# Source code for openquake.hazardlib.gsim.lanzano_luzi_2019

```# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2022 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:`LanzanoLuzi2019shallow`,
:class:`LanzanoLuzi2019deep`
"""
import numpy as np
from scipy.constants import g

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

def _compute_distance(rval2, C, kind):
"""
Compute the distance function
"""
if kind == 'shallow':  # equation (9)
h1 = 2
rval = np.sqrt(rval2 ** 2 + h1 ** 2)
return C['c1'] * np.log10(rval)
elif kind == 'deep':  # equation (5)
h2 = 5
rval = np.sqrt(rval2 ** 2 + h2 ** 2)
return C['c2'] * np.log10(rval) + C['c3'] * rval
raise ValueError(kind)

def _compute_magnitude(ctx, C):
"""
Compute the magnitude function, equation (9):
"""
return C['a'] + C['b'] * ctx.mag

def _get_site_amplification(ctx, C):
"""
Compute the site amplification function given by FS = eiSi, for
i = 1,2,3 where Si are the coefficients determined through regression
analysis, and ei are dummy variables (0 or 1) used to denote the
different EC8 site classes.
"""
ssb, ssc = _get_site_type_dummy_variables(ctx)

return (C['sB'] * ssb) + (C['sC'] * ssc)

def _get_site_type_dummy_variables(ctx):
"""
Get site type dummy variables, which classified the ctx into
different site classes based on the shear wave velocity in the
upper 30 m (Vs30) according to the EC8 (CEN 2003):
class A: Vs30 > 800 m/s
class B: Vs30 = 360 - 800 m/s
class C: Vs30 = 180 - 360 m/s
class D: Vs30 < 180 m/s
"""
ssb = np.zeros(len(ctx.vs30))
ssc = np.zeros(len(ctx.vs30))
# Class C; Vs30 < 360 m/s.
idx = (ctx.vs30 < 360.0)
ssc[idx] = 1.0
# Class B; 360 m/s <= Vs30 <= 800 m/s.
idx = (ctx.vs30 >= 360.0) & (ctx.vs30 < 800.0)
ssb[idx] = 1.0

return ssb, ssc

[docs]class LanzanoLuzi2019shallow(GMPE):
"""
Implements GMPE developed by Giovanni Lanzano and Lucia Luzi (2019) and
submitted as "A ground motion model for volcanic areas in Italy"
Bulletin of Earthquake Engineering.

GMPE derives from earthquakes in the volcanic areas in Italy in the
magnitude range 3<ML<5 for hypocentral distances <200 km, and for
rock (EC8-A), stiff soil (EC8-B) and soft soil (EC8-C and EC8-D).

The GMPE distinguishes between shallow volcano-tectonic events related to
flank movements (focal depths <5km) and deeper events occurring due to
regional tectonics (focal depths >5km), considering two different
attenuations with distances.

Test tables are generated from a spreadsheet provided by the authors, and
modified according to OQ format (e.g. conversion from cm/s2 to m/s2).
"""
kind = 'shallow'

#: Supported tectonic region type is 'volcanic'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC

#: Supported intensity measure types are PGA and SA
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}

#: Supported intensity measure component is the geometric mean of two
#: horizontal components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL

#: Supported standard deviation types are inter-event, intra-event
#: and total, page 1904
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}

#: Required site parameter is Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}

#: Required rupture parameter is magnitude.
REQUIRES_RUPTURE_PARAMETERS = {'mag'}

#: Required distance measure is Rhypo.
