# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
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#
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"""
Module exports :class:`Bradley2013`, :class:`Bradley2013Volc`.
"""
import numpy as np

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


class Bradley2013(GMPE):
    """
    Implements GMPE developed by Brendan Bradley for Active Shallow Crust
    Earthquakes for New Zealand, and published as "A New Zealand-Specific
    Pseudospectral Acceleration Ground-Motion Prediction Equation for Active
    Shallow Crustal Earthquakes Based on Foreign Models" (2013, Bulletin of
    the Seismological Society of America, Volume 103, No. 3, pages 1801-1822).

    This model is modified from Chiou and Youngs, 2008 and has been adapted
    for New Zealand conditions. Specifically, the modifications are related to:
    1) small magnitude scaling;
    2) scaling of short period ground motion from normal faulting events in
    volcanic crust;
    3) scaling of ground motions on very hard rock sites;
    4) anelastic attenuation in the New Zealand crust;
    5) consideration of the increates anelastic attenuation in the Taupo
    Volcanic Zone (not implemented in this model, use Bradley2013Volc)
    """
    #: Supported tectonic region type is active shallow crust, see page 1801
    DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST

    #: Supported intensity measure types are spectral acceleration,
    #: peak ground velocity and peak ground acceleration. Note that PGV is
    #: the Chiou & Youngs PGV and has not been modified for New Zealand.
    DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
        PGA,
        SA
    ])

    #: Supported intensity measure component is geometric mean
    #: of two horizontal components
    #: attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
    #: see abstract page 1801.
    DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL

    #: Supported standard deviation types are inter-event, intra-event
    #: and total, see chapter "Variance model".
    DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
        const.StdDev.TOTAL,
        const.StdDev.INTER_EVENT,
        const.StdDev.INTRA_EVENT
    ])

    #: Required site parameters are Vs30 (eq. 13b), Vs30 measured flag (eq. 20)
    #: and Z1.0 (eq. 13b).
    REQUIRES_SITES_PARAMETERS = {'vs30', 'vs30measured', 'z1pt0'}

    #: Required rupture parameters are magnitude, rake (eq. 13a and 13b),
    #: dip (eq. 13a) and ztor (eq. 13a).
    REQUIRES_RUPTURE_PARAMETERS = {'dip', 'rake', 'mag', 'ztor'}

    #: Required distance measures are RRup, Rjb and Rx (all are in eq. 13a).
    REQUIRES_DISTANCES = {'rrup', 'rjb', 'rx'}

    def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
        """
        See :meth:`superclass method
        <.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
        for spec of input and result values.
        """
        # extracting dictionary of coefficients specific to required
        # intensity measure type.
        C = self.COEFFS[imt]
        # intensity on a reference soil is used for both mean
        # and stddev calculations.
        ln_y_ref = self._get_ln_y_ref(rup, dists, C)
        # exp1 and exp2 are parts of eq. 7
        exp1 = np.exp(C['phi3'] * (sites.vs30.clip(-np.inf, 1130) - 360))
        exp2 = np.exp(C['phi3'] * (1130 - 360))
        # v1 is the period dependent site term. The Vs30 above which, the
        # amplification is constant
        v1 = self._get_v1(imt)

        mean = self._get_mean(sites, C, ln_y_ref, exp1, exp2, v1)
        stddevs = self._get_stddevs(sites, rup, C, stddev_types,
                                    ln_y_ref, exp1, exp2)
        return mean, stddevs

    def _get_mean(self, sites, C, ln_y_ref, exp1, exp2, v1):
        """
        Add site effects to an intensity.

        Implements eq. 5
        """
        # we do not support estimating of basin depth and instead
        # rely on it being available (since we require it).
        z1pt0 = sites.z1pt0

        # we consider random variables being zero since we want
        # to find the exact mean value.
        eta = epsilon = 0

        ln_y = (
            # first line of eq. 13b
            ln_y_ref + C['phi1'] *
            np.log(np.clip(sites.vs30, -np.inf, v1) / 1130)
            # second line
            + C['phi2'] * (exp1 - exp2)
            * np.log((np.exp(ln_y_ref) + C['phi4']) / C['phi4'])
            # third line
            + C['phi5']
            * (1.0 - 1.0 / np.cosh(
                C['phi6'] * (z1pt0 - C['phi7']).clip(0, np.inf)))
            + C['phi8'] / np.cosh(0.15 * (z1pt0 - 15).clip(0, np.inf))
            # fourth line
            + eta + epsilon
        )

        return ln_y

    def _get_stddevs(self, sites, rup, C, stddev_types, ln_y_ref, exp1, exp2):
        """
        Get standard deviation for a given intensity on reference soil.

