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<HTML>
<HEAD>
<TITLE>surface</TITLE>
</HEAD>
<BODY>
<H1>surface</H1>
<HR>
<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
surface - adjustable tension continuous curvature surface
gridding algorithm
</PRE>
<H2>SYNOPSIS</H2><PRE>
<B>surface</B> [ <I>xyzfile</I> ] <B>-G</B><I>outputfile.grd</I>
<B>-I</B><I>x</I><B>_</B><I>inc</I>[<B>m|c</B>][/<I>y</I><B>_</B><I>inc</I>[<B>m|c</B>]] <B>-R</B><I>west/east/south/north</I>[<B>r</B>] [
<B>-A</B><I>aspect</I><B>_</B><I>ratio</I> ] [ <B>-C</B><I>convergence</I><B>_</B><I>limit</I> ] [ <B>-H</B>[<I>nrec</I>] ] [
<B>-Ll</B><I>lower</I> ] [ <B>-Lu</B><I>upper</I> ] [ <B>-N</B><I>max</I><B>_</B><I>iterations</I> ] [ <B>-Q</B> ] [
<B>-S</B><I>search</I><B>_</B><I>radius</I>[<B>m</B>] ] [ <B>-T</B><I>tension</I><B>_</B><I>factor</I>[<B>ib</B>] ] [ <B>-V</B>[<B>l</B>] ] [
<B>-Z</B><I>over-relaxation</I><B>_</B><I>factor</I> ] [ <B>-:</B> ] [ <B>-bi</B>[<B>s</B>][<I>n</I>] ]
</PRE>
<H2>DESCRIPTION</H2><PRE>
<B>surface</B> reads randomly-spaced (x,y,z) triples from stan
dard input [or <I>xyzfile</I>] and produces a binary grdfile 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 indi
cates 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 sup
press 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 har
monic 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 grd
file with values, or simply be the minimum/maximum input
data values.
<I>xyzfile</I>
3 column ASCII file [or binary, see <B>-b</B>] holding
(x,y,z) data values. If no file is specified, <B>sur</B>
<B>face</B> will read from standard input.
<B>-G</B> Output file name. Output is a binary 2-D <I>.grd</I> file.
<B>-I</B> <I>x</I><B>_</B><I>inc</I> [and optionally <I>y</I><B>_</B><I>inc</I>] is the grid spacing.
Append <B>m</B> to indicate minutes or <B>c</B> to indicate sec
onds.
<B>-R</B> <I>west,</I> <I>east,</I> <I>south,</I> and <I>north</I> specify the Region of
interest. To specify boundaries in degrees and min
utes [and seconds], use the dd:mm[:ss] format.
Append <B>r</B> if lower left and upper right map coordi
nates are given instead of wesn.
<B>-A</B> Aspect ratio. If desired, grid anisotropy can be
added to the equations. Enter <I>aspect</I><B>_</B><I>ratio</I>, where
dy = dx / <I>aspect</I><B>_</B><I>ratio</I> relates the grid dimensions.
[Default = 1 assumes isotropic grid.]
<B>-C</B> Convergence limit. Iteration is assumed to have
converged when the maximum absolute change in any
grid value is less than <I>convergence</I><B>_</B><I>limit</I>. (Units
same as data z units). [Default is scaled to 0.1
percent of typical gradient in input data.]
<B>-H</B> Input file(s) has Header record(s). Number of
header records can be changed by editing your .gmt
defaults file. If used, <B><A HREF="GMT.html">GMT</A></B> default is 1 header
record. Not used with binary data.
<B>-L</B> Without any modifier, this option indicates that x
is longitude and may be periodic in 360 degrees.
With optional arguments it will instead impose lim
its on the output solution. <B>l</B><I>lower</I> sets the lower
bound. <I>lower</I> can be the name of a grdfile with
lower bound values, a fixed value, <B>d</B> to set to min
imum 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 grdfile with upper bound values, a fixed value, <B>d</B>
to set to maximum input value, or <B>u</B> for uncon
strained [Default].
<B>-N</B> Number of iterations. Iteration will cease when
<I>convergence</I><B>_</B><I>limit</I> is reached or when number of
iterations reaches <I>max</I><B>_</B><I>iterations</I>. [Default is
250.]
<B>-Q</B> Suggest grid dimensions which have a highly compos
ite 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 grdsample or grdcut on the out
put of surface.
<B>-S</B> Search radius. Enter <I>search</I><B>_</B><I>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 itera
tion; it is not worth the time unless the grid lat
tice is prime and cannot have regional stages.
[Default = 0.0 and no search is made.]
<B>-T</B> Tension factor[s]. These must be between 0 and 1.
Tension may be used in the interior solution (above
equation, where it suppresses spurious oscilla
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</I><B>_</B><I>factor</I><B>i</B> to
set interior tension, and <B>-T</B><I>tension</I><B>_</B><I>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.]
<B>-V</B> 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.
<B>-Z</B> 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.]
<B>-:</B> Toggles between (longitude,latitude) and (lati
tude,longitude) input/output. [Default is (longi
tude,latitude)]. Applies to geographic coordinates
only.
<B>-bi</B> Selects binary input. Append <B>s</B> for single precision
[Default is double]. Append <I>n</I> for the number of
columns in the binary file(s). [Default is 3 input
columns].
</PRE>
<H2>EXAMPLES</H2><PRE>
To grid 5 by 5 minute gravity block means from the ASCII
data in hawaii_5x5.xyg, using a <I>tension</I><B>_</B><I>factor</I> = 0.25, a
<I>convergence</I><B>_</B><I>limit</I> = 0.1 milligal, writing the result to a
file called <I>hawaii</I><B>_</B><I>grd.grd</I>, and monitoring each iteration,
try:
surface hawaii_5x5.xyg <B>-R</B>198/208/18/25 <B>-I</B>5<B>m</B>
<B>-G</B>hawaii_grd.grd <B>-T</B>0.25 <B>-C</B>0.1 <B>-VL</B>
</PRE>
<H2>BUGS</H2><PRE>
<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 deci
binary input and/or output using single or double preci
sion storage.
</PRE>
<H2>SEE ALSO</H2><PRE>
<I><A HREF="blockmean.html">blockmean</A></I>(l), <I><A HREF="blockmedian.html">blockmedian</A></I>(l), <I><A HREF="blockmode.html">blockmode</A></I>(l), <I>gmt</I>(l),
<I><A HREF="nearneighbor.html">nearneighbor</A></I>(l), <I><A HREF="triangulate.html">triangulate</A></I>(l)
</PRE>
<H2>REFERENCES</H2><PRE>
Smith, W. H. F, and P. Wessel, 1990, Gridding with contin
uous curvature splines in tension, <I>Geophysics</I>, 55,
293-305.
</PRE>
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