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<title>SURFACE</title>
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<body bgcolor="#ffffff">
<h1 align="center">SURFACE</h1>
<a href="#NAME">NAME</a><br>
<a href="#SYNOPSIS">SYNOPSIS</a><br>
<a href="#DESCRIPTION">DESCRIPTION</a><br>
<a href="#OPTIONS">OPTIONS</a><br>
<a href="#GRID VALUES PRECISION">GRID VALUES PRECISION</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#BUGS">BUGS</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<a href="#REFERENCES">REFERENCES</a><br>
<hr>
<h2>NAME
<a name="NAME"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">surface −
adjustable tension continuous curvature surface gridding
algorithm</p>
<h2>SYNOPSIS
<a name="SYNOPSIS"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><b>surface</b>
[ <i>xyzfile</i> ] <b>−G</b><i>outputfile.grd</i>
<b>−I</b><i>xinc</i>[<i>unit</i>][<b>=</b>|<b>+</b>][/<i>yinc</i>[<i>unit</i>][<b>=</b>|<b>+</b>]]
<b>−R</b><i>west</i>/<i>east</i>/<i>south</i>/<i>north</i>[<b>r</b>]
[ <b>−A</b><i>aspect_ratio</i> ] [
<b>−C</b><i>convergence_limit</i> ] [
<b>−H</b>[<b>i</b>][<i>nrec</i>] ] [
<b>−Ll</b><i>lower</i> ] [
<b>−Lu</b><i>upper</i> ] [
<b>−N</b><i>max_iterations</i> ] [ <b>−Q</b> ] [
<b>−S</b><i>search_radius</i>[<b>m</b>] ] [
<b>−T</b><i>tension_factor</i>[<b>i</b>|<b>b</b>] ] [
<b>−V</b>[<b>l</b>] ] [
<b>−Z</b><i>over-relaxation_factor</i> ] [
<b>−:</b>[<b>i</b>|<b>o</b>] ] [
<b>−bi</b>[<b>s</b>|<b>S</b>|<b>d</b>|<b>D</b>[<i>ncol</i>]|<b>c</b>[<i>var1</i><b>/</b><i>...</i>]]
] [ <b>−f</b><i>colinfo</i> ]</p>
<h2>DESCRIPTION
<a name="DESCRIPTION"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><b>surface</b>
reads randomly-spaced (x,y,z) triples from standard input
[or <i>xyzfile</i>] and produces a binary grid file of
gridded values z(x,y) by solving:</p>
<table width="100%" border="0" rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="8%"></td>
<td width="7%"></td>
<td width="85%">
<p>(1 - T) * L (L (z)) + T * L (z) = 0</p></td></tr>
</table>
<p style="margin-left:11%; margin-top: 1em">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 <b><A HREF="blockmean.html">blockmean</A></b>, <b><A HREF="blockmedian.html">blockmedian</A></b>, or
<b><A HREF="blockmode.html">blockmode</A></b> 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. <i><br>
xyzfile</i></p>
<p style="margin-left:22%;">3 column ASCII file [or binary,
see <b>−b</b>] holding (x,y,z) data values. If no file
is specified, <b>surface</b> will read from standard
input.</p>
<table width="100%" border="0" rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−G</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>Output file name. Output is a binary 2-D <i>.grd</i>
file. Note that the smallest grid dimension must be at least
4.</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−I</b></p></td>
<td width="8%"></td>
<td width="78%">
<p><i>x_inc</i> [and optionally <i>y_inc</i>] is the grid
spacing. Optionally, append a suffix modifier.
<b>Geographical (degrees) coordinates</b>: Append <b>m</b>
to indicate arc minutes or <b>c</b> to indicate arc seconds.