        Implements equations 19, 20 and 21 of Chiou & Youngs, 2008 for
        inter-event, intra-event and total standard deviations respectively.
        This has not been modified for NZ conditions.
        """
        # aftershock flag is zero, we consider only main shock.
        AS = 0
        Fmeasured = sites.vs30measured
        Finferred = 1 - sites.vs30measured

        # eq. 19 to calculate inter-event standard error
        mag_test = min(max(rup.mag, 5.0), 7.0) - 5.0
        tau = C['tau1'] + (C['tau2'] - C['tau1']) / 2 * mag_test

        # b and c coeffs from eq. 10
        b = C['phi2'] * (exp1 - exp2)
        c = C['phi4']

        y_ref = np.exp(ln_y_ref)
        # eq. 20
        NL = b * y_ref / (y_ref + c)
        sigma = (
            # first line of eq. 20
            (C['sig1']
             + 0.5 * (C['sig2'] - C['sig1']) * mag_test
             + C['sig4'] * AS)
            # second line
            * np.sqrt((C['sig3'] * Finferred + 0.7 * Fmeasured)
                      + (1 + NL) ** 2)
        )

        ret = []
        for stddev_type in stddev_types:
            assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
            if stddev_type == const.StdDev.TOTAL:
                # eq. 21
                ret += [np.sqrt(((1 + NL) ** 2) * (tau ** 2) + (sigma ** 2))]
            elif stddev_type == const.StdDev.INTRA_EVENT:
                ret.append(sigma)
            elif stddev_type == const.StdDev.INTER_EVENT:
                # this is implied in eq. 21
                ret.append(np.abs((1 + NL) * tau))

        return ret

    def _get_ln_y_ref(self, rup, dists, C):
        """
        Get an intensity on a reference soil.

        Implements eq. 4 in Bradley 2013. This is the same as Chiou and
        Youngs 2008, with addition of TVZ attentuation term, and addition of
        c8 which constains the ZTOR. Note that the TVZ scaling is set to 1
        (i.e. no TVZ attenuation)
        """
        # Taupo Volcanic Zone Path Distance. Set to zero.
        rtvz = self._get_tvz_path_distance(dists.rrup)

        # reverse faulting flag
        Frv = 1 if 30 <= rup.rake <= 150 else 0
        # normal faulting flag
        Fnm = 1 if -120 <= rup.rake <= -60 else 0
        # hanging wall flag
        Fhw = (dists.rx >= 0)
        # aftershock flag. always zero since we only consider main shock
        AS = 0

        ln_y_ref = (
            # first line of eq. 4 in Bradley 2013
            C['c1']
            + (C['c1a'] * Frv
               + C['c1b'] * Fnm
               + C['c7'] * (np.clip(rup.ztor, -np.inf, C['c8']) - 4))
            * (1 - AS)
            + (C['c10'] + C['c7a'] * (rup.ztor - 4)) * AS
            # second line
            + C['c2'] * (rup.mag - 6)
            + ((C['c2'] - C['c3']) / C['cn'])
            * np.log(1 + np.exp(C['cn'] * (C['cm'] - rup.mag)))
            # third line
            + C['c4']
            * np.log(dists.rrup
                     + C['c5']
                     * np.cosh(C['c6'] * max(rup.mag - C['chm'], 0)))
            # fourth line
            + (C['c4a'] - C['c4'])
            * np.log(np.sqrt(dists.rrup ** 2 + C['crb'] ** 2))
            # fifth line
            + (C['cg1'] + C['cg2'] / (np.cosh(max(rup.mag - C['cg3'], 0))))
            # sixth line
            * ((1 + C['ctvz'] * (rtvz / dists.rrup)) * dists.rrup)
            # seventh line
            + C['c9'] * Fhw
            * np.tanh(dists.rx
                      * (np.cos(np.radians(rup.dip)) ** 2)
                      / C['c9a'])
            * (1 - np.sqrt(dists.rjb ** 2 + rup.ztor ** 2)
               / (dists.rrup + 0.001))
        )

        return ln_y_ref

    def _get_v1(self, imt):
        """
        Calculates Bradley's V1 term. Equation 2 (page 1814) and 6 (page 1816)
        based on SA period
        """

        if imt == PGA():
            v1 = 1800.

