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Spatial Interpolation of SHmax

Source: R/interpolation.R
stress2grid.Rd

Stress field interpolation and wavelength analysis using a kernel (weighted) mean/median and standard deviation/IQR of stress data. Parameters can be adjusted to have inverse-distance-weighting (IDW) or nearest-neighbor interpolations (NN).

Usage

stress2grid(
  x,
  stat = c("mean", "median", "tensor"),
  grid = NULL,
  lon_range = NULL,
  lat_range = NULL,
  gridsize = 2,
  min_data = 3L,
  max_data = Inf,
  max_sd = Inf,
  threshold = deprecated(),
  min_dist_threshold = 200,
  arte_thres = deprecated(),
  method_weighting = FALSE,
  quality_weighting = TRUE,
  dist_weighting = c("inverse", "linear", "none"),
  idp = 1,
  qp = 1,
  mp = 1,
  dist_threshold = 0.1,
  R_range = seq(50, 1000, 50),
  axial = TRUE
)

stress2grid_stats(
  x,
  grid = NULL,
  lon_range = NULL,
  lat_range = NULL,
  gridsize = 2,
  min_data = 4L,
  max_data = Inf,
  threshold = deprecated(),
  min_dist_threshold = 200,
  arte_thres = deprecated(),
  method_weighting = FALSE,
  quality_weighting = TRUE,
  dist_weighting = c("inverse", "linear", "none"),
  idp = 1,
  qp = 1,
  mp = 1,
  dist_threshold = 0.1,
  R_range = seq(50, 1000, 50),
  mode = FALSE,
  kappa = 10,
  axial = TRUE,
  ...
)

Arguments

x

sf object containing

azi

\(\sigma_\text{Hmax}\) in degree

unc

(optional) Uncertainties of SHmax in degree

type

(optional) Methods used for the determination of the direction of \(\sigma_\text{Hmax}\)

stat

whether the direction of interpolated \(\sigma_\text{Hmax}\) is based on the circular mean and standard deviation ("mean", the default), the quasi-circular median and quasi-interquartile range ("median"), or the orientation tensor based principal direction and dispersion ("tensor").

grid

(optional) Point object of class sf.

lon_range, lat_range

(optional) numeric vector specifying the minimum and maximum longitudes and latitudes (ignored if grid is specified).

gridsize

numeric. Target spacing of the regular grid in decimal degree. Default is 2.5. (is ignored if grid is specified)

min_data

integer. If the number of observations within distance R_range is less than min_data, a missing value NA will be generated. Default is 3 for stress2grid() and 4 for stress2grid_stats().

max_data

integer. The number of nearest observations that should be used for prediction, where "nearest" is defined in terms of the space of the spatial locations. Default is Inf.

max_sd

numeric. Threshold for deviation of direction in degrees; if exceeds, missing values will be generated.

threshold

[Deprecated] is no longer supported; use max_sd instead.

min_dist_threshold

numeric. Distance threshold for smallest distance of the prediction location to the next observation location. Default is 200 km.

arte_thres

[Deprecated] is no longer supported; use min_dist_threshold instead.

method_weighting

logical. If a method weighting should be applied: Default is FALSE. If FALSE, overwrites mp.

quality_weighting

logical. If a quality weighting should be applied: Default is TRUE. If FALSE, overwrites qp.

dist_weighting

Distance weighting method which should be used. One of "none", "linear", or "inverse" (the default).

idp, qp, mp

numeric. The weighting power of inverse distance, quality and method (the higher the value, the more weight). Default is 1. When set to 0, no weighting is applied. Only effective when dist_weighting=="inverse".

dist_threshold

numeric. Distance weight to prevent overweight of data nearby (0 to 1). Default is 0.1

R_range

numeric value or vector specifying the kernel half-width(s) search radii, i.e. the maximum distance from the prediction location to be used for prediction (in km). Default is seq(50, 1000, 50). If combined with max_data, both criteria apply.

axial

Logical. Whether angles in x$azi are uniaxial (FALSE) or biaxial (TRUE, the default).

mode

logical. Should the circular mode be included in the statistical summary (slow)?

kappa

numeric. von Mises distribution concentration parameter used for the circular mode. Will be estimated using est.kappa() if not provided.

...

