simulate_aftershocks {ETASbootstrap}

Simulate a catalog of aftershocks

Description

When a catalog of background earthquakes is given, this function can be applied to simulate aftershocks under the intensity function \sum_{i:t_i<t}\hat{k}(m_i)\hat{g}(t-t_i)\hat{f}(x-x_i,y-y_i \mid m_i), which is determined by the target parameter values given by the user.

Usage

simulate_aftershocks(
  parameters_target,
  background_catalog,
  time_begin_background = NULL,
  longitude_limit = NULL,
  latitude_limit = NULL,
  time_limit = NULL,
  magnitude_sample = NULL,
  magnitude_threshold = NULL,
  time_zone = "GMT"
)

Arguments

parameters_target

A numerical vector of size 7, (\hat{A},\hat{c},\hat{\alpha},\hat{p},\hat{D},\hat{q},\hat{\gamma}), specifying the target values of parameters in the ETAS model.

background_catalog

An object of class "data.frame" with 5 columns: recording date, time, longitude, latitude, and magnitude of the background events, in this order and in a format consistent with that of earthquake_data in the function ETAS_Boots.

time_begin_background

A character string, in the date-time format, that specifies the beginning of the time span in background_catalog. If NULL, it will be set by the program to the date-time of the first earthquake in background_catalog.

longitude_limit

A vector of size 2 (xlim_min, xlim_max) specifying the longitude boundaries for the simulated aftershocks. If NULL, xlim_min and xlim_max will be set by the program to the minimum and maximum values of the longitude for the earthquakes in background_catalog, respectively. Only the simulated aftershocks with a longitude inside longitude_limit will be kept.

latitude_limit

A vector of size 2 (ylim_min, ylim_max) specifying the latitude boundaries for the simulated aftershocks. If NULL, ylim_min and ylim_max will be set by the program to the minimum and maximum values of latitude for the earthquakes in background_catalog, respectively. Only the simulated aftershocks with a latitude inside latitude_limit will be kept.

time_limit

A vector of size 2 (tlim_min, tlim_max) specifying the time span for the simulated aftershocks. If NULL, tlim_min and tlim_max will be set by the program to the date-time of the first and last earthquakes (in chronological order) in background_catalog, respectively. Only the simulated aftershocks inside the specified time span will be kept.

magnitude_sample

A vector recording the sample from the distribution of earthquake magnitudes (s_{\beta}(m)). If NULL, the magnitudes of earthquakes in background_catalog will be used.

magnitude_threshold

A decimal value specifying the magnitude threshold to be applied. Only the simulated aftershocks with a magnitude of at least mag_threshold will be kept. If NULL, the minimum magnitude of the events in background_catalog will be used as magnitude_threshold.

time_zone

A character string specifying the time zone. The default setting "GMT" is the UTC (Universal Time Coordinated).

Value

aftershocks_simulated: An object of class "data.frame" with 5 columns: recording the date, time, longitude, latitude and magnitude of the simulated aftershocks, 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.

Examples

set.seed(1)
simulate_aftershocks(parameters_target = c(0.2424, 0.0068, 0.9771, 1.2200, 
                                           0.0033, 2.4778, 0.1718),
                     background_catalog = VCI_simulated_background_earthquakes,
                     time_begin_background = "2000/01/01",
                     longitude_limit = c(-131, -126.25),
                     latitude_limit = c(48, 50),
                     time_limit = c("2000/01/01", "2018/04/27"),
                     magnitude_sample = VCI_magnitude_sample,
                     magnitude_threshold = 3.5,
                     time_zone="GMT")