        else:
            T = imt.period
            v1a = np.clip((1130 * (T / 0.75)**-0.11), 1130, np.inf)
            v1 = np.clip(v1a, -np.inf, 1800.)

        return v1

    def _get_tvz_path_distance(self, rrup):
        """
        Returns Taupo Volcanic Zone (TVZ) path distance.
        Set to zero.
        """

        return 0

    #: Coefficient tables are constructed from values in tables 1, 2 and 3
    #: (pages 197, 198 and 199) in Chiou & Youngs,2008. Only Coefficients c1,
    #: c1b, c3, cm, c8, cg1, cg2, ctvz are modified by Bradley 2013.
    #: Spectral acceleration is defined for damping of 5%, see page 208 (CY08).
    COEFFS = CoeffsTable(sa_damping=5, table="""\
    IMT    c2   c3       c4   c4a crb  chm cg3  c1      c1a     c1b    cn    cm      c5     c6     c7     c7a    c8    c9     c9a     c10     cg1      cg2     ctvz    phi1    phi2    phi3     phi4     phi5   phi6     phi7   phi8   tau1   tau2   sig1   sig2   sig3   sig4
    pga    1.06 1.50000 -2.1 -0.5 50.0 3.0 4.0 -1.1985  0.1000 -0.4550 2.996 5.85000 6.1600 0.4893 0.0512 0.0860 10.00 0.7900 1.5005 -0.3218 -0.00960 -0.00480 2.000 -0.4417 -0.1417 -0.007010 0.102151 0.2289 0.014996 580.0  0.0700 0.3437 0.2637 0.4458 0.3459 0.8000 0.0663
    0.010  1.06 1.50299 -2.1 -0.5 50.0 3.0 4.0 -1.1958  0.1000 -0.4550 2.996 5.81711 6.1600 0.4893 0.0512 0.0860 10.00 0.7900 1.5005 -0.3218 -0.00960 -0.00481 2.000 -0.4417 -0.1417 -0.007010 0.102151 0.2289 0.014996 580.0  0.0700 0.3437 0.2637 0.4458 0.3459 0.8000 0.0663
    0.020  1.06 1.50845 -2.1 -0.5 50.0 3.0 4.0 -1.1756  0.1000 -0.4550 3.292 5.80023 6.1580 0.4892 0.0512 0.0860 10.00 0.8129 1.5028 -0.3323 -0.00970 -0.00486 2.000 -0.4340 -0.1364 -0.007279 0.108360 0.2289 0.014996 580.0  0.0699 0.3471 0.2671 0.4458 0.3459 0.8000 0.0663
    0.030  1.06 1.51549 -2.1 -0.5 50.0 3.0 4.0 -1.0909  0.1000 -0.4550 3.514 5.78659 6.1550 0.4890 0.0511 0.0860 10.00 0.8439 1.5071 -0.3394 -0.01010 -0.00503 2.000 -0.4177 -0.1403 -0.007354 0.119888 0.2289 0.014996 580.0  0.0701 0.3603 0.2803 0.4535 0.3537 0.8000 0.0663
    0.040  1.06 1.52380 -2.1 -0.5 50.0 3.0 4.0 -0.9793  0.1000 -0.4550 3.563 5.77472 6.1508 0.4888 0.0508 0.0860 10.00 0.8740 1.5138 -0.3453 -0.01050 -0.00526 2.000 -0.4000 -0.1591 -0.006977 0.133641 0.2289 0.014996 579.9  0.0702 0.3718 0.2918 0.4589 0.3592 0.8000 0.0663
