Douglas et al., 2013

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q200K005

Implements the GMPE for induced seismicity in Geothermal Areas derived from stochastic simulations of ground motion constructed by:

Douglas, J., Edwards, B., Convertito, V., Sharma, N., Tramelli, A.,

Kraaijpoel, D., Cabrera, B. M., Maercklin, N., and Troise, C. (2013) “Predicting Ground Motion for Induced Earthquakes in Geothermal Areas” Bulleting of the Seismological Society of America, 103(3), 1875 - 1897

The stochastic model by Douglas et al. (2013) provides coefficients for 36 GMPEs, corresponding to different values of Stress Drop (1 bar, 10 bar, 100 bar), Attentuation Quality Factor Q (200, 600, 1800) and high-frequency Kappa (0.005, 0.02, 0.04, 0.05 s).

The present model is implemented for Stress Drop 1 bar, Q 200 and Kappa 0.005 s.

The models for each combination of Stress Drop, Q and Kappa are implemented in subclasses, with only the median coefficients modified in each subclass

Notes on implementation:

1. Aleatory uncertainty terms are not supplied for the stochastic coefficients. Instead the adjusted aleatory uncertainty coefficients derived from empirical observations are applied to the stochastic model.
2. In the initial coefficient set for the stochastic model coefficients for spectral accelerations up to 10 s are provided. However, the empirical aleatory uncertainties are provided only for periods up to 0.5012 s. Therefore, after consulation with J. Douglas, it is decided to limit longest applicable spectral period to Sa (0.5 s), rather than extrapolate the empricial aleatory coefficients to longer periods.
3. For PGA and Sa (< 0.01 s) the aleatory uncertainty coefficients for Sa (0.01 s) are applied (J. Douglas, pers. comm.)
4. For Sa (< 0.01 s) the coefficients are interpolated assuming PGA occurs at Sa (0.005 s) (J. Dougla, pers. comm.). We therefore limit the short period range to 0.005 s

DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = 'Average horizontal'

The supported intensity measure component is ‘average horizontal’, see section entitiled “Empirical Analysis”, paragraph 1

DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([<class 'openquake.hazardlib.imt.PGA'>, <class 'openquake.hazardlib.imt.SA'>, <class 'openquake.hazardlib.imt.PGV'>])

The supported intensity measure types are PGA, PGV, and SA, see table 4.a, pages 22-23

DEFINED_FOR_STANDARD_DEVIATION_TYPES = set(['Intra event', 'Inter event', 'Total'])

The supported standard deviations are total, inter and intra event, see table 4.a, pages 22-23

DEFINED_FOR_TECTONIC_REGION_TYPE = 'Geothermal'

The supported tectonic region type is Geothermal because the equations have been developed for geothermal regions

REQUIRES_DISTANCES = set(['rhypo'])

The required distance parameter is hypocentral distance

REQUIRES_RUPTURE_PARAMETERS = set(['mag'])

The required rupture parameters are magnitude

REQUIRES_SITES_PARAMETERS = set([])

No additional site term is defined

get_distance_scaling_term(C, rhyp)

Returns the distance scaling term (equation 1)

get_magnitude_scaling_term(C, mag)

Returns the magnitude scaling term (equation 1)

get_mean_and_stddevs(sites, rup, dists, imt, stddev_types)

See superclass method for spec of input and result values.

get_stddevs(C_SIG, stddev_types, num_sites)

Returns the standard deviations

N.B. In the paper, and with confirmation from the author, the aleatory variability terms from the empirical model are used in conjunction with the median coefficients from the stochastic model. In the empirical model, coefficients for a single-station intra-event sigma are derived. These are labeled as “phi”. Inter-event coefficients corresponding to two observed geothermal sequences (Soultz-Sous-Forets and Basel) are also derived. The inter-event standard deviation is therefore taken as the ordinary mean of the two inter-event sigma terms

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q200K020

Stress Drop 001 - Q 200 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q200K040

Stress Drop 001 - Q 200 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q200K060

Stress Drop 001 - Q 200 - Kappa 0.06

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q600K005

Stress Drop 001 - Q 600 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q600K020

Stress Drop 001 - Q 600 - Kappa 0.020

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q600K040

Stress Drop 001 - Q 600 - Kappa 0.040

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q600K060

Stress Drop 001 - Q 600 - Kappa 0.060

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q1800K005

Stress Drop 001 - Q 1800 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q1800K020

Stress Drop 001 - Q 1800 - Kappa 0.020

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q1800K040

Stress Drop 001 - Q 1800 - Kappa 0.040

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD001Q1800K060

Stress Drop 001 - Q 1800 - Kappa 0.060

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K005

Stress Drop 100 - Q 200 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K020

Stress Drop 100 - Q 200 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K040

Stress Drop 100 - Q 200 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K060

Stress Drop 100 - Q 200 - Kappa 0.06

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K005

Stress Drop 100 - Q 600 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K020

Stress Drop 100 - Q 600 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K040

Stress Drop 100 - Q 600 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K060

Stress Drop 100 - Q 600 - Kappa 0.06

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K005

Stress Drop 100 - Q 1800 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K020

Stress Drop 100 - Q 1800 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K040

Stress Drop 100 - Q 1800 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K060

Stress Drop 100 - Q 1800 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K005

Stress Drop 100 - Q 200 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K020

Stress Drop 100 - Q 200 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K040

Stress Drop 100 - Q 200 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q200K060

Stress Drop 100 - Q 200 - Kappa 0.06

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K005

Stress Drop 100 - Q 600 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K020

Stress Drop 100 - Q 600 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K040

Stress Drop 100 - Q 600 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q600K060

Stress Drop 100 - Q 600 - Kappa 0.06

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K005

Stress Drop 100 - Q 1800 - Kappa 0.005

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K020

Stress Drop 100 - Q 1800 - Kappa 0.02

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K040

Stress Drop 100 - Q 1800 - Kappa 0.04

class openquake.hazardlib.gsim.douglas_stochastic_2013.DouglasEtAl2013StochasticSD100Q1800K060

Stress Drop 100 - Q 1800 - Kappa 0.04