gpsgridder
gpsgridder - Interpolate GPS strain vectors using Green’s functions for elastic deformation
Synopsis
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 ]
[ -fflags ]
[ -hheaders ]
[ -oflags ]
[ -x[[-]n] ]
[ -:[i|o] ]
Note: No space is allowed between the option flag and the associated arguments.
Description
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 effecting 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.
Required Arguments
- table
- table with GPS strain rates at discrete locations. We expect the input
format 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.
Optional Arguments
- -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 -Cv to use the
largest eigenvalues needed to explain value % of the data variance.
Specify -Cr 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 data uncertainties.
Alternatively, use -Cn 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.
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 estimate and the misfit.
- -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 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][=|+][/yinc[unit][=|+]]
- 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 = 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 + 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 GMT File Formats for
details. Note: if -Rgrdfile is used then the grid spacing has
already been initialized; use -I to override the values.
- -L
- Do not remove a linear (1-D) or planer (2-D) trend when -D
selects mode 0-3 [For those Cartesian cases a least-squares line or
plane is modeled and removed, then restored after fitting a spline
to the residuals]. However, in mixed cases with both data values and
gradients, or for spherical surface data, only the mean data value
is removed (and later and restored).
- -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.
- -R[unit]xmin/xmax/ymin/ymax[r] (more ...)
- Specify the region of interest.
- -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]
- Data one-sigma 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 this only has an effect if -C is used.
[Default uses no weights or uncertainties].
- -V[level] (more ...)
- Select verbosity level [c].
- -fg
- Geographic grids (dimensions of longitude, latitude) will be converted to
meters via a “Flat Earth” approximation using the current ellipsoid parameters.
- -h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
- Skip or produce header record(s). Not used with binary data.
- -icols[l][sscale][ooffset][,...] (more ...)
- Select input columns (0 is first column).
- -r (more ...)
- Set pixel node registration [gridline].
- -:[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 use just -).
- -+ 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 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).
Examples
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
References
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., in press.