    0.050  1.06 1.53319 -2.1 -0.5 50.0 3.0 4.0 -0.8549  0.1000 -0.4550 3.547 5.76402 6.1441 0.4884 0.0504 0.0860 10.00 0.8996 1.5230 -0.3502 -0.01090 -0.00549 2.000 -0.3903 -0.1862 -0.006467 0.148927 0.2290 0.014996 579.9  0.0701 0.3848 0.3048 0.4630 0.3635 0.8000 0.0663
    0.075  1.06 1.56053 -2.1 -0.5 50.0 3.0 4.0 -0.6008  0.1000 -0.4540 3.448 5.74056 6.1200 0.4872 0.0495 0.0860 10.00 0.9442 1.5597 -0.3579 -0.01170 -0.00588 2.000 -0.4040 -0.2538 -0.005734 0.190596 0.2292 0.014996 579.6  0.0686 0.3878 0.3129 0.4702 0.3713 0.8000 0.0663
    0.10   1.06 1.59241 -2.1 -0.5 50.0 3.0 4.0 -0.4700  0.1000 -0.4530 3.312 5.72017 6.0850 0.4854 0.0489 0.0860 10.00 0.9677 1.6104 -0.3604 -0.01170 -0.00591 2.000 -0.4423 -0.2943 -0.005604 0.230662 0.2297 0.014996 579.2  0.0646 0.3835 0.3152 0.4747 0.3769 0.8000 0.0663
    0.15   1.06 1.66640 -2.1 -0.5 50.0 3.0 4.0 -0.4139  0.1000 -0.4500 3.044 5.68493 5.9871 0.4808 0.0479 0.0860 10.00 0.9660 1.7549 -0.3565 -0.01110 -0.00540 2.000 -0.5162 -0.3113 -0.005845 0.266468 0.2326 0.014988 577.2  0.0494 0.3719 0.3128 0.4798 0.3847 0.8000 0.0612
    0.20   1.06 1.75021 -2.1 -0.5 50.0 3.0 4.0 -0.5237  0.1000 -0.4149 2.831 5.65435 5.8699 0.4755 0.0471 0.0860 10.00 0.9334 1.9157 -0.3470 -0.01000 -0.00479 2.000 -0.5697 -0.2927 -0.006141 0.255253 0.2386 0.014964 573.9 -0.0019 0.3601 0.3076 0.4816 0.3902 0.8000 0.0530
    0.25   1.06 1.84052 -2.1 -0.5 50.0 3.0 4.0 -0.6678  0.1000 -0.3582 2.658 5.62686 5.7547 0.4706 0.0464 0.0860 10.50 0.8946 2.0709 -0.3379 -0.00910 -0.00427 2.000 -0.6109 -0.2662 -0.006439 0.231541 0.2497 0.014881 568.5 -0.0479 0.3522 0.3047 0.4815 0.3946 0.7999 0.0457
    0.30   1.06 1.93480 -2.1 -0.5 50.0 3.0 4.0 -0.8277  0.0999 -0.3113 2.505 5.60162 5.6527 0.4665 0.0458 0.0860 11.00 0.8590 2.2005 -0.3314 -0.00820 -0.00384 2.500 -0.6444 -0.2405 -0.006704 0.207277 0.2674 0.014639 560.5 -0.0756 0.3438 0.3005 0.4801 0.3981 0.7997 0.0398
    0.40   1.06 2.12764 -2.1 -0.5 50.0 3.0 4.0 -1.1284  0.0997 -0.2646 2.261 5.55602 5.4997 0.4607 0.0445 0.0850 12.00 0.8019 2.3886 -0.3256 -0.00690 -0.00317 3.200  -0.6931 -0.1975 -0.007125 0.165464 0.3120 0.013493 540.0 -0.0960 0.3351 0.2984 0.4758 0.4036 0.7988 0.0312
    0.50   1.06 2.31684 -2.1 -0.5 50.0 3.0 4.0 -1.3926  0.0991 -0.2272 2.087 5.51513 5.4029 0.4571 0.0429 0.0830 13.00 0.7578 2.5000 -0.3189 -0.00590 -0.00272 3.500 -0.7246 -0.1633 -0.007435 0.133828 0.3610 0.011133 512.9 -0.0998 0.3353 0.3036 0.4710 0.4079 0.7966 0.0255
