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.
spatial_track(
data,
coupling,
window,
overlap = 0,
d_map,
aoi,
v,
q,
f,
k,
qt = 1,
dt,
model = "SurfSpreadAtten",
cpu,
verbose = FALSE,
plot = FALSE
)A List object with summarising statistics of the fits.
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.
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.
Numeric value, time window for which the source is
tracked. If omitted, ten time steps are generated.
Numeric value between 0 and 1, fraction of overlap
of time windows used for source tracking. Default is 0.
List object, distance maps for each station (i.e.,
SpatialGridDataFrame objects). Output of spatial_distance.
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.
Numeric value, mean velocity of seismic waves (m/s).
Numeric value, quality factor of the ground.
Numeric value, frequency for which to model the
attenuation.
Numeric value, fraction of surface wave contribution to
signals. Only relevant for models that include mixture of surface and
body waves (see model_amplitude).
Numeric value, quantile threshold that defines acceptable
location estimates. Default is 1 (only single best estimate is
kept).
Numeric value, sampling frequency. Only required if
input signals are no eseis objects.
Character value,
Numeric value, fraction of CPUs to use for parallel
processing. If omitted, one CPU is used
Logical value, optional screen output of processing
progress. Default is FALSE.
Logical value, enable graphical output of key results.
Default is FALSE.
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.
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.
if (FALSE) {
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)
}
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