If one of the units <b>e</b>, <b>k</b>, <b>i</b>, or
<b>n</b> is appended instead, the increment is assumed to be
given in meter, km, miles, or nautical miles, respectively,
and will be converted to the equivalent degrees longitude at
the middle latitude of the region (the conversion depends on
<b><A HREF="gmtdefaults.html#ELLIPSOID">ELLIPSOID</A></b>). If /<i>y_inc</i> is given but set to 0 it
will be reset equal to <i>x_inc</i>; otherwise it will be
converted to degrees latitude. <b>All coordinates</b>: If
<b>=</b> is appended then the corresponding max <i>x</i>
(<i>east</i>) or <i>y</i> (<i>north</i>) 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
<i>number of nodes</i> desired by appending <b>+</b> 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
Appendix B for details. Note: if
<b>−R</b><i>grdfile</i> is used then grid spacing has
already been initialized; use <b>−I</b> to override
the values.</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−R</b></p></td>
<td width="8%"></td>
<td width="78%">
<p><i>xmin</i>, <i>xmax</i>, <i>ymin</i>, and <i>ymax</i>
specify the Region of interest. For geographic regions,
these limits correspond to <i>west, east, south,</i> and
<i>north</i> and you may specify them in decimal degrees or
in [+-]dd:mm[:ss.xxx][W|E|S|N] format. Append <b>r</b> if
lower left and upper right map coordinates are given instead
of w/e/s/n. The two shorthands <b>−Rg</b> and
<b>−Rd</b> stand for global domain (0/360 and
-180/+180 in longitude respectively, with -90/+90 in
latitude). Alternatively, specify the name of an existing
grid file and the <b>−R</b> settings (and grid
spacing, if applicable) are copied from the grid. For
calendar time coordinates you may either give (a) relative
time (relative to the selected <b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b> and in the
selected <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b>; append <b>t</b> to
<b>−JX</b>|<b>x</b>), or (b) absolute time of the form
[<i>date</i>]<b>T</b>[<i>clock</i>] (append <b>T</b> to
<b>−JX</b>|<b>x</b>). At least one of <i>date</i> and
<i>clock</i> must be present; the <b>T</b> is always
required. The <i>date</i> string must be of the form
[-]yyyy[-mm[-dd]] (Gregorian calendar) or yyyy[-Www[-d]]
(ISO week calendar), while the <i>clock</i> string must be
of the form hh:mm:ss[.xxx]. The use of delimiters and their
type and positions must be exactly as indicated (however,
input, output and plot formats are customizable; see
<b><A HREF="gmtdefaults.html">gmtdefaults</A></b>).</p> </td></tr>
</table>
<h2>OPTIONS
<a name="OPTIONS"></a>
</h2>
<table width="100%" border="0" rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em"><b>−A</b></p></td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em">Aspect ratio. If desired, grid
anisotropy can be added to the equations. Enter
<i>aspect_ratio</i>, where dy = dx / <i>aspect_ratio</i>
relates the grid dimensions. [Default = 1 assumes isotropic
grid.]</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−C</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Convergence limit. Iteration is assumed to have
converged when the maximum absolute change in any grid value
is less than <i>convergence_limit</i>. (Units same as data z
units). [Default is scaled to 0.1 percent of typical
gradient in input data.]</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−H</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Input file(s) has header record(s). If used, the default
number of header records is <b><A HREF="gmtdefaults.html#N_HEADER_RECS">N_HEADER_RECS</A></b>. Use
<b>−Hi</b> if only input data should have header
records [Default will write out header records if the input
data have them]. Blank lines and lines starting with # are
always skipped. Not used with binary data.</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−L</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Impose limits on the output solution.
<b>l</b><i>lower</i> sets the lower bound. <i>lower</i> can
be the name of a grid file with lower bound values, a fixed
value, <b>d</b> to set to minimum input value, or <b>u</b>
for unconstrained [Default]. <b>u</b><i>upper</i> sets the
upper bound and can be the name of a grid file with upper
bound values, a fixed value, <b>d</b> to set to maximum
input value, or <b>u</b> for unconstrained [Default].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−N</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Number of iterations. Iteration will cease when
<i>convergence_limit</i> is reached or when number of
iterations reaches <i>max_iterations</i>. [Default is
250.]</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−Q</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>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
<b>−Q</b> can be achieved by altering <b>−R</b>
and/or <b>−I</b>. You can recover the <b>−R</b>
and <b>−I</b> you want later by using <b><A HREF="grdsample.html">grdsample</A></b>
or <b><A HREF="grdcut.html">grdcut</A></b> on the output of <b>surface</b>.</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−S</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Search radius. Enter <i>search_radius</i> in same units
as x,y data; append <b>m</b> to indicate minutes. 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.]</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−T</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>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
<b>−T</b><i>tension_factor</i><b>i</b> to set interior
tension, and <b>−T</b><i>tension_factor</i><b>b</b> to
set boundary tension. If you do not append <b>i</b> or
<b>b</b>, both will be set to the same value. [Default = 0
for both gives minimum curvature solution.]</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−V</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Selects verbose mode, which will send progress reports
to stderr [Default runs "silently"].