    0.75   1.06 2.73064 -2.1 -0.5 50.0 3.0 4.0 -1.8664  0.0936 -0.1620 1.812 5.38632 5.2900 0.4531 0.0387 0.0690 14.00 0.6788 2.6224 -0.2702 -0.00450 -0.00209 4.500 -0.7708 -0.1028 -0.008120 0.085153 0.4353 0.006739 441.9 -0.0765 0.3429 0.3205 0.4621 0.4157 0.7792 0.0175
    1.0    1.06 3.03000 -2.1 -0.5 50.0 3.0 4.0 -2.1935  0.0766 -0.1400 1.648 5.31000 5.2480 0.4517 0.0350 0.0450 15.00 0.6196 2.6690 -0.2059 -0.00370 -0.00175 5.000 -0.7990 -0.0699 -0.008444 0.058595 0.4629 0.005749 391.8 -0.0412 0.3577 0.3419 0.4581 0.4213 0.7504 0.0133
    1.5    1.06 3.43384 -2.1 -0.5 50.0 3.0 4.0 -2.6883  0.0022 -0.1184 1.511 5.29995 5.2194 0.4507 0.0280 0.0134 16.00 0.5101 2.6985 -0.0852 -0.00280 -0.00142 5.400 -0.8382 -0.0425 -0.007707 0.031787 0.4756 0.005544 348.1  0.0140 0.3769 0.3703 0.4493 0.4213 0.7136 0.0090
    2.0    1.06 3.67464 -2.1 -0.5 50.0 3.0 4.0 -3.1040 -0.0591 -0.1100 1.470 5.32730 5.2099 0.4504 0.0213 0.0040 18.00 0.3917 2.7085  0.0160 -0.00230 -0.00143 5.800 -0.8663 -0.0302 -0.004792 0.019716 0.4785 0.005521 332.5  0.0544 0.4023 0.4023 0.4459 0.4213 0.7035 0.0068
    3.0    1.06 3.64933 -2.1 -0.5 50.0 3.0 4.0 -3.7085 -0.0931 -0.1040 1.456 5.43850 5.2040 0.4501 0.0106 0.0010 19.00 0.1244 2.7145  0.1876 -0.00190 -0.00115 6.000 -0.9032 -0.0129 -0.001828 0.009643 0.4796 0.005517 324.1  0.1232 0.4406 0.4406 0.4433 0.4213 0.7006 0.0045
    4.0    1.06 3.60999 -2.1 -0.5 50.0 3.0 4.0 -4.1486 -0.0982 -0.1020 1.465 5.59770 5.2020 0.4501 0.0041 0.0000 19.75 0.0086 2.7164  0.3378 -0.00180 -0.00104 6.150 -0.9231 -0.0016 -0.001523 0.005379 0.4799 0.005517 321.7  0.1859 0.4784 0.4784 0.4424 0.4213 0.7001 0.0034
    5.0    1.06 3.50000 -2.1 -0.5 50.0 3.0 4.0 -4.4881 -0.0994 -0.1010 1.478 5.72760 5.2010 0.4500 0.0010 0.0000 20.00 0.0000 2.7172  0.4579 -0.00170 -0.00099 6.300 -0.9222  0.0000 -0.001440 0.003223 0.4799 0.005517 320.9  0.2295 0.5074 0.5074 0.4420 0.4213 0.7000 0.0027
    7.5    1.06 3.45000 -2.1 -0.5 50.0 3.0 4.0 -5.0891 -0.0999 -0.1010 1.498 5.98910 5.2000 0.4500 0.0000 0.0000 20.00 0.0000 2.7177  0.7514 -0.00170 -0.00094 6.425 -0.8346  0.0000 -0.001369 0.001134 0.4800 0.005517 320.3  0.2660 0.5328 0.5328 0.4416 0.4213 0.7000 0.0018
    10.0   1.06 3.45000 -2.1 -0.5 50.0 3.0 4.0 -5.5530 -0.1000 -0.1000 1.502 6.19300 5.2000 0.4500 0.0000 0.0000 20.00 0.0000 2.7180  1.1856 -0.00170 -0.00091 6.550 -0.7332  0.0000 -0.001361 0.000515 0.4800 0.005517 320.1  0.2682 0.5542 0.5542 0.4414 0.4213 0.7000 0.0014
    """)