REQUIRES_DISTANCES = {'rhypo'}

[docs]    def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]

imean = (_compute_magnitude(ctx, C) +
_compute_distance(ctx.rhypo, C, self.kind) +
_get_site_amplification(ctx, C))

istddevs = [C['sigma'], C['phi'], C['tau']]

# Convert units to g, but only for PGA and SA (not PGV)
if imt.string.startswith(("SA", "PGA")):
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
else:  # PGV:
mean[m] = np.log(10.0 ** imean)
# Return stddevs in terms of natural log scaling
sig[m], tau[m], phi[m] = np.log(10.0 ** np.array(istddevs))
# mean_LogNaturale = np.log((10 ** mean) * 1e-2 / g)

# Sigma values in log10
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT		a		b		c1		c2		c3		sB		sC		tau	 	phiS2S	sigma0	phi		sigma
pga		-0.4185	0.8146	-2.0926	-1.5694	-0.0062	0.088	0.3382	0.1892	0.2624	0.2215	0.3434	0.3921
pgv		-2.5366	0.9809	-1.8482	-1.5676	-0.0042	0.0995	0.3747	0.1433	0.2126	0.2099	0.2988	0.3313
0.025	-0.3849	0.8113	-2.0995	-1.5689	-0.0063	0.0866	0.3373	0.1887	0.2644	0.2228	0.3458	0.3939
0.040	-0.2622	0.7983	-2.1271	-1.5777	-0.0065	0.0861	0.3306	0.1908	0.2725	0.2246	0.3531	0.4014
0.050	-0.1428	0.7870	-2.1536	-1.5859	-0.0069	0.0863	0.3323	0.1955	0.2846	0.2284	0.3649	0.4140
0.070	 0.0810	0.7714	-2.2186	-1.5859	-0.0076	0.0774	0.3139	0.2039	0.3078	0.2392	0.3898	0.4399
0.100	 0.4160	0.7293	-2.2624	-1.6135	-0.0075	0.0609	0.2997	0.2164	0.3240	0.2312	0.3980	0.4531
0.150	 0.2806	0.7569	-2.2177	-1.5882	-0.0069	0.0714	0.3465	0.2193	0.3204	0.2155	0.3861	0.4441
0.200	 0.0339	0.8028	-2.1606	-1.5803	-0.0060	0.0716	0.3297	0.2200	0.3039	0.2126	0.3709	0.4312
0.250	-0.2205	0.8577	-2.1228	-1.5948	-0.0052	0.0512	0.3204	0.1995	0.2837	0.2101	0.3530	0.4055
0.300	-0.4404	0.8872	-2.0652	-1.5829	-0.0047	0.0752	0.3468	0.1932	0.2726	0.2053	0.3413	0.3922
0.350	-0.6916	0.9169	-2.0099	-1.5577	-0.0042	0.0838	0.3818	0.1838	0.2607	0.2043	0.3312	0.3788
0.400	-1.0431	0.9744	-1.9542	-1.5409	-0.0038	0.0820	0.3672	0.1850	0.2576	0.2034	0.3282	0.3768
0.450	-1.2374	1.0111	-1.9411	-1.5544	-0.0038	0.0878	0.3882	0.1794	0.2467	0.2053	0.3210	0.3677
0.500	-1.3532	1.0303	-1.9337	-1.5871	-0.0034	0.1033	0.4053	0.1736	0.2461	0.2039	0.3196	0.3637
0.600	-1.6118	1.0629	-1.8831	-1.6015	-0.0029	0.1161	0.4056	0.1681	0.2336	0.2006	0.3079	0.3508
0.700	-1.9639	1.1092	-1.8177	-1.5795	-0.0027	0.1086	0.4195	0.1550	0.2300	0.1974	0.3031	0.3404
0.750	-2.0659	1.1181	-1.7968	-1.5618	-0.0029	0.1159	0.4277	0.1581	0.2314	0.195	0.3026	0.3414
0.800	-2.1093	1.1189	-1.7961	-1.5741	-0.0027	0.1174	0.4371	0.1541	0.2289	0.1944	0.3003	0.3375
0.900	-2.2763	1.1315	-1.7722	-1.5776	-0.0023	0.1212	0.4374	0.1552	0.2287	0.1885	0.2964	0.3345
1.000	-2.5171	1.1553	-1.7230	-1.5615	-0.0018	0.1201	0.448	0.1496	0.2279	0.1904	0.2970	0.3325
1.200	-2.698	1.1748	-1.7111	-1.6079	-0.0013	0.1195	0.4313	0.1595	0.2286	0.1865	0.2950	0.3354
1.400	-2.9144	1.1842	-1.6536	-1.5777	-0.0015	0.1155	0.4136	0.1846	0.2217	0.1855	0.2891	0.3430
1.600	-3.0714	1.2011	-1.6641	-1.6102	-0.0013	0.1269	0.377	0.1953	0.2226	0.1823	0.2877	0.3477
1.800	-3.1426	1.1967	-1.6553	-1.6305	-0.0012	0.1337	0.3756	0.1888	0.2221	0.1793	0.2854	0.3422
2.000	-3.2273	1.1995	-1.6524	-1.6597	-0.0009	0.1440	0.3917	0.1929	0.2187	0.1824	0.2848	0.3440
2.500	-3.4744	1.2057	-1.6227	-1.642	-0.0011	0.1388	0.3712	0.2060	0.2111	0.185	0.2807	0.3482
3.000	-3.7121	1.2118	-1.5741	-1.6063	-0.0012	0.1261	0.3836	0.2356	0.2139	0.1825	0.2812	0.3668
3.500	-3.4558	1.1198	-1.5393	-1.6194	-0.0011	0.1101	0.3639	0.2506	0.2098	0.1816	0.2775	0.3739
4.000	-3.5044	1.0943	-1.4949	-1.6025	-0.0012	0.1064	0.3447	0.2442	0.2093	0.1832	0.2782	0.3701
4.500	-3.3949	1.0490	-1.475	-1.6088	-0.0011	0.0908	0.3587	0.2287	0.1952	0.1835	0.2679	0.3522
5.000	-3.4022	1.0258	-1.4711	-1.6097	-0.0011	0.0856	0.3386	0.2273	0.1954	0.1835	0.2681	0.3515
""")

[docs]class LanzanoLuzi2019deep(LanzanoLuzi2019shallow):
kind = 'deep'

[docs]class LanzanoLuzi2019shallow_scaled(LanzanoLuzi2019shallow):
"""
Implements GMPE developed by Giovanni Lanzano and Lucia Luzi (2019) and
submitted as "A ground motion model for volcanic areas in Italy"
Bulletin of Earthquake Engineering.

