Ground motion models¶

Generic Interface¶

The interfaces for models have been simplified to use same parameter names and values where possible.

All model share the following interface:

class pygmm.model.Model(**kwds)[source]¶

Abstract class for ground motion prediction models.

Compute the response predicted the model.

No default implementation.

interp_ln_stds(periods)[source]¶

Return the logarithmic standard deviation (\(\sigma_{ \ln}\)) of spectral acceleration at the provided damping at specified periods.

Parameters:	period (numpy.array) – periods of interest (sec).
Returns:	numpy.array pseudo-spectral accelerations.

interp_spec_accels(periods)[source]¶

Return the pseudo-spectral acceleration at the provided damping at specified periods.

Parameters:	period (numpy.array) – periods of interest (sec).
Returns:	pseudo-spectral accelerations.
Return type:	(numpy.array)

ln_std_pga¶

Logarithmic standard deviation (\(\sigma_{ \ln}\)) of the peak ground acceleration computed by the model.

Returns:	float
Raises:	NotImplementedError – If model does not provide an estimate.

ln_std_pgd¶

Logarithmic standard deviation (\(\sigma_{ \ln}\)) of the peak ground displacement computed by the model.

Returns:	float
Raises:	NotImplementedError – If model does not provide an estimate.

ln_std_pgv¶

Logarithmic standard deviation (\(\sigma_{ \ln}\)) of the peak ground velocity computed by the model.

Returns:	float
Raises:	NotImplementedError – If model does not provide an estimate.

ln_stds¶

Logarithmic standard deviation of the pseudo-spectral accelerations.

Returns:	numpy.array

periods¶

Periods specified by the model.

Returns:	numpy.array

pga¶

Peak ground acceleration (PGA) computed by the model (g).

Returns:	float
Raises:	NotImplementedError If model does not provide an estimate.

pgd¶

Peak ground displacement (PGD) computed by the model (cm).

Returns:	float
Raises:	NotImplementedError – If model does not provide an estimate.

pgv¶

Peak ground velocity (PGV) computed by the model (cm/sec).

Returns:	float
Raises:	NotImplementedError – If model does not provide an estimate.

spec_accels¶

Pseudo-spectral accelerations computed by the model (g).

Returns:	numpy.array

Specific Models¶

class pygmm.AbrahamsonSilvaKamai2014(**kwds)[source]¶

The Abrahamson, Silva, and Kamai (2014) [1] ground motion model for active tectonic regions.

__init__(**kwds)[source]¶

Initialize the model.

Keyword Arguments:

depth_1_0 (Optional[float]) – depth to the 1.0 km∕s shear-wave velocity horizon beneath the site, \(Z_{1.0}\) in (km). Used to estimate depth_2_5. depth_2_5 (Optional[float]) – depth to the 2.5 km∕s shear-wave velocity horizon beneath the site, \(Z_{2.5}\) in (km). If None, then it is computed from depth_1_0 or v_s30 and the region parameter. depth_tor (Optional[float]) – depth to the top of the rupture plane (\(Z_{tor}\), km). If None, then the average model is used. depth_bor (Optional[float]) – depth to the bottom of the rupture plane (\(Z_{bor}\), km). If None, then the average model is used. dip (float) – fault dip angle (\(\phi\), deg). dist_jb (float) – Joyner-Boore distance to the rupture plane (\(R_\text{JB}\), km) dist_rup (float) – closest distance to the rupture plane (\(R_\text{rup}\), km) dist_x (float) – site coordinate measured perpendicular to the fault strike from the fault line with the down-dip direction being positive (\(R_x\), km). dist_y0 (Optional[float]) – the horizontal distance off the end of the rupture measured parallel to strike (\(R_{y0}\), km). mag (float) – moment magnitude of the event (\(M_w\)) mechanism (str) – fault mechanism. Valid options: “SS”, “NS”, “RS”. on_hanging_wall (Optional[bool]) – If the site is located on the hanging wall of the fault. If None, then False is assumed. region (Optional[str]) – region. Valid options: “global”, “california”, “china”, “italy”, “japan”, “taiwan”. If None, then “global” is used as a default value. v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s). vs_source (Optional[str]) – source of the v_s30 value. Valid options: “measured”, “inferred” width (Optional[float]) – Down-dip width of the fault. If None, then the model average is used.

static calc_depth_1_0(v_s30, region='california')[source]¶

Estimate the depth to 1 km/sec horizon (\(Z_{1.0}\)) based on \(V_{s30}\) and region.

