spatial_track {eseis}

Track a spatially mobile seismic source

Description

This function allows tracking a spatially mobile seismic source and thereby estimating the source amplitude and the model's variance reduction as a measure of quality or robustness of the time-resolved estimates.

Usage

spatial_track(
  data,
  coupling,
  window,
  overlap = 0,
  d_map,
  aoi,
  v,
  q,
  f,
  k,
  qt = 1,
  dt,
  model = "SurfSpreadAtten",
  cpu,
  verbose = FALSE,
  plot = FALSE
)

Arguments

data

Numeric matrix or eseis object, seismic signals used for source tracking. Note that the function will start tracking within a smaller time window, narrows be the maximum signal arrival time differences as defined by the maximum inter station distance and the seismic velocity. The signals should be the envelopes of waveforms.

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.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.

window

Numeric value, time window for which the source is tracked. If omitted, ten time steps are generated.

overlap

Numeric value between 0 and 1, fraction of overlap of time windows used for source tracking. Default is 0.

d_map

List object, distance maps for each station (i.e., SpatialGridDataFrame objects). Output of spatial_distance.

aoi

Raster object (optional) 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.

k

Numeric value, fraction of surface wave contribution to signals. Only relevant for models that include mixture of surface and body waves (see model_amplitude).

qt

Numeric value, quantile threshold that defines acceptable location estimates. Default is 1 (only single best estimate is kept).

dt

Numeric value, sampling frequency. Only required if input signals are no eseis objects.

model

Character value,

cpu

Numeric value, fraction of CPUs to use for parallel processing. If omitted, one CPU is used

verbose

Logical value, optional screen output of processing progress. Default is FALSE.

plot

Logical value, enable graphical output of key results. Default is FALSE.

Details

The method is based on ideas published by Burtin et al. (2016), Walter et al. 82017) and Perez-Guillen et al. (2019) and implemented in the R package eseis by Dietze (2018). It is related to the function spatial_amplitude, which can be used to locate spatially stable seismic sources by the same technique, and it resuires prepared input data as delivered by the function spatial_distance.

The input data (data) should ideally be a list of eseis objects (alternatively a matrix with seismic signal traces) containing the envelopes of the seismic event to track (i.e., describe by its location and amplitude as a function of propagation time). The temporal resolution of the track is defined by the arguments window and overlap (as a fraction between 0 and 1). The approach is based on fitting known amplitude-distance functions (for an overview of available functions see model_amplitude) to the envelope time snippets for each pixel of a grid, which provides the distance from a pixel to each seismic station, i.e., the distance map set d_map. To avoid fitting each of the pixels of the distance map, one can provide an area of interest, AOI (aoi), which has the same extent and resolution as the distance map set and pixel values are either TRUE or FALSE. Depending on which amplitude-distance function is chosen, further arguments need to be provided (ground quality factor q, center frequency of the signal f). The apparent seismic wave velocity v is required regardless, either as fit model parameter or to correct the amplitude time snippets for the travel time delay from the source to the respective pixel of the distance map set. The output of the function can be provided with uncertainty estimates on all output values. The uncertainty is based on the size of accepted location estimates per time step, as defined by the variance reduction quantile threshold qt (i.e., all locations above this quantile will be assumed to be valid location estimates, whose parameters will be used to estimate the uncertainty). Note that usually, qt should be set to around 0.99, a value that depends on the number of pixels in the distance map set and that affects the location uncertainty, which in many cases is about 10 Note however, that this value is purely arbitrary and should be based on field-based control data. It is possible to run the function in a multi-CPU mode, to speed up computational time, using the argument cpu. Also, the function can generate generic plot output of the results, a panel of three plots: source trajectory, source amplitude and variance reduction.

Note that depending on the resolution of the distance map set, number of included seismic stations, and number of time windows, the function can take significant processing time. 50 time steps for 5 stations and 5000 pixels per distance map requires about 10 minutes time on a normal grade computer using a single CPU.

Value

A List object with summarising statistics of the fits.

References

Burtin, A., Hovius, N., and Turowski, J. M.: Seismic monitoring of torrential and fluvial processes, Earth Surf. Dynam., 4, 285–307, https://doi.org/10.5194/esurf-4-285-2016, 2016.

Dietze, M.: The R package 'eseis' – a software toolbox for environmental seismology, Earth Surf. Dynam., 6, 669–686, https://doi.org/10.5194/esurf-6-669-2018, 2018.

Perez-Guillen, C., Tsunematsu, K., Nishimura, K., and Issler, D.: Seismic location and tracking of snow avalanches and slush flows on Mt. Fuji, Japan, Earth Surf. Dynam., 7, 989–1007, https://doi.org/10.5194/esurf-7-989-2019, 2019.

Walter, F., Burtin, A., McArdell, B. W., Hovius, N., Weder, B., and Turowski, J. M.: Testing seismic amplitude source location for fast debris-flow detection at Illgraben, Switzerland, Nat. Hazards Earth Syst. Sci., 17, 939–955, https://doi.org/10.5194/nhess-17-939-2017, 2017.

Examples

## Not run: 

x <- spatial_track(data = data, 
                   window = 5, 
                   overlap = 0.5,
                   d_map = D$maps, 
                   aoi = aoi, 
                   v = 800, 
                   q = 40, 
                   f = 12, 
                   qt = 0.99)


## End(Not run)