<b>−Vl</b> will report the convergence after each
iteration; <b>−V</b> will report only after each
regional grid is converged.</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−Z</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>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 <b>−Vl</b> option. [Default =
1.4 converges quickly and is almost always stable.]</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−:</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Toggles between (longitude,latitude) and
(latitude,longitude) input and/or output. [Default is
(longitude,latitude)]. Append <b>i</b> to select input only
or <b>o</b> to select output only. [Default affects
both].</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−bi</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Selects binary input. Append <b>s</b> for single
precision [Default is <b>d</b> (double)]. Uppercase <b>S</b>
or <b>D</b> will force byte-swapping. Optionally, append
<i>ncol</i>, the number of columns in your binary input file
if it exceeds the columns needed by the program. Or append
<b>c</b> if the input file is netCDF. Optionally, append
<i>var1</i><b>/</b><i>var2</i><b>/</b><i>...</i> to specify
the variables to be read. [Default is 3 input columns].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−f</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Special formatting of input and/or output columns (time
or geographical data). Specify <b>i</b> or <b>o</b> to make
this apply only to input or output [Default applies to
both]. Give one or more columns (or column ranges) separated
by commas. Append <b>T</b> (absolute calendar time),
<b>t</b> (relative time in chosen <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b> since
<b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b>), <b>x</b> (longitude), <b>y</b>
(latitude), or <b>f</b> (floating point) to each column or
column range item. Shorthand
<b>−f</b>[<b>i</b>|<b>o</b>]<b>g</b> means
<b>−f</b>[<b>i</b>|<b>o</b>]0<b>x</b>,1<b>y</b>
(geographic coordinates).</p></td></tr>
</table>
<h2>GRID VALUES PRECISION
<a name="GRID VALUES PRECISION"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">Regardless of
the precision of the input data, GMT programs that create
grid files will internally hold the grids in 4-byte floating
point arrays. This is done to conserve memory and
furthermore most if not all real data can be stored using
4-byte floating point values. Data with higher precision
(i.e., double precision values) will lose that precision
once GMT operates on the grid or writes out new grids. To
limit loss of precision when processing data you should
always consider normalizing the data prior to
processing.</p>
<h2>EXAMPLES
<a name="EXAMPLES"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">To grid 5 by 5
minute gravity block means from the ASCII data in
hawaii_5x5.xyg, using a <i>tension_factor</i> = 0.25, a
<i>convergence_limit</i> = 0.1 milligal, writing the result
to a file called hawaii_grd.grd, and monitoring each
iteration, try:</p>
<p style="margin-left:11%; margin-top: 1em"><b>surface</b>
hawaii_5x5.xyg <b>−R</b> 198/208/18/25 <b>−I</b>
5<b>m −G</b> hawaii_grd.grd <b>−T</b> 0.25
<b>−C</b> 0.1 <b>−Vl</b></p>
<h2>BUGS
<a name="BUGS"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><b>surface</b>
will complain when more than one data point is found for any
node and suggest that you run <b><A HREF="blockmean.html">blockmean</A></b>,
<b><A HREF="blockmedian.html">blockmedian</A></b>, or <b><A HREF="blockmode.html">blockmode</A></b> first. If you did
run <b>blockm*</b> 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 by <b>blockm*</b>. You
may specify more decimal places by editing the parameter
<b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b> in your .gmtdefaults4 file prior to running
<b>blockm*</b>, or choose binary input and/or output using
single or double precision storage. <br>
Note that only gridline registration is possible with
<b>surface</b>. If you need a pixel-registered grid you can
resample a gridline registered grid using <b>grdsample
−T</b>.</p>
<h2>SEE ALSO
<a name="SEE ALSO"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="blockmean.html">blockmean</A></i>(1),
<i><A HREF="blockmedian.html">blockmedian</A></i>(1), <i><A HREF="blockmode.html">blockmode</A></i>(1), <i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="nearneighbor.html">nearneighbor</A></i>(1), <i><A HREF="triangulate.html">triangulate</A></i>(1)</p>
<h2>REFERENCES
<a name="REFERENCES"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">Smith, W. H. F,
and P. Wessel, 1990, Gridding with continuous curvature
splines in tension, <i>Geophysics</i>, 55,
293−305.</p>
<hr>
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