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).
| GMIM | Key | Unit |
|---|---|---|
| Peak ground acceleration | PGA | g |
| Peak ground velocity | PGV | cm/s |
| Arias intensity | Ia | m/s |
| Cumulative absolute velocity | CAV | m/s |
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 |
|---|---|---|---|---|
| 1968 M8.2 Tokachi-Oki | No | No | Yes | Yes |
| 1971 M6.6 San Fernando | Yes | Yes | Yes | Yes |
| 1978 M7.7 Miyagiken-Oki | No | No | Yes | Yes |
| 1979 M6.5 Imperial Valley | Yes | Yes | Yes | Yes |
| 1980 M6.3 Victoria | Yes | Yes | Yes | Yes |
| 1981 M5.9 Westmorland | Yes | Yes | Yes | Yes |
| 1983 M7.7 Nihonkai-Chubu | No | No | Yes | Yes |
| 1983 M6.8 Nihonkai-Chubu | No | No | Yes | Yes |
| 1987 M6.5 Superstition Hills | Yes | Yes | Yes | Yes |
| 1989 M6.9 Loma Prieta | Yes | Yes | Yes | Yes |
| 1993 M7.6 Kushiro-Oki Hokkaido | No | No | Yes | Yes |
| 1994 M6.7 Northridge | Yes | Yes | Yes | Yes |
| 1994 M8.3 Toho-Oki Hokkaido | No | No | Yes | Yes |
| 1995 M6.9 Kobe | Yes | Yes | Yes | Yes |
| 1999 M7.5 Kocaeli | Yes | Yes | Yes | Yes |
| 1999 M7.6 Chi-Chi | Yes | Yes | Yes | Yes |
| 2000 M6.6 Tottori | Yes | Yes | Yes | Yes |
| 2003 M8.3 Tokachi | No | No | Yes | Yes |
| 2007 M6.8 Chuetsu-oki | Yes | Yes | Yes | Yes |
| 2010 M7.2 El Mayor-Cucapah | Yes | Yes | Yes | Yes |
| 2010 M7.0 Darfield | Yes | Yes | Yes | Yes |
| 2010 M8.8 Maule | No | No | Yes | Yes |
| 2011 M6.2 Christchurch | Yes | Yes | Yes | Yes |
| 2011 M5.0 Christchurch | Yes | No | No | No |
| 2011 M6.0 Christchurch | Yes | Yes | Yes | Yes |
| 2011 M5.9 Lyttelton | Yes | Yes | Yes | Yes |
| 2011 M9.1 Tohoku-Oki | No | No | Yes | Yes |
| 2012 M6.1 Emilia | Yes | Yes | Yes | Yes |
| 2012 M6.0 Emilia | Yes | Yes | Yes | Yes |
| 2019 M7.06 Ridgecrest | Yes | Yes | Yes | Yes |
| 2019 M6.48 Ridgecrest | Yes | Yes | Yes | Yes |
| 2020 M7.0 Samos | Yes | Yes | Yes | Yes |
| 2023 M7.81 Pazarcik | Yes | Yes | Yes | Yes |
| 2023 M7.74 Kahramanmaras | Yes | Yes | Yes | Yes |
| 2023 M6.81 Nurdagi | Yes | Yes | Yes | Yes |
| 2023 M6.37 Yayladagi | Yes | Yes | Yes | Yes |
Install the following Python libraries. Important: gmKriger currently requires the below specific pygmm commit.
pip install git+https://github.com/arkottke/pygmm@46403fd0a2c5ac1273e5837956971316360fa081
pip install gmKrigergmKriger leverages both Cython and Python implementations of geostats. For small problems, computational performance is comparable for the two. The Cython implementation can significantly improve performance for larger problems. The Cython backend requires a C/C++ compiler toolchain.
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.
gmim:
Ground motion intensity measure from the available models (e.g., 'PGA').
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 Bay Farm Island | 37.734 | -122.250 | 0.151 | 0.396 |
| Alameda Naval Air Station | 37.786 | -122.309 | 0.204 | 0.294 |
| Farris Farm | 36.910 | -121.744 | 0.350 | 0.350 |
| POO7 | 37.805 | -122.340 | 0.152 | 0.322 |
| Treasure Island | 37.826 | -122.371 | 0.133 | 0.250 |
- Example 1: Compute PGAs for the 1989 Loma Prieta Earthquake using all the 1000 spatial correlation models. here.
- Example 2: Cython backend. Compute PGA, PGV, Ia, and CAV for the 1989 Loma Prieta Earthquake using 1000 spatial correlation models. here.
- Example 3: Python backend. Compute PGA, PGV, Ia, and CAV for the 1989 Loma Prieta Earthquake using 1000 spatial correlation models. here.
- Example 4: Compute PGA, PGV, Ia, and CAV for the 2023 M7.8 Pazarcik Earthquake using the maximum a posteriori spatial correlation model. here.
- Example 5: Compute PGA, PGV, Ia, and CAV for the 1987 M6.5 Superstition Hills Earthquake all the 1000 spatial correlation models. here.
Albert R. Kottke kindly allowed modifications to the pygmm NGAWest2 GMM implementations that benefit gmKriger. This is greatly appreciated.
Pretell, R., Brandenberg, S.J., and Stewart, J.P. (2026). gmKriger: A Kriging-based ground motion intensity measure calculator (1.1.1). Zenodo. https://doi.org/10.5281/zenodo.10399418
Pretell, R., Brandenberg, S.J., and Stewart, J.P. (2026). “Ground motion intensity measures at liquefaction field case history sites.” *Journal of Geotechnical and Geoenvironmental Engineering. 10.1061/JGGEFK/GTENG-14212 (In Press).
Pretell, R., Brandenberg, S.J., Stewart, J.P. (2024). Ground motion intensity measures at liquefaction field case history sites. Report submitted to CALTRANS. GIRS-2024-02. http://doi.org/10.34948/N35K59
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
Pretell, R., Brandenberg, S., and Stewart, J. (2026). "Consistently computed ground motion intensity measures for liquefaction triggering assessment." DesignSafe-CI. https://doi.org/10.17603/ds2-6vj1-t096 v3
For any questions or comments, contact Renmin Pretell (rpretell at unr.edu).