spatial_amplitude: Locate the source of a seismic event by modelling amplutide attenuation

Description

The function fits a model of signal amplitude attenuation for all grid cells of the distance data sets and returns the residual sum as measure of the most likely source location of an event.

Usage

spatial_amplitude(
  data,
  coupling,
  d_map,
  aoi,
  v,
  q,
  f,
  a_0,
  normalise = TRUE,
  output = "variance",
  n_cores = 1
)

Value

A raster object with the location output metrics for each grid cell.

Arguments

data: Numeric matrix or eseis object, seismic signals to work with. Since the function will calculate the maxima of the data it is usually the envolopes of the data that should be used here.
coupling: Numeric vector, coupling efficiency factors for each seismic station. The best coupled station (or the one with the highest amplification) must receive 1, the others must be scaled relatively to this one.
d_map: List object, distance maps for each station (i.e., SpatialGridDataFrame objects). Output of spatial_distance.
aoi: raster object that defines which pixels are used to locate the source. If omitted, the entire distance map extent is used. aoi and d_map objects must have the same extents, projections and pixel sizes. The aoi map must be of logical values.
v: Numeric value, mean velocity of seismic waves (m/s).
q: Numeric value, quality factor of the ground.
f: Numeric value, frequency for which to model the attenuation.
a_0: Logical value, start parameter of the source amplitude, if not provided, a best guess is made as 100 times the maximum amplitude value of the data set.
normalise: Logical value, option to normalise sum of residuals between 0 and 1. Default is TRUE.
output: Character value, type of metric the function returns. One out of "residuals" (sums of the squared model residuals) or "variance" (variance reduction, cf. Walter et al. (2017)). Default is "variance".
n_cores: Numeric value, number of CPU cores to use. Disabled by setting to 1. Default is 1.

Author

Michael Dietze

Examples

Run this code


if (FALSE) {

## create synthetic DEM
dem <- raster::raster(nrows = 20, ncols = 20, 
                     xmn = 0, xmx = 10000, 
                     ymn= 0, ymx = 10000, 
                     vals = rep(0, 400))

## define station coordinates
sta <- data.frame(x = c(1000, 9000, 5000),
                 y = c(1000, 1000, 9000),
                 ID = c("A", "B", "C"))

## create synthetic signal (source in towards lower left corner of the DEM)
s <- rbind(dnorm(x = 1:1000, mean = 500, sd = 50) * 100,
          dnorm(x = 1:1000, mean = 500, sd = 50) * 2,
          dnorm(x = 1:1000, mean = 500, sd = 50) * 1)

## plot DEM and stations
raster::plot(dem)
text(x = sta$x, 
    y = sta$y, 
    labels = sta$ID)

## calculate spatial distance maps and inter-station distances
D <- eseis::spatial_distance(stations = sta[,1:2],
                            dem = dem)

## locate signal
e <- spatial_amplitude(data = s, 
                      d_map = D$maps, 
                      v = 500, 
                      q = 50, 
                      f = 10)

## get most likely location coordinates (example contains two equal points)
xy <- matrix(sp::coordinates(e)[raster::values(e) == max(raster::values(e))],
            ncol = 2)[1,]

## plot output
raster::plot(e)
points(xy[1], 
      xy[2],
      pch = 20)
points(sta[,1:2])

}