gpsgridder - Interpolate GPS strain vectors using Green's
functions for elastic deformation
gpsgridder [ table ]
-Goutfile [ -Iincrement ] [
-Rregion ] [
-C[n|r|v]value[+ffile] ] [
-E[misfitfile] ] [ -F[d|f]fudge] [
-L ] [ -Nnodefile ] [ -Snu ] [
-Tmaskgrid ] [ -V[level] ] [
-W[w]] [ -bbinary ] [ -dnodata ] [
-eregexp ] [ -fflags ] [ -hheaders ] [ -oflags ]
[ -x[[-]n] ] [ -:[i|o] ]
Note: No space is allowed between the option flag and the
associated arguments.
gpsgridder grids 2-D vector data such as GPS velocities by
using a coupled model based on 2-D elasticity. The degree of coupling can be
tuned by adjusting the effective Poisson's ratio. The solution field can be
tuned to extremes such as incompressible (1), typical elastic (0.5) or even
an unphysical value of -1 that basically removes the elastic coupling of
vector interpolation. Smoothing is offered via the optional elimination of
small eigenvalues.
- table
- table with GPS strain rates at discrete locations. We expect the input
format to be x y u v [ du dv ] (see -W to specify
data uncertainties or weights). If lon lat is given you must supply
-fg and we will use a flat Earth approximation in the calculation
of distances.
- -Goutfile
- Name of resulting output file. (1) If options -R, -I, and
possibly -r are set we produce two equidistant output grids. In
this case, outfile must be a name template containing the C format
specifier %s, which will be replaced with u and v, respectively. (2) If
option -T is selected then -R, -I cannot be given as
the maskgrid determines the region and increments. Again, the
outfile must be a name template for the two output grids. (3) If
-N is selected then the output is a single ASCII (or binary; see
-bo) table written to outfile; if -G is not given
then this table is written to standard output. The -G option is
ignored if -C or -C0 is given.
- -C[n|r|v]value[+ffile]
- Find an approximate surface fit: Solve the linear system for the spline
coefficients by SVD and eliminate the contribution from all eigenvalues
whose ratio to the largest eigenvalue is less than value [Default
uses Gauss-Jordan elimination to solve the linear system and fit the data
exactly]. Optionally, append +ffile to save the eigenvalue
ratios to the specified file for further analysis. Finally, if a negative
value is given then +ffile is required and execution
will stop after saving the eigenvalues, i.e., no surface output is
produced. Specify -Cvvalue to use the largest eigenvalues
needed to explain value % of the data variance. Specify
-Crvalue to use the largest eigenvalues needed to leave
approximately value as the model misfit. If value is not
given then -W is required and we compute value as the rms of
the given data uncertainties. Alternatively, use -Cnvalue to
select the value largest eigenvalues. If a file is given
with -Cv then we save the eigenvalues instead of the ratios. Note:
1/4 of the total number of data constraints is a good starting point for
further experiments.
E[misfitfile]
Evaluate the spline exactly at the input data locations
and report statistics of the misfit (mean, standard deviation, and rms) for
u and v separately and combined. Optionally, append a filename
and we will write the data table, augmented by two extra columns after each of
the u and v columns holding the spline estimates and
misfits.
-
-F[d|f]fudge
- The Green's functions are proportional to terms like 1/r^2 and log(r) and
thus blow up for r == 0. To prevent that we offer two fudging schemes:
-Fddel_radius lets you add a constant offset to all radii
and must be specified in the user units. Alternatively, use
-Fffactor which will compute del_radius from the
product of the shortest inter-point distance and factor
[0.01].
- -Ixinc[unit][+e|n][/yinc[unit][+e|n]]
- x_inc [and optionally y_inc] is the grid spacing.
Optionally, append a suffix modifier. Geographical (degrees)
coordinates: Append m to indicate arc minutes or s to
indicate arc seconds. If one of the units e, f, k,
M, n or u is appended instead, the increment is
assumed to be given in meter, foot, km, Mile, nautical mile or US survey
foot, respectively, and will be converted to the equivalent degrees
longitude at the middle latitude of the region (the conversion depends on
PROJ_ELLIPSOID). If y_inc is given but set to 0 it will be reset
equal to x_inc; otherwise it will be converted to degrees latitude.
