.. index:: ! surface
*******
surface
*******
.. only:: not man
surface - Grid table data using adjustable tension continuous curvature splines
Synopsis
--------
.. include:: common_SYN_OPTs.rst_
**surface** [ *table* ] |-G|\ *outputfile.nc*
|SYN_OPT-I|
|SYN_OPT-R|
[ |-A|\ *aspect_ratio* ]
[ |-C|\ *convergence_limit*\ [%] ]
[ |-L|\ **l**\ *lower* ] [ **-Lu**\ *upper* ]
[ |-N|\ *max_iterations* ]
[ |-Q| ]
[ |-S|\ *search_radius*\ [**m**\ \|\ **s**] ]
[ |-T|\ [**i**\ \|\ **b**]\ *tension_factor* ]
[ |SYN_OPT-V| ]
[ |-Z|\ *over-relaxation_factor* ]
[ |SYN_OPT-a| ]
[ |SYN_OPT-bi| ]
[ |SYN_OPT-di| ]
[ |SYN_OPT-e| ]
[ |SYN_OPT-f| ]
[ |SYN_OPT-h| ]
[ |SYN_OPT-i| ]
[ **-r** ]
[ |SYN_OPT-:| ]
|No-spaces|
Description
-----------
**surface** reads randomly-spaced (x,y,z) triples from standard input
[or *table*] and produces a binary grid file of gridded values z(x,y) by
solving:
(1 - T) \* L (L (z)) + T \* L (z) = 0
where T is a tension factor between 0 and 1, and L indicates the
Laplacian operator. T = 0 gives the "minimum curvature" solution which
is equivalent to SuperMISP and the ISM packages. Minimum curvature can
cause undesired oscillations and false local maxima or minima (See Smith
and Wessel, 1990), and you may wish to use T > 0 to suppress these
effects. Experience suggests T ~ 0.25 usually looks good for potential
field data and T should be larger (T ~ 0.35) for steep topography data.
T = 1 gives a harmonic surface (no maxima or minima are possible except
at control data points). It is recommended that the user pre-process the
data with :doc:`blockmean`, :doc:`blockmedian`, or :doc:`blockmode` to avoid
spatial aliasing and eliminate redundant data. You may impose lower
and/or upper bounds on the solution. These may be entered in the form of
a fixed value, a grid with values, or simply be the minimum/maximum
input data values. Natural boundary conditions are applied at the edges,
except for geographic data with 360-degree range where we apply periodic
boundary conditions in the longitude direction.
Required Arguments
------------------
.. _-G:
**-G**\ *outputfile.nc*
Output file name. Output is a binary 2-D *.nc* file. Note that the
smallest grid dimension must be at least 4.
.. _-I:
.. include:: explain_-I.rst_
.. _-R:
.. |Add_-R| unicode:: 0x20 .. just an invisible code
.. include:: explain_-R.rst_
Optional Arguments
------------------
.. |Add_intables| unicode:: 0x20 .. just an invisible code
.. include:: explain_intables.rst_
.. _-A:
**-A**\ *aspect_ratio*
Aspect ratio. If desired, grid anisotropy can be added to the
equations. Enter *aspect_ratio*, where dy = dx / *aspect_ratio*
relates the grid dimensions. [Default = 1 assumes isotropic grid.]
.. _-C:
**-C**\ *convergence_limit*\ [%]
Convergence limit. Iteration is assumed to have converged when the
maximum absolute change in any grid value is less than
*convergence_limit*. (Units same as data z units). Alternatively,
give limit in percentage of rms deviation by appending %. [Default is
scaled to 1e-4 of the root-mean-square deviation of the data
from a best-fit (least-squares) plane.].
This is the final convergence limit at the desired grid spacing; for
intermediate (coarser) grids the effective convergence limit is divided
by the grid spacing multiplier.
.. _-L:
**-Ll**\ *lower* and **-Lu**\ *upper*
Impose limits on the output solution. **l**\ *lower* sets the lower
bound. *lower* can be the name of a grid file with lower bound
values, a fixed value, **d** to set to minimum input value, or **u**
for unconstrained [Default]. **u**\ *upper* sets the upper bound and
can be the name of a grid file with upper bound values, a fixed
value, **d** to set to maximum input value, or **u** for
unconstrained [Default]. Grid files used to set the limits may
contain NaNs. In the presence of NaNs, the limit of a node masked
with NaN is unconstrained.
.. _-N:
**-N**\ *max_iterations*
Number of iterations. Iteration will cease when *convergence_limit*
is reached or when number of iterations reaches *max_iterations*.
