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: ```Python 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

```Python 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.getKgmim(site,latitude,longitude,Vs30,earthquake,model,gmim) ``` | Site | Lat (deg) | Lon (deg) | PGA (g) | sigmaPGA (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., 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. (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

Relevant references

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.