All coordinates: If +e is appended then the corresponding
max x (east) or y (north) may be slightly
adjusted to fit exactly the given increment [by default the increment may
be adjusted slightly to fit the given domain]. Finally, instead of giving
an increment you may specify the number of nodes desired by
appending +n to the supplied integer argument; the increment is
then recalculated from the number of nodes and the domain. The resulting
increment value depends on whether you have selected a gridline-registered
or pixel-registered grid; see App-file-formats for details. Note: if
-Rgrdfile is used then the grid spacing has already been
initialized; use -I to override the values.
- -L
- Leave trend alone. Do not remove a planer (2-D) trend from the data
before fitting the spline. [Default removes least squares plane, fits
normalized residuals, and restores plane].
- -Nnodefile
- ASCII file with coordinates of desired output locations x in the
first column(s). The resulting w values are appended to each record
and written to the file given in -G [or stdout if not specified];
see -bo for binary output instead. This option eliminates the need
to specify options -R, -I, and -r.
- -Snu
- Specify Poisson's ratio to use for this 2-D elastic sheet [0.5]. Note: 1.0
is incompressible in a 2-D formulation while -1 removes all coupling
between the two directions.
- -Tmaskgrid
- Only evaluate the solutions at the nodes in the maskgrid that are
not set to NaN. This option eliminates the need to specify options
-R, -I (and -r).
- -W[w]
- One-sigma data uncertainties for u and v are provided in the
last two columns. We then compute weights that are inversely proportional
to the uncertainties. Append w if weights are given instead of
uncertainties. This results in a weighted least squares fit. Note that
-W only has an effect if -C is used. [Default uses no
weights or uncertainties]. Note: At present the -W option is
unstable. We do not yet know if it reflects a coding bug or a
theoretical limitation. Users beware, and make sure you compare the
results with non-weighted output for basic sanity checking.
- -e[~]"pattern"
| -e[~]/regexp/[i] (more ...)
- Only accept data records that match the given pattern.
- -fg
- Geographic grids (dimensions of longitude, latitude) will be converted to
meters via a "Flat Earth" approximation using the current
ellipsoid parameters.
- -:[i|o] (more ...)
- Swap 1st and 2nd column on input and/or output.
- -^ or just -
- Print a short message about the syntax of the command, then exits (NOTE:
on Windows just use -).
- -+ or just +
- Print an extensive usage (help) message, including the explanation of any
module-specific option (but not the GMT common options), then exits.
- -? or no arguments
- Print a complete usage (help) message, including the explanation of all
options, then exits.
For map distance unit, append unit d for arc degree,
m for arc minute, and s for arc second, or e for meter
[Default], f for foot, k for km, M for statute mile,
n for nautical mile, and u for US survey foot. By default we
compute such distances using a spherical approximation with great circles.
Prepend - to a distance (or the unit is no distance is given) to
perform "Flat Earth" calculations (quicker but less accurate) or
prepend + to perform exact geodesic calculations (slower but more
accurate).
To compute the u and v strain rate grids from the
GPS data set gps.txt, containing x y u v du dv, on a 2x2 arc
minute grid for California, try
gmt gpsgridder gps.txt -R-125/-114/31/41 -I2m -fg -W -r -Ggps_strain_%s.nc -V
Haines, A. J. et al., 2015, Enhanced Surface Imaging of Crustal
Deformation, SpringerBriefs in Earth Sciences,
doi:10.1007/978-3-319-21578-5_2.
Sandwell, D. T. and P. Wessel, 2016, Interpolation of 2-D Vector
Data Using Constraints from Elasticity, Geophys. Res. Lett., 43,
10,703-10,709, http://dx.doi.org/10.1002/2016GL070340
gmt, greenspline nearneighbor, surface
2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F.
Wobbe