(optional) arguments to circular_summary()

Value

sf object containing

lon,lat

longitude and latitude in degrees

azi

Circular mean od median SHmax in degree

sd

Circular standard deviation or Quasi-IQR on the Circle of \(\sigma_\text{Hmax}\) in degrees

R

Search radius in km

mdr

Mean distance between grid point and datapoints per search radius

N

Number of data points in search radius

When stress2grid_stats(), azi and sd are replaced by the output of circular_summary().

Details

stress2grid() is originally based on the MATLAB script "stress2grid" by Ziegler and Heidbach (2019): https://github.com/MorZieg/Stress2Grid. The tectonicr version has been significantly modified to provide better performance and more flexibility.

stress2grid_stats() is based on stress2grid() but calculates circular summary statistics (see circular_summary()).

Note

Although specialized for stress fields, this spatial interpolation algorithm can be applied to type of data. Please adjust the axial argument when applied to different, directional data sets.

References

Ziegler, M. and Heidbach, O. (2019). Matlab Script Stress2Grid v1.1. GFZ Data Services. doi:10.5880/wsm.2019.002

See also

dist_greatcircle(), PoR_stress2grid(), compact_grid(), circular_mean(), circular_median(), circular_sd(), circular_summary()

Examples

data("san_andreas")

# Inverse Distance Weighting interpolation:
stress2grid(san_andreas, stat = "median") |> head()
#> Simple feature collection with 6 features and 7 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: -112.82 ymin: 24.08 xmax: -112.82 ymax: 24.08
#> Geodetic CRS:  WGS 84
#>       lon   lat      azi sd   R  N       mdr              geometry
#> 1 -112.82 24.08       NA  0  50  0        NA POINT (-112.82 24.08)
#> 2 -112.82 24.08       NA  0 100  0        NA POINT (-112.82 24.08)
#> 3 -112.82 24.08 150.8269  7 150  4 0.8224433 POINT (-112.82 24.08)
#> 4 -112.82 24.08 150.8269  7 200  4 0.6168325 POINT (-112.82 24.08)
#> 5 -112.82 24.08 147.0000  7 250  7 0.6785179 POINT (-112.82 24.08)
#> 6 -112.82 24.08 163.0000  1 300 17 0.7787910 POINT (-112.82 24.08)

stress2grid(san_andreas, stat = "tensor") |> head()
#> Simple feature collection with 6 features and 7 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: -112.82 ymin: 24.08 xmax: -112.82 ymax: 24.08
#> Geodetic CRS:  WGS 84
#>       lon   lat       azi         sd   R  N       mdr              geometry
#> 1 -112.82 24.08        NA 0.00000000  50  0        NA POINT (-112.82 24.08)
#> 2 -112.82 24.08        NA 0.00000000 100  0        NA POINT (-112.82 24.08)
#> 3 -112.82 24.08 -10.76635 0.13089882 150  4 0.8224433 POINT (-112.82 24.08)
#> 4 -112.82 24.08 -10.76635 0.13089882 200  4 0.6168325 POINT (-112.82 24.08)
#> 5 -112.82 24.08 -16.83535 0.11629943 250  7 0.6785179 POINT (-112.82 24.08)
#> 6 -112.82 24.08 -14.82624 0.07587942 300 17 0.7787910 POINT (-112.82 24.08)

# Nearest Neighbor interpolation:
stress2grid(san_andreas, stat = "median", max_data = 5) |> head()
#> Simple feature collection with 6 features and 7 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: -112.82 ymin: 24.08 xmax: -112.82 ymax: 24.08
#> Geodetic CRS:  WGS 84
#>       lon   lat      azi sd   R N       mdr              geometry
#> 1 -112.82 24.08       NA  0  50 0        NA POINT (-112.82 24.08)
#> 2 -112.82 24.08       NA  0 100 0        NA POINT (-112.82 24.08)
#> 3 -112.82 24.08 150.8269  7 150 4 0.8224433 POINT (-112.82 24.08)
#> 4 -112.82 24.08 150.8269  7 200 4 0.6168325 POINT (-112.82 24.08)
#> 5 -112.82 24.08 147.0000  7 250 5 0.5653079 POINT (-112.82 24.08)
#> 6 -112.82 24.08 147.0000  7 300 5 0.4710899 POINT (-112.82 24.08)

if (FALSE) { # \dontrun{
stress2grid_stats(san_andreas, mode = TRUE) |> head()
} # }