -0.18],
    [-3.27, -3.04, -2.81, -2.58, -2.35, -2.12, -1.90, -1.69, -1.50, -1.32, -1.17, -1.04, -0.91, -0.80, -0.70, -0.61, -0.52, -0.44, -0.36, -0.28],
    [-3.40, -3.16, -2.92, -2.69, -2.45, -2.22, -2.00, -1.79, -1.60, -1.43, -1.27, -1.14, -1.02, -0.91, -0.81, -0.71, -0.62, -0.54, -0.46, -0.39],
    [-3.52, -3.28, -3.03, -2.79, -2.55, -2.32, -2.10, -1.89, -1.70, -1.53, -1.38, -1.24, -1.12, -1.01, -0.91, -0.82, -0.73, -0.65, -0.57, -0.49],
    [-3.64, -3.39, -3.14, -2.90, -2.66, -2.42, -2.20, -1.99, -1.80, -1.63, -1.48, -1.35, -1.22, -1.12, -1.02, -0.92, -0.83, -0.75, -0.67, -0.60],
    [-3.76, -3.50, -3.25, -3.00, -2.76, -2.52, -2.30, -2.09, -1.90, -1.73, -1.58, -1.45, -1.33, -1.22, -1.12, -1.03, -0.94, -0.86, -0.78, -0.70],
    [-3.87, -3.61, -3.36, -3.11, -2.86, -2.63, -2.40, -2.19, -2.01, -1.84, -1.69, -1.56, -1.44, -1.33, -1.23, -1.14, -1.05, -0.96, -0.89, -0.81],
    [-3.93, -3.67, -3.42, -3.16, -2.92, -2.68, -2.45, -2.25, -2.06, -1.89, -1.75, -1.61, -1.49, -1.39, -1.29, -1.19, -1.10, -1.02, -0.94, -0.86],
    [-3.95, -3.69, -3.43, -3.18, -2.93, -2.69, -2.47, -2.26, -2.07, -1.90, -1.76, -1.63, -1.51, -1.40, -1.30, -1.20, -1.12, -1.03, -0.95, -0.87],
    [-3.97, -3.71, -3.45, -3.20, -2.95, -2.71, -2.48, -2.27, -2.09, -1.92, -1.77, -1.64, -1.52, -1.42, -1.32, -1.22, -1.13, -1.05, -0.97, -0.89],
    [-4.05, -3.78, -3.52, -3.26, -3.01, -2.77, -2.55, -2.34, -2.15, -1.99, -1.84, -1.71, -1.59, -1.48, -1.38, -1.28, -1.19, -1.11, -1.03, -0.95],
    [-4.14, -3.87, -3.60, -3.34, -3.09, -2.85, -2.62, -2.42, -2.23, -2.06, -1.91, -1.78, -1.66, -1.56, -1.45, -1.36, -1.27, -1.18, -1.10, -1.02],
    [-4.23, -3.96, -3.69, -3.43, -3.18, -2.94, -2.71, -2.50, -2.31, -2.15, -2.00, -1.87, -1.75, -1.64, -1.54, -1.44, -1.35, -1.26, -1.18, -1.10],
    [-4.34, -4.06, -3.79, -3.53, -3.27, -3.03, -2.80, -2.59, -2.40, -2.24, -2.09, -1.96, -1.84, -1.73, -1.62, -1.53, -1.44, -1.35, -1.26, -1.18],
    [-4.45, -4.18, -3.90, -3.64, -3.38, -3.13, -2.90, -2.69, -2.51, -2.34, -2.19, -2.06, -1.94, -1.83, -1.72, -1.62, -1.53, -1.44, -1.35, -1.27],
    [-4.58, -4.30, -4.02, -3.75, -3.49, -3.25, -3.02, -2.81, -2.62, -2.45, -2.30, -2.17, -2.04, -1.93, -1.83, -1.73, -1.63, -1.54, -1.46, -1.37],
    [-4.71, -4.43, -4.15, -3.88, -3.62, -3.37, -3.14, -2.93, -2.74, -2.57, -2.42, -2.29, -2.17, -2.05, -1.95, -1.85, -1.75, -1.66, -1.57, -1.48],
    [-4.86, -4.58, -4.30, -4.03, -3.76, -3.51, -3.28, -3.07, -2.88, -2.71, -2.56, -2.42, -2.30, -2.19, -2.08, -1.98, -1.88, -1.79, -1.70, -1.61],
    [-5.03, -4.74, -4.46, -4.19, -3.92, -3.67, -3.44, -3.23, -3.03, -2.86, -2.71, -2.58, -2.45, -2.34, -2.23, -2.13, -2.03, -1.93, -1.84, -1.75]
])

# dictionary relating supported imts and associated tables
IMTS_TABLES = {
    PGA(): PGA_TBL,
    SA(0.1): SA01_TBL,
    SA(0.2): SA02_TBL,
    SA(0.3): SA03_TBL,
    SA(0.5): SA05_TBL,
    SA(1.0): SA1_TBL,
    SA(2.0): SA2_TBL}


def _compute_mean(kind, imt, mag, rhypo):
    """
    Compute mean value from lookup table.

