# gpsgridder

Interpolate GPS velocities using Green’s functions for elastic deformation

## Synopsis

**gmt gpsgridder** [ *table* ]
**-G***outgrid*
[ **-C**[[**n**|**r**|**v**]*value*[%]][**+c**][**+f***file*][**+i**][**+n**] ]
[ **-E**[*misfitfile*][**+r***reportfile*] ]
[ **-F**[**d**|**f**]*fudge* ]
[ **-I***increment* ]
[ **-L** ]
[ **-N***nodefile* ]
[ **-R***region* ]
[ **-S***nu* ]
[ **-T***maskgrid* ]
[ **-V**[*level*] ]
[ **-W**[**+s**|**w**] ]
[ **-b**binary ]
[ **-d**nodata[**+c***col*] ]
[ **-e**regexp ]
[ **-f**flags ]
[ **-h**headers ]
[ **-o**flags ]
[ **-qi**flags ]
[ **-x**[[-]n] ]
[ **-:**[**i**|**o**] ]
[ **--PAR**=*value* ]

**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 effective Poisson’s ratio, \(\nu\). 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. The solutions
for the two component grids are evaluated as

where the three 2-D elastic coupled Green’s functions are given by

Here, *r* is the radial distance between points **a** and **b** and *x* and *y* are the components of that
distance. The body forces \(\alpha_j\) and \(\beta_j\) are obtained by evaluating the solution at the data
locations and inverting the square linear system that results; see *Sandwell and Wessel* [2016] and
*Haines et al.* [2015] for details.

## Required Arguments

*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.

**-G***outgrid*[=*ID*][**+d***divisor*][**+n***invalid*][**+o***offset*|**a**][**+s***scale*|**a**][:*driver*[*dataType*][**+c***options*]]

Optionally, append =

IDfor writing a specific file format. The following modifiers are supported:

+d- Divide data values by givendivisor[Default is 1].

+n- Replace data values matchinginvalidwith a NaN.

+o- Offset data values by the givenoffset, or appendafor automatic range offset to preserve precision for integer grids [Default is 0].

+s- Scale data values by the givenscale, or appendafor automatic scaling to preserve precision for integer grids [Default is 1].

Note: Any offset is added before any scaling.+saalso sets+oa(unless overridden). To write specific formats via GDAL, use =gdand supplydriver(and optionallydataType) and/or one or more concatenated GDAL-cooptions using+c. See the “Writing grids and images” cookbook section for more details.

## Optional Arguments

**-C**[[**n**|**r**|**v**]*value*[%]][**+c**][**+f***file*][**+i**][**+n**]- Find an approximate surface fit: Solve the linear system for the
spline coefficients by SVD and eliminate the contribution from smaller eigenvalues [Default uses Gauss-Jordan elimination to solve the linear system and fit the data exactly (unless

**-W**is used)]. Append a directive and*value*to determine which eigenvalues to keep:**n**- Retain only the*value*numbers largest eigenvalues [all]. Optionally, append % to indicate*value*is given in percentage.**r**- Retain those eigenvalues whose ratio to the largest eigenvalue is less than*value*[Default, with*value*= 0].**v**- Retain the eigenvalues needed to ensure the model prediction variance fraction is at least*value*. Optionally, append % to indicate*value*is given in percentage.

Several optional modifiers are available:

**+c**- Produce the cumulative sum of these contributions, two (*u*and*v*) grids per eigenvalue (2-D only).**+f**- Append*file*to save the eigenvalues to the specified file for further analysis.**+i**- Produce the incremental sum of these contributions, two (*u*and*v*) grids per eigenvalue (2-D only).**+n**- If given then**+f***file*is required and execution will stop after saving the eigenvalues, i.e., no surface output is produced.

**Notes**: (1) Modifiers**++c**and**+i**require a file name with a suitable extension to be given via**-G**(we automatically insert “_cum_###” or “_inc_###” before the extension, using a fixed integer format for the eigenvalue number, starting at 0). (2) Use both modifiers to write both types of intermediate grids.

**-E**[*misfitfile*][**+r***reportfile*]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. If**-W**is given we also add two more columns with \(\chi_u^2\) and \(\chi_v^2\) values. Alternatively, if**-C**is used and history is computed (via one or more of modifiers**+c**and**+i**), then we will instead write a table with eigenvalue number, eigenvalue, percent of model variance explained, and overall rms, rms_u, and rms_v misfits. If**-W**is used we also append \(\chi^2\), \(\chi_u^2\), and \(\chi_v^2\).Optionally append this modifier:

**-F**[**d**|**f**]*fudge*The Green’s functions are proportional to \(r^{-2}\) and \(\log(r)\) and thus blow up for

*r == 0*. To prevent that we offer two fudging schemes:**-Fd***del_radius*lets you add a constant offset to all radii and must be specified in the user units. Alternatively, use**-Ff***factor*which will compute*del_radius*from the product of the shortest inter-point distance and*factor*[0.01].