This is based on equations 18 and 19 in the [1] and differs from the equations in the [2].

Parameters:	v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s).
Keyword Arguments:
	region (Optional[str]) – region of basin model. Valid options: “california”, “japan”. If None, then “california” is used as the default value.
Returns:	depth to a shear-wave velocity of 1,000 m/sec (\(Z_{1.0}\), km).
Return type:	float

static calc_depth_tor(mag)[source]¶

Calculate the depth to top of rupture (km).

Parameters:	mag (float) – moment magnitude of the event (\(M_w\))
Returns:	estimated depth (km)
Return type:	float

static calc_width(mag, dip)[source]¶

Compute the fault width based on equation in NGW2 spreadsheet.

This equation is not provided in the paper.

Parameters:	mag (float) – moment magnitude of the event (\(M_w\)) dip (float) – Fault dip angle (\(\phi\), deg)
Returns:	estimated fault width (\(W\), km)
Return type:	float

class pygmm.AtkinsonBoore2006(**kwds)[source]¶

Atkinson and Boore (2006) [3] ground motion prediction model.

Developed for the Eastern North America with a reference velocity of 760 or 2000 m/s.

__init__(**kwds)[source]¶

Initialize the model.

Parameters:	mag (float) – moment magnitude of the event (\(M_w\)) dist_rup (float) – Closest distance to the rupture plane (\(R_\text{rup}\), km) v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s).

class pygmm.BooreStewartSeyhanAtkinson2014(**kwds)[source]¶

Boore, Stewart, Seyhan, and Atkinson (2014) [4] ground motion model.

Developed for the California and other active tectonic environments.

The BSSA14 model defines the following distance attenuation models:

Name	Description
global	Global; California and Taiwan
china_turkey	China and Turkey
italy_japan	Italy and Japan

and the following basin region models:

Name	Description
global	Global / California
japan	Japan

These are simplified into one regional parameter with the following possibilities:

Region	Attenuation	Basin
global	global	global
california	global	global
china	china_turkey	global
italy	italy_japan	global
japan	italy_japan	japan
new zealand	italy_japan	global
taiwan	global	global
turkey	china_turkey	global

__init__(**kwds)[source]¶

Compute the response predicted the Boore, Stewart, Seyhan, and Atkinson (2014) ground motion model.

Keyword Arguments:

mag (float) – moment magnitude of the event (\(M_w\)) depth_1_0 (Optional[float]) – depth to the 1.0 km∕s shear-wave velocity horizon beneath the site, \(Z_{1.0}\) in (km). If None is specified, then no adjustment is applied. dist_jb (float) – Joyner-Boore distance to the rupture plane (\(R_\text{JB}\), km) v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s). mechanism (str) – fault mechanism. Valid options: “U”, “SS”, “NS”, “RS” region (Optional[str]) – region for distance attenuation and basin model. Valid options: “global”, “california”, “china”, “italy”, “japan”, “new_zealand”, “taiwan”, “turkey”. If None is specified, then “global” is used as default.

class pygmm.Campbell2003(**kwds)[source]¶

Campbell (2003) [5] ground motion model for Eastern US.

__init__(**kwds)[source]¶

Initialize the ground motion model.

Keyword Arguments:
	mag (float) – moment magnitude of the event (\(M_w\)) dist_rup (float) – closest distance to the rupture plane (\(R_\text{rup}\), km)

class pygmm.CampbellBozorgnia2014(**kwds)[source]¶

Campbell and Bozorgnia (2014) [6] ground motion model for active tectonic regions.

