gmKriger

gmKriger: A Kriging-based ground motion intensity measure (GMIM) calculator. gmKriger computes GMIMs for past earthquake events given a site's location (latitude and longitude) and the site's Vs30. gmKriger uses Ordinary Kriging interpolation and spatial correlation model developed using a Bayesian approach, ground motion data, and the functional forms proposed by Bodenmann et al. (2023).

Ground motion intensity measures (GMIMs) and units

GMIM	Key	Unit
Peak ground aceleration	PGA	g
Peak ground velocity	PGV	cm/s
Arias intensity	Ia	m/s
Cumulative absolute velocity	CAV	m/s
Damage-potential CAV	CAVdp	g-s
Pseudo-spectral acceleration @ 0.1 s	PSA(0.100)	g
Pseudo-spectral acceleration @ 0.3 s	PSA(0.300)	g
Pseudo-spectral acceleration @ 0.6 s	PSA(0.600)	g
Pseudo-spectral acceleration @ 1.0 s	PSA(1.000)	g
Pseudo-spectral acceleration @ 3.0 s	PSA(3.000)	g
Pseudo-spectral acceleration @ 6.0 s	PSA(6.000)	g
Pseudo-spectral acceleration @ 10.0 s	PSA(10.000)	g

Models available

Get them using this code.

The spatial correlation models for the events and ground motion intensity measures below are accessible via DesignSafe (Pretell et al. 2023).

Earthquake	PGA	PGV	Ia	CAV	CAVdp
1968 M8.2 Tokachi-Oki	No	No	Yes	Yes	No
1971 M6.6 San Fernando	Yes	Yes	Yes	Yes	No
1978 M7.7 Miyagiken-Oki	No	No	Yes	Yes	No
1979 M6.5 Imperial Valley	Yes	Yes	Yes	Yes	No
1980 M6.3 Victoria	Yes	Yes	Yes	Yes	No
1981 M5.9 Westmorland	Yes	Yes	Yes	Yes	No
1983 M7.7 Nihonkai-Chubu	No	No	Yes	Yes	No
1983 M6.8 Nihonkai-Chubu	No	No	Yes	Yes	No
1987 M6.5 Superstition Hills	Yes	Yes	Yes	Yes	No
1989 M6.9 Loma Prieta	Yes	Yes	Yes	Yes	No
1993 M7.6 Kushiro-Oki Hokkaido	No	No	Yes	Yes	No
1994 M6.7 Northridge	Yes	Yes	Yes	Yes	No
1994 M8.3 Toho-Oki Hokkaido	No	No	Yes	Yes	No
1995 M6.9 Kobe	Yes	Yes	Yes	Yes	No
1999 M7.5 Kocaeli	Yes	Yes	Yes	Yes	No
1999 M7.6 Chi-Chi	Yes	Yes	Yes	Yes	No
2000 M6.6 Tottori	Yes	Yes	Yes	Yes	No
2002 M5.0 Au Sable Forks	No	No	No	No	No
2003 M8.3 Tokachi	No	No	Yes	Yes	No
2007 M6.8 Chuetsu-oki	Yes	Yes	Yes	Yes	No
2010 M7.2 El Mayor-Cucapah	Yes	Yes	Yes	Yes	No
2010 M7.0 Darfield	Yes	Yes	Yes	Yes	No
2010 M8.8 Maule	No	No	Yes	Yes	No
2011 M6.2 Christchurch	Yes	Yes	Yes	Yes	No
2011 M5.0 Christchurch	Yes	No	No	No	No
2011 M6.0 Christchurch	Yes	Yes	Yes	Yes	No
2011 M5.9 Lyttleton	Yes	Yes	Yes	Yes	No
2011 M9.1 Tohoku-Oki	No	No	Yes	Yes	No
2012 M6.1 Emilia	Yes	Yes	Yes	Yes	No
2012 M6.0 Emilia	Yes	Yes	Yes	Yes	No
2019 M7.06 Ridgecrest	Yes	Yes	Yes	Yes	No
2019 M6.48 Ridgecrest	Yes	Yes	Yes	Yes	No
2020 M7.0 Samos	Yes	Yes	Yes	Yes	No
2023 M7.81 Pazarcik	Yes	Yes	Yes	Yes	Yes
2023 M7.74 Kahramanmaras	Yes	Yes	Yes	Yes	Yes
2023 M6.81 Nurdagi	Yes	Yes	Yes	Yes	Yes
2023 M6.37 Yayladagi	Yes	Yes	Yes	Yes	Yes