**-I***x_inc*[**+e**|**n**][/*y_inc*[**+e**|**n**]]Set the grid spacing as

*x_inc*[and optionally*y_inc*].**Geographical (degrees) coordinates**: Optionally, append an increment unit. Choose among:**d**- Indicate arc degrees**m**- Indicate arc minutes**s**- Indicate arc seconds

If one of

**e**(meter),**f**(foot),**k**(km),**M**(mile),**n**(nautical mile) or**u**(US survey foot), the the increment 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 not given or given but set to 0 it will be reset equal to*x_inc*; otherwise it will be converted to degrees latitude.**All coordinates**: The following modifiers are supported:**+e**- Slightly adjust the max*x*(*east*) or*y*(*north*) to fit exactly the given increment if needed [Default is to slightly adjust the increment to fit the given domain].**+n**- Define the*number of nodes*rather than the increment, in which case the increment is recalculated from the number of nodes, the*registration*(see GMT File Formats), and the domain.**Note**: If**-R***grdfile*is used then the grid spacing and the registration have already been initialized; use**-I**and**-R**to override these 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].

**-N***nodefile*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 standard output if not specified]; see**-bo**for binary output instead. This option eliminates the need to specify options**-R**,**-I**, and**-r**.

**-R***xmin*/*xmax*/*ymin*/*ymax*[**+r**][**+u***unit*]Specify the region of interest. (See full description) (See cookbook information).

**-S***nu*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.

**-T***maskgrid*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**[**+s**|**w**]One-sigma data uncertainties for

*u*and*v*are provided in the last two columns. We then compute least squares weights that are inversely proportional to the square of the uncertainties [Default, or**+s**]. Instead, append**+w**if weights are given instead of uncertainties, in which case we just use the weights as provided (no squaring). 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].

**-V**[*level*]Select verbosity level [

**w**]. (See full description) (See cookbook information).

**-d**[**i**|**o**][**+c***col*]*nodata*(more …)Replace input columns that equal

*nodata*with NaN and do the reverse on output.

**-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.

**-h**[**i**|**o**][*n*][**+c**][**+d**][**+m***segheader*][**+r***remark*][**+t***title*] (more …)Skip or produce header record(s). Not used with binary data.

**-i***cols*[**+l**][**+d***divisor*][**+s***scale*|**d**|**k**][**+o***offset*][,*…*][,**t**[*word*]] (more …)Select input columns and transformations (0 is first column,

**t**is trailing text, append*word*to read one word only).

**-qi**[~]*rows*|*limits*[**+c***col*][**+a**|**t**|**s**] (more …)Select input rows or data limit(s) [default is all rows].

**-r**[**g**|**p**] (more …)Set 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 exit (

**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 exit.

**-?**or no argumentsPrint a complete usage (help) message, including the explanation of all options, then exit.

**--PAR**=*value*Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.

## Units

For map distance unit, append *unit* **d** for arc degree, **m** for arc
minute, and **s** for arc second, or **e** for meter [Default unless stated otherwise], **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 (**-jg**) using the authalic radius
(see PROJ_MEAN_RADIUS). You can use **-jf** to perform
“Flat Earth” calculations (quicker but less accurate) or **-je** to perform
exact geodesic calculations (slower but more accurate; see
PROJ_GEODESIC for method used).

## Notes on SVD solution

It may be difficult to know how many eigenvalues are needed for a suitable
approximate fit. The **-C** modifiers allow you to explore this further
by creating solutions for all cutoff selections and estimate model variance
and data misfit as a function of how many eigenvalues are used. The large
set of such solutions can be animated so it is easier to explore the changes
between solutions and to make a good selection for the **-C** directive values.
See the animations for one or more examples of this exploration.

## 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, and just
using about 25% of the largest eigenvalues, try:

```
gmt gpsgridder gps.txt -R-125/-114/31/41 -I2m -fg -W -r -Cn25% -Ggps_strain_%s.nc -V
```

## Deprecations

## 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., 43*, 10,703-10,709,
https://doi.org/10.1002/2016GL070340