ETASbootstrap (version 0.2.1)

simulate_aftershocks: 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"
)

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.

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).

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")