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<title>SURFACE</title>
</head>
<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>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">surface −
adjustable tension continuous curvature surface gridding
algorithm</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</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>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</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 valign="top">(1 - T) * L (L (z)) + T * L (z) = 0</p></td>
</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 style="margin-top: 1em" valign="top"><b>−G</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−I</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><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 valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−R</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><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>
</table>
<a name="OPTIONS"></a>
<h2>OPTIONS</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" valign="top"><b>−A</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−C</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−H</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−L</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−N</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−Q</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−S</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−T</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−Z</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−:</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−bi</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−f</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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>
</table>
<a name="GRID VALUES PRECISION"></a>
<h2>GRID VALUES PRECISION</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>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</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>
<a name="BUGS"></a>
<h2>BUGS</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>
<a name="SEE ALSO"></a>
<h2>SEE ALSO</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>
<a name="REFERENCES"></a>
<h2>REFERENCES</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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