This page presents the code found on the spatial correlation repository: https://github.com/ucgmsim/stochastic_event_set. The repository has all the references cited here, which can be consulted when something is not clear.
Spatial Correlation
There are two main usages of the spatial correlation. The first one is related to Ground Motion Prediction Equations (GMPE) and the second is relevant for physics-based simulations (like CS).
GMPE
Spatial correlation can used in two ways for GMPE. In the first case, it will allow us to generate consistent IMs for a set of close geolocations. The second usage is to use spatial correlation between sites with observed IMs, coming from Strong Motion Stations (SMS) to obtain GMPE median and sigma values that are more in accordance to what has been observed.
Spatially correlated IMs
The idea is to allow the study the impact over several close locations at the same time, in opposition to the more common approach of generating IM observations for a single location.
For this purpose, we have implemented the equations as in Jayaram, 2018 and Loth and Baker, 2013. Basically, the algorithm is as follows:
- Calculate the correlation matrix for all sites. For the correlation, we need the distance that is then fed to the Loth and Baker, 2013 model, which works for several pSA periods.
- Perform the Cholesky decomposition on the correlation.
- Generate uncorrelated within-event values. Generate a unique intra-event value for all sites.
- Use Cholesky result to correlate within-event values. IM values for all sites are then given by the sum of the mean, the intra-event term and the correlated within-event values.
- Repeat N times as need.
The main script that calls all the needed functions is generate_realisations.py.
TODO:
- Add more testing.
- The script takes lots of parameters, see if we can use something like a config file instead?
Improved GMPE with SMS observations
In this part, we use SMS observations to influence mean and sigma values from GMPEs. The way to do that is to use the spatial correlation between the sites where we have data and all the other sites.
The implementation follows both Bradley, 2013 and Stafford, 2009:
Physics-based simulations
For the case of the simulated correlations, we have explored two types of prototypes. The first one to analyse one simulation and the GMPE to compare the simulated spatial correlation with the Jayaram et al. model. The second type of computation is applied to a set of simulations for a given rupture, to obtain an estimation of the correlation. In the following, both will be explained, including what needs to be done going further.
Stochastic event set
The stochastic event set is a subset of a large number of
References
Bradley, B.A. (2013) Estimation of site-specific and spatially-distributed ground motion in the Christchurch earthquakes: Application to liquefaction evaluation and ground motion selection for post-event investigation. Queenstown, New Zealand: 19th New Zealand Geotechnical Society (NZGS) Symposium, 20-23 Nov 2013.
Loth, C. and Baker, J.W. (2013), A spatial cross‐correlation model of spectral accelerations at multiple periods. Earthquake Engng Struct. Dyn., 42: 397-417. https://doi.org/10.1002/eqe.2212
Jayaram, N. (2010) Probabilistic seismic lifeline risk assessment using efficient sampling and data reduction techniques. Stanford University.