GMPE derives from earthquakes in the volcanic areas in Italy in the
magnitude range 3<ML<5 for hypocentral distances <200 km, and for
rock (EC8-A), stiff soil (EC8-B) and soft soil (EC8-C and EC8-D).

The GMPE distinguishes between shallow volcano-tectonic events related to
flank movements (focal depths <5km) and deeper events occurring due to
regional tectonics (focal depths >5km), considering two different
attenuations with distances.

Test tables are generated from a spreadsheet provided by the authors, and
modified according to OQ format (e.g. conversion from cm/s2 to m/s2).

Application of a scaling factor that converts the prediction of
LanzanoLuzi2019shallow to the corresponding
prediction for the Maximum value.
"""

# Sigma values in log10
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT		a				b		c1		c2		c3		sB		sC		tau		phiS2S	sigma0	phi		sigma
pga		-0.378174621	0.8146	-2.0926	-1.5694	-0.0062	0.088	0.3382	0.1892	0.2624	0.2215	0.3434	0.3921
0.05	-0.103901788	0.787	-2.1536	-1.5859	-0.0069	0.0863	0.3323	0.1955	0.2846	0.2284	0.3649	0.414
0.1		0.45951946		0.7293	-2.2624	-1.6135	-0.0075	0.0609	0.2997	0.2164	0.324	0.2312	0.398	0.4531
0.15	0.326392233		0.7569	-2.2177	-1.5882	-0.0069	0.0714	0.3465	0.2193	0.3204	0.2155	0.3861	0.4441
0.2		0.08296289		0.8028	-2.1606	-1.5803	-0.006	0.0716	0.3297	0.22	0.3039	0.2126	0.3709	0.4312
0.3		-0.38839902		0.8872	-2.0652	-1.5829	-0.0047	0.0752	0.3468	0.1932	0.2726	0.2053	0.3413	0.3922
0.4		-0.9877599		0.9744	-1.9542	-1.5409	-0.0038	0.082	0.3672	0.185	0.2576	0.2034	0.3282	0.3768
0.5		-1.299085099	1.0303	-1.9337	-1.5871	-0.0034	0.1033	0.4053	0.1736	0.2461	0.2039	0.3196	0.3637
0.75	-2.009414407	1.1181	-1.7968	-1.5618	-0.0029	0.1159	0.4277	0.1581	0.2314	0.195	0.3026	0.3414
1		-2.463138493	1.1553	-1.723	-1.5615	-0.0018	0.1201	0.448	0.1496	0.2279	0.1904	0.297	0.3325
2		-3.172265876	1.1995	-1.6524	-1.6597	-0.0009	0.144	0.3917	0.1929	0.2187	0.1824	0.2848	0.344
3		-3.65485242		1.2118	-1.5741	-1.6063	-0.0012	0.1261	0.3836	0.2356	0.2139	0.1825	0.2812	0.3668
4		-3.445025941	1.0943	-1.4949	-1.6025	-0.0012	0.1064	0.3447	0.2442	0.2093	0.1832	0.2782	0.3701
pgv		-2.493041253	0.9809	-1.8482	-1.5676	-0.0042	0.0995	0.3747	0.1433	0.2126	0.2099	0.2988	0.3313
""")

[docs]class LanzanoLuzi2019deep_scaled(LanzanoLuzi2019shallow_scaled):
kind = 'deep'
```