__init__(**kwds)[source]¶

Compute the response predicted the Campbell and Bozorgnia (2014) ground motion model.

Keyword Arguments:

depth_1_0 (Optional[float]) – depth to the 1.0 km∕s shear-wave velocity horizon beneath the site, \(Z_{1.0}\) in (km). Used to estimate depth_2_5. depth_2_5 (Optional[float]) – depth to the 2.5 km∕s shear-wave velocity horizon beneath the site, \(Z_{2.5}\) in (km). If None, then it is computed from depth_1_0 or v_s30 and the region parameter. depth_tor (Optional[float]) – depth to the top of the rupture plane (\(Z_{tor}\), km). If None, then the average model is used. depth_bor (Optional[float]) – depth to the bottom of the rupture plane (\(Z_{bor}\), km). If None, then the average model is used. depth_bot (Optional[float]) – depth to bottom of seismogenic crust (km). Used to calculate fault width if none is specified. If None, then a value of 15 km is used. depth_hyp (Optional[float]) – depth of the hypocenter (km). If None, then the model average is used. dip (float) – fault dip angle (\(\phi\), deg). dist_jb (float) – Joyner-Boore distance to the rupture plane (\(R_\text{JB}\), km) dist_rup (float) – closest distance to the rupture plane (\(R_\text{rup}\), km) dist_x (float) – site coordinate measured perpendicular to the fault strike from the fault line with the down-dip direction being positive (\(R_x\), km). mag (float) – moment magnitude of the event (\(M_w\)) mechanism (str) – fault mechanism. Valid values: “SS”, “NS”, “RS”. region (Optional[str]) – region. Valid values: “california”, “china”, “italy”, “japan”. If None, then “california” is used as a default value. v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s). width (Optional[float]) – Down-dip width of the fault. If None, then the model average is used.

static calc_depth_2_5(v_s30, region='global', depth_1_0=None)[source]¶

Calculate the depth to a shear-wave velocity of 2.5 km/sec (\(Z_{2.5}\)).

Provide either v_s30 or depth_1_0.

Parameters:	v_s30 (Optional[float]) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s).
Keyword Arguments:
	region (Optional[str]) – region of the basin model. Valid values: “california”, “japan”. depth_1_0 (Optional[float]) – depth to the 1.0 km∕s shear-wave velocity horizon beneath the site, \(Z_{1.0}\) in (km).
Returns:	estimated depth to a shear-wave velocity of 2.5 km/sec (km).
Return type:	float

static calc_depth_bor(depth_tor, dip, width)[source]¶

Compute the depth to bottom of the rupture (km).

Parameters:	dip (float) – fault dip angle (\(\phi\), deg). depth_tor (float) – depth to the top of the rupture plane (\(Z_{tor}\), km). width (float) – Down-dip width of the fault.
Returns:	depth to bottom of the fault rupture (km)
Return type:	float

static calc_depth_hyp(mag, dip, depth_tor, depth_bor)[source]¶

Estimate the depth to hypocenter.

Parameters:	mag (float) – moment magnitude of the event (\(M_w\)) dip (float) – fault dip angle (\(\phi\), deg). depth_tor (float) – depth to the top of the rupture plane (\(Z_{tor}\), km). depth_bor (float) – depth to the bottom of the rupture plane (\(Z_{bor}\), km).
Returns:	estimated hypocenter depth (km)
Return type:	float

static calc_width(mag, dip, depth_tor, depth_bot=15.0)[source]¶

Estimate the fault width using Equation (39) of CB14.

Parameters:	mag (float) – moment magnitude of the event (\(M_w\)) dip (float) – fault dip angle (\(\phi\), deg). depth_tor (float) – depth to the top of the rupture plane (\(Z_{tor}\), km).
Keyword Arguments:
	depth_bot (Optional[float]) – depth to bottom of seismogenic crust (km). Used to calculate fault width if none is specified. If None, then a value of 15 km is used.
Returns:	estimated fault width (km)
Return type:	float

class pygmm.ChiouYoungs2014(**kwds)[source]¶

Chiou and Youngs (2014) [2] model.