This is the final iteration limit at the desired grid spacing; for
intermediate (coarser) grids the effective iteration limit is scaled
by the grid spacing multiplier.
[Default is 500.]
.. _-Q:
**-Q**
Suggest grid dimensions which have a highly composite greatest
common factor. This allows surface to use several intermediate steps
in the solution, yielding faster run times and better results. The
sizes suggested by **-Q** can be achieved by altering **-R** and/or
**-I**. You can recover the **-R** and **-I** you want later by
using :doc:`grdsample` or :doc:`grdcut` on the output of **surface**.
.. _-S:
**-S**\ *search_radius*\ [**m**\ \|\ **s**]
Search radius. Enter *search\_radius* in same units as x,y data;
append **m** to indicate arc minutes or **s** for arc seconds. This
is used to initialize the grid before the first iteration; it is not
worth the time unless the grid lattice is prime and cannot have
regional stages. [Default = 0.0 and no search is made.]
.. _-T:
**-T**\ [**i**\ \|\ **b**]\ *tension_factor*
Tension factor[s]. These must be between 0 and 1. Tension may be
used in the interior solution (above equation, where it suppresses
spurious oscillations) and in the boundary conditions (where it
tends to flatten the solution approaching the edges). Using zero for
both values results in a minimum curvature surface with free edges,
i.e., a natural bicubic spline. Use **-Ti**\ *tension_factor*
to set interior tension, and **-Tb**\ *tension_factor* to set
boundary tension. If you do not prepend **i** or **b**, both will be
set to the same value. [Default = 0 for both gives minimum curvature
solution.]
.. _-V:
.. |Add_-V| replace::
**-V3** will report the convergence after each iteration;
**-V** will report only after each regional grid is converged.
.. include:: explain_-V.rst_
.. _-Z:
**-Z**\ *over-relaxation_factor*
Over-relaxation factor. This parameter is used to accelerate the
convergence; it is a number between 1 and 2. A value of 1 iterates
the equations exactly, and will always assure stable convergence.
Larger values overestimate the incremental changes during
convergence, and will reach a solution more rapidly but may become
unstable. If you use a large value for this factor, it is a good
idea to monitor each iteration with the **-Vl** option. [Default =
1.4 converges quickly and is almost always stable.]
.. include:: explain_-aspatial.rst_
.. |Add_-bi| replace:: [Default is 3 input columns].
.. include:: explain_-bi.rst_
.. |Add_-di| unicode:: 0x20 .. just an invisible code
.. include:: explain_-di.rst_
.. |Add_-e| unicode:: 0x20 .. just an invisible code
.. include:: explain_-e.rst_
.. |Add_-f| unicode:: 0x20 .. just an invisible code
.. include:: explain_-f.rst_
.. |Add_-h| replace:: Not used with binary data.
.. include:: explain_-h.rst_
.. include:: explain_-icols.rst_
.. |Add_nodereg| unicode:: 0x20 .. just an invisible code
.. include:: explain_nodereg.rst_
.. include:: explain_colon.rst_
.. include:: explain_help.rst_
.. include:: explain_float.rst_
Examples
--------
To grid 5 by 5 minute gravity block means from the ASCII data in
hawaii_5x5.xyg, using a *tension_factor* = 0.25, a
*convergence_limit* = 0.1 milligal, writing the result to a file called
hawaii_grd.nc, and monitoring each iteration, try:
::
gmt surface hawaii_5x5.xyg -R198/208/18/25 -I5m -Ghawaii_grd.nc -T0.25 -C0.1 -Vl
Bugs
----
**surface** will complain when more than one data point is found for any
node and suggest that you run :doc:`blockmean`, :doc:`blockmedian`, or
:doc:`blockmode` first. If you did run these decimators and still get this
message it usually means that your grid spacing is so small that you
need more decimals in the output format used. You may
specify more decimal places by editing the parameter
**FORMAT_FLOAT_OUT** in your :doc:`gmt.conf` file prior to running
the decimators or choose binary input and/or output using single or
double precision storage.
Note that only gridline registration is possible with **surface**. If
you need a pixel-registered grid you can resample a gridline registered
grid using :doc:`grdsample` **-T**.
See Also
--------
:doc:`blockmean`,
:doc:`blockmedian`,
:doc:`blockmode`,
:doc:`gmt`,
:doc:`grdcut`,
:doc:`grdsample`,
:doc:`greenspline`,
:doc:`nearneighbor`,
:doc:`triangulate`,
:doc:`sphtriangulate`
References
----------
Smith, W. H. F, and P. Wessel, 1990, Gridding with continuous curvature
splines in tension, *Geophysics*, 55, 293-305.