Also, PSA at several oscillator periods for some events:

Earthquake	PSA(0.100)	PSA(0.300)	PSA(0.600)	PSA(1.000)	PSA(3.000)	PSA(6.000)	PSA(10.000)
2023 M7.81 Pazarcik	Yes	Yes	Yes	Yes	Yes	Yes	Yes
2023 M7.74 Kahramanmaras	Yes	Yes	Yes	Yes	Yes	Yes	Yes
2023 M6.81 Nurdagi	Yes	Yes	Yes	Yes	Yes	Yes	Yes
2023 M6.37 Yayladagi	Yes	Yes	Yes	Yes	Yes	Yes	Yes

Note: The CAVdp values estimated by gmKriger require close attention. Some estimates might be unexpectedly high at R_JB > 100 km, when no seismic station is nearby.

Installation

Need the following packages:

pip install nvector
pip install torch
pip install geopy
pip install shapely
pip install nvector

pip install geostats
pip install gmms
pip install pygmm
pip install gmKriger

How to use

Inputs

site:
Site ID(s) or site name(s).

latitude:
Site's latitude(s).

longitude:
Site's longitude(s).

Vs30:
Time-average shear-wave velocity in the top 30 m for the site(s).

earthquake:
Event from the available models (e.g., '1989 M6.9 Loma Prieta').

model:

• realizations: To use 1000 spatial correlation models.
  
• MAP: To use the maximum a posteriori spatial correlation model.
  
• all: To use all the 1000 and the maximum a posteriori spatial correlation models.
  

gmim:
Ground motion intensity measure from the available models (e.g., 'PGA').

Run

import gmKriger

site      = ['Alameda Naval Air Station', 'Treasure Island', 'Alameda Bay Farm Island', 'Farris Farm', 'POO7']
latitude  = [37.785748,37.8261394,37.73380567,36.91026828,37.805242]
longitude = [-122.309346,-122.3712351,-122.250101,-121.7437891,-122.339702]
Vs30      = [186.2,181.1,230.7,209.5,223]

earthquake = '1989 M6.9 Loma Prieta'
model      = 'realizations'
gmim       = 'PGA'

gmKriger.get_Kgmim(site,latitude,longitude,Vs30,earthquake,model,gmim)

Site	Lat (deg)	Lon (deg)	PGA (g)	sigma_PGA (ln)
Alameda Naval Air Station	37.7857	-122.309	0.189312	0.386172
Treasure Island	37.8261	-122.371	0.135361	0.273654
Alameda Bay Farm Island	37.7338	-122.250	0.151978	0.429026
Farris Farm	36.9103	-121.744	0.458404	0.494209
POO7	37.8052	-122.339	0.154422	0.350264

Examples

• Example 1: Compute PGA for the 1989 Loma Prieta Earthquake using all the 1000 spatial correlation models. here.
• Example 2: Compute several ground motion intensity measures for the 2023 M7.8 Pazarcik Earthquake using the maximum aposteriori spatial correlation model. here.
• Example 3: Compute several ground motion intensity measures for the 1987 M6.5 Superstition Hills Earthquake all the 1000 and the maximum aposteriori spatial correlation model. here.

Acknowledgements

• The implementation of gmKriger greatly benefitted from discussions with Scott J. Brandenberg and Jonathan P. Stewart.

Citation

If you use these codes, please cite:

Pretell, R. (2024). gmKriger: A Kriging-based ground motion intensity measure calculator (0.2.0). Zenodo. https://doi.org/10.5281/zenodo.10691892

Pretell, R., Brandenberg, S., and Stewart, J. (2023) "Consistently computed ground motion intensity measures for liquefaction triggering assessment." DesignSafe-CI. https://doi.org/10.17603/ds2-6vj1-t096 v2

Pretell, R., Brandenberg, S.J., Stewart, J.P. (2024). "Consistent framework for PGA estimation at liquefaction case history sites: Application to the 1989 M6.9 Loma Prieta Earthquake." In: Proceedings of Geo-Congress 2024, Vancouver, Canada, Feb. 25-28, 2024. https://doi.org/10.1061/9780784485316.018

Contact

For any questions or comments, contact Renmin Pretell at rpretell@unr.edu.