__init__(**kwds)[source]¶

Compute the response predicted the Chiou and Youngs (2014) ground motion model.

Keyword Arguments:

depth_1_0 (Optional[float]) – depth to the 1.0 km∕s shear-wave velocity horizon beneath the site, \(Z_{1.0}\) in (km). Used to estimate depth_2_5. depth_tor (Optional[float]) – depth to the top of the rupture plane (\(Z_{tor}\), km). If None, then the average model is used. dist_jb (float) – Joyner-Boore distance to the rupture plane (\(R_\text{JB}\), km) dist_rup (float) – closest distance to the rupture plane (\(R_\text{rup}\), km) dist_x (float) – site coordinate measured perpendicular to the fault strike from the fault line with the down-dip direction being positive (\(R_x\), km). dip (float) – fault dip angle (\(\phi\), deg). dpp_centered (Optional[float]) – direct point parameter for directivity effect (see Chiou and Spudich (2014)) centered on the earthquake-specific average DPP for California. If None, then value of 0 used to provide the average directivity. mag (float) – moment magnitude of the event (\(M_w\)) mechanism (str) – fault mechanism. Valid options: “U”, “SS”, “NS”, “RS”. on_hanging_wall (Optional[bool]) – If the site is located on the hanging wall of the fault. If None, then False is assumed. region (Optional[str]) – region. Valid options: “california”, “china”, “italy”, “japan”. If None, then “california” is used as a default value. v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s). vs_source (Optional[str]) – source of the v_s30 value. Valid options: “measured”, “inferred”

static calc_depth_1_0(v_s30, region)[source]¶

Calculate an estimate of the depth to 1 km/sec (\(Z_{1.0}\)) based on \(V_{s30}\) and region.

Parameters:	v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s). region (str) – basin region. Valid options: “california”, “japan”
Returns:	estimated depth to a shear-wave velocity of 1 km/sec (km)
Return type:	float

static calc_depth_tor(mag, mechanism)[source]¶

Calculate an estimate of the depth to top of rupture (km).

Parameters:	mag (float) – moment magnitude of the event (\(M_w\)) mechanism (str) – fault mechanism. Valid options: “U”, “SS”, “NS”, “RS”.
Returns:	estimated depth to top of rupture (km)
Return type:	float

class pygmm.Idriss2014(**kwds)[source]¶

Idriss (2014) [7] ground motion model.

__init__(**kwds)[source]¶

Initialize the ground motion model.

Keyword Arguments:
	dist_rup (float) – Closest distance to the rupture plane (\(R_\text{rup}\), km) mag (float) – moment magnitude of the event (\(M_w\)) mechanism (str) – fault mechanism. Valid options: “SS”, “NS”, “RS”. SS and NS mechanism are treated the same with \(F=0\) in the model. v_s30 (float) – time-averaged shear-wave velocity over the top 30 m of the site (\(V_{s30}\), m/s).

class pygmm.PezeshkZandiehTavakoli2011(**kwds)[source]¶

Pezeshk, Zandieh, and Tavakoli (2011) [8] ground motion prediction model.

Developed for the Eastern North America with a reference velocity of 2000 m/s.

__init__(**kwds)[source]¶

Initialize the model.

Keyword Arguments:
	mag (float) – moment magnitude of the event (\(M_w\)) dist_rup (float) – Closest distance to the rupture plane (\(R_\text{rup}\), km)

class pygmm.TavakoliPezeshk05(**kwds)[source]¶

Tavakoli and Pezeshk (2005) [9] ground motion prediction model.

Developed for the Eastern North America with a reference velocity of 2880 m/s.

__init__(**kwds)[source]¶

Initialize the model.

Keyword Arguments:
	mag (float) – moment magnitude of the event (\(M_w\)) dist_rup (float) – Closest distance to the rupture plane (\(R_\text{rup}\), km)