class Bradley2013Volc(Bradley2013):
    """
    Extend :class:`Bradley2013` for earthquakes with paths across the Taupo
    Volcanic Zone (rtvz) that have increased anelastic attenuation.

    Implements GMPE developed by Brendan Bradley for Active Shallow Crust
    Earthquakes for New Zealand, and published as "A New Zealand-Specific
    Pseudospectral Acceleration Ground-Motion Prediction Equation for Active
    Shallow Crustal Earthquakes Based on Foreign Models" (2013, Bulletin of
    the Seismological Society of America, Volume 103, No. 3, pages 1801-1822).

    This model is modified from Chiou and Youngs, 2008 and has been adapted
    for New Zealand conditions. Specifically, the modifications are related to:
    1) small magnitude scaling;
    2) scaling of short period ground motion from normal faulting events in
    volcanic crust;
    3) scaling of ground motions on very hard rock sites;
    4) anelastic attenuation in the New Zealand crust;
    5) consideration of the increates anelastic attenuation in the Taupo
    Volcanic Zone (rtvz is equal to rrup)
    """

    DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC

    def _get_tvz_path_distance(self, rrup):
        """
        Returns Taupo Volcanic Zone (TVZ) path distance.
        rtvz = rrup as implemented for New Zealand seismic hazard model
        """

        return rrup


class Bradley2013LHC(Bradley2013):
    """
    Extend :class:`Bradley2013` to provide the model in terms of the larger
    of two as-recorded horizontal components. This definition is required
    by New Zealand building design standards.
    """
    DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = \
        const.IMC.GREATER_OF_TWO_HORIZONTAL

    #: This implementation is non-verified because this version of the
    #: model has not been published, nor is independent code available.
    non_verified = True

    def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
        """
        See :meth:`superclass method
        <.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
        for spec of input and result values.
        """
        # extracting dictionary of coefficients specific to required
        # intensity measure type.
        C = self.COEFFS[imt]
        # intensity on a reference soil is used for both mean
        # and stddev calculations.
        ln_y_ref = self._get_ln_y_ref(rup, dists, C)
        # exp1 and exp2 are parts of eq. 7
        exp1 = np.exp(C['phi3'] * (sites.vs30.clip(-np.inf, 1130) - 360))
        exp2 = np.exp(C['phi3'] * (1130 - 360))
        # v1 is the period dependent site term. The Vs30 above which, the
        # amplification is constant
        v1 = self._get_v1(imt)

        mean = self._get_mean(sites, C, ln_y_ref, exp1, exp2, v1)
        mean += convert_to_LHC(imt)

        stddevs = self._get_stddevs(sites, rup, C, stddev_types,
                                    ln_y_ref, exp1, exp2)
        return mean, stddevs


class Bradley2013VolcLHC(Bradley2013LHC):
    """
    Extend :class:`Bradley2013LHC` for earthquakes with paths across the Taupo
    Volcanic Zone (rtvz) that have increased anelastic attenuation.
    """

    DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC

    def _get_tvz_path_distance(self, rrup):
        """
        Returns Taupo Volcanic Zone (TVZ) path distance.
        rtvz = rrup as implemented for New Zealand seismic hazard model
        """

        return rrup


def convert_to_LHC(imt):
    """
    Converts from GMRotI50 to Larger of two horizontal components using
    global equation of:
    Boore, D and Kishida, T (2016). Relations between some horizontal-
    component ground-motion intensity measures used in practice.
    Bulletin of the Seismological Society of America, 107(1), 334-343.
    doi:10.1785/0120160250
    No standard deviation modification required.
    """
    # get period t
    if isinstance(imt, SA):
        t = imt.period
    else:
        t = 0.01

    T1 = 0.08
    T2 = 0.56
    T3 = 4.40
    T4 = 8.70
    R1 = 1.106
    R2 = 1.158
    R3 = 1.178
    R4 = 1.241
    R5 = 1.241

    Ratio = max(R1,
                max(min(R1+(R2-R1)/np.log(T2/T1)*np.log(t/T1),
                        R2+(R3-R2)/np.log(T3/T2)*np.log(t/T2)),
                    min(R3+(R4-R3)/np.log(T4/T3)*np.log(t/T3), R5)))
    SF = np.log(Ratio)

    return SF