    Lookup table defines log10(IMT) (in g) for combinations of Mw and
    log10(rhypo) values. ``mag`` is therefore converted from Mblg to Mw
    using Atkinson and Boore 1987 conversion equation. Mean value is
    finally converted from base 10 to base e.
    """
    mag = np.zeros_like(rhypo) + _convert_magnitude(kind, mag)

    # to avoid run time warning in case rhypo is zero set minimum distance
    # to 10, which is anyhow the minimum distance allowed by the tables
    rhypo[rhypo < 10] = 10
    rhypo = np.log10(rhypo)

    # create lookup table and interpolate it at magnitude/distance values
    table = RectBivariateSpline(MAGS, DISTS, IMTS_TABLES[imt].T)
    mean = table.ev(mag, rhypo)

    # convert mean from base 10 to base e
    return mean * np.log(10)


def _compute_stddevs(C, imt, num_sites, stddev_types):
    """
    Return total standard deviation (converted to base e)
    """
    stddevs = []
    for _ in stddev_types:
        stddevs.append(np.zeros(num_sites) + C['sigma'] * np.log(10))

    return stddevs


_convert_magnitude = CallableDict()


@_convert_magnitude.add("Mblg87")
def _convert_magnitude_87(kind, mag):
    """
    Convert magnitude from Mblg to Mw using Atkinson and Boore 1987
    equation
    """
    return mblg_to_mw_atkinson_boore_87(mag)


@_convert_magnitude.add("Mblg96")
def _convert_magnitude_96(kind, mag):
    """
    Convert magnitude from Mblg to Mw using Johnston 1996 equation
    """
    return mblg_to_mw_johnston_96(mag)


@_convert_magnitude.add("Mw")
def _convert_magnitude_Mw(kind, mag):
    """
    Return magnitude value unchanged
    """
    return mag


[docs]class FrankelEtAl1996MblgAB1987NSHMP2008(GMPE): """ Implements GMPE developed by Arthur Frankel et al. and documented in "National Seismic-Hazard Maps: Documentation June 1996" (USGS - Open File Report 96-532) available at: http://earthquake.usgs.gov/hazards/products/conterminous/1996/documentation/ofr96-532.pdf The GMPE is used by the National Seismic Hazard Mapping Project (NSHMP) for the 2008 central and eastern US hazard model. This class replicates the algorithm as implemented in ``subroutine getFEA`` in the ``hazgridXnga2.f`` Fortran code available at: http://earthquake.usgs.gov/hazards/products/conterminous/2008/software/ The GMPE is defined by a set of lookup tables (see Appendix A) defined from minimum magnitude Mw=4.4 to maximum magnitude Mw=8.2, and from (hypocentral) distance 10 km to 1000 km. Values outside these range are clipped. Lookup tables are defined for PGA, and SA at the following periods: 0.1, 0.2, 0.3, 0.5, 1.0, 2.0. The GMPE does not allow for interpolation on unsupported periods. The class assumes rupture magnitude to be in Mblg scale (given that MFDs for central and eastern US are given in this scale). However lookup tables are defined for Mw. Therefore Mblg is converted to Mw by using Atkinson and Boore 1987 conversion equation. Coefficients are given for the B/C site conditions. """ kind = "Mblg87" #: Supported tectonic region type is stable continental crust, #: given that the equations have been derived for central and eastern #: north America DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: Supported intensity measure types are spectral acceleration, #: and peak ground acceleration DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA} #: Supported intensity measure component is the geometric mean of #: two horizontal components #: attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation type is only total. DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL} #: No site parameters required REQUIRES_SITES_PARAMETERS = set() #: Required rupture parameter is only magnitude (Mblg). REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: Required distance measure is rhypo REQUIRES_DISTANCES = {'rhypo'} #: Shear-wave velocity for reference soil conditions in [m s-1] DEFINED_FOR_REFERENCE_VELOCITY = 760.
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.compute>` for spec of input and result values. :raises ValueError: if imt is instance of :class:`openquake.hazardlib.imt.SA` with unsupported period. """ for m, imt in enumerate(imts): if imt not in IMTS_TABLES: raise ValueError( 'IMT %s not supported in FrankelEtAl1996NSHMP. ' % imt.string + 'FrankelEtAl1996NSHMP does not allow ' 'interpolation for unsupported periods.') mean[m] = _compute_mean(self.kind, imt, ctx.mag, ctx.rhypo.copy()) mean[m] = clip_mean(imt, mean[m]) sig[m] = self.COEFFS[imt]['sigma'] * np.log(10)
# period dependent standard deviations (in base 10) COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT sigma pga 0.326 0.1 0.326 0.2 0.326 0.3 0.326 0.5 0.326 1.0 0.347 2.0 0.347 """)
[docs]class FrankelEtAl1996MblgJ1996NSHMP2008(FrankelEtAl1996MblgAB1987NSHMP2008): """ Extend :class:`FrankelEtAl1996MblgAB1987NSHMP2008` but uses Johnston 1996 equation for converting from Mblg to Mw. """ kind = "Mblg96"
[docs]class FrankelEtAl1996MwNSHMP2008(FrankelEtAl1996MblgAB1987NSHMP2008): """ Extend :class:`FrankelEtAl1996MblgAB1987NSHMP2008` but assumes magnitude to be in Mw scale and therefore no conversion is applied. """ kind = "Mw"