simulate_background_earthquakes {ETASbootstrap}

Simulate a catalog of background earthquakes

Description

In fitting the ETAS model to the earthquake data catalog of interest (earthquake_data), the background intensity function {\mu} is estimated. This function performs a simulation of background events based on the estimate \hat{{\mu}}. The time period for the simulated background catalog is consistent with that of earthquake_data.

Usage

simulate_background_earthquakes(earthquake_data_plus)

Arguments

earthquake_data_plus

An object of data.frame with 7 columns: date, time, longitude, latitude, magnitude, bandwidth, and probability, in this order and in a consistent format for the first 5 columns. The columns bandwidth and probability are two numeric vectors. The column bandwidth records the smoothness bandwidths used in variable kernel estimation and the column probability contains the probability for each earthquake in the catalog of interest (observed earthquakes) to be a background event; see the etas function in the ETAS package (Jalilian, 2019) and the articles of Zhuang et al. (2002, 2004).

Value

background_catalog: An object of data.frame with 5 columns: date, time, longitude, latitude, and magnitude of the simulated background earthquakes, in this order and a consistent format.

References

Dutilleul, P., Genest, C., Peng, R., 2024. Bootstrapping for parameter uncertainty in the space-time epidemic-type aftershock sequence model. Geophysical Journal International 236, 1601–1608.

Jalilian, A. (2019). ETAS: An R package for fitting the space-time ETAS model to earthquake data. Journal of Statistical Software, Code Snippets, 88(1), 1–39. doi:10.18637/jss.v088.c01.

Zhuang, J., Y. Ogata, and D. Vere-Jones (2002). Stochastic declustering of space-time earthquake occurrences. Journal of the American Statistical Association 97(458), 369–380.

Zhuang, J., Y. Ogata, and D. Vere-Jones (2004). Analyzing earthquake clustering features by using stochastic reconstruction. Journal of Geophysical Research: Solid Earth 109(B05301).

Examples

set.seed(1)
simulate_background_earthquakes(VCI_earthquakes_plus)