## NAME

          surface - adjustable tension continuous curvature surface gridding
          algorithm

## SYNOPSIS

          surface [ xyzfile ] -Goutputfile.grd -Ix_inc[m|c][/y_inc[m|c]]
          -Rwest/east/south/north[r] [ -Aaspect_ratio ] [ -Cconvergence_limit ] [
          -H[nrec] ] [ -Lllower ] [ -Luupper ] [ -Nmax_iterations ] [ -Q ] [
          -Ssearch_radius[m] ] [ -Ttension_factor[ib] ] [ -V[l] ] [ -Zover-
          relaxation_factor ] [ -: ] [ -bi[s][n] ]

## DESCRIPTION

          surface reads randomly-spaced (x,y,z) triples from standard input [or
          xyzfile] 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 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 blockmean, blockmedian, or
          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 grdfile with values, or simply
          be the minimum/maximum input data values.

          xyzfile
               3 column ASCII file [or binary, see -b] holding (x,y,z) data
               values.  If no file is specified, surface will read from standard
               input.

          -G   Output file name.  Output is a binary 2-D .grd file.

          -I   x_inc [and optionally y_inc] is the grid spacing. Append m to
               indicate minutes or c to indicate seconds.

          -R   west, east, south, and north specify the Region of interest.  To
               specify boundaries in degrees and minutes [and seconds], use the
               dd:mm[:ss] format.  Append r if lower left and upper right map
               coordinates are given instead of wesn.

## OPTIONS

          -A   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   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).  [Default is
               scaled to 0.1 percent of typical gradient in input data.]

          -H   Input file(s) has Header record(s).  Number of header records can
               be changed by editing your .gmtdefaults file.  If used, GMT
               default is 1 header record.  Not used with binary data.

          -L   Impose limits on the output solution.  llower sets the lower
               bound.  lower can be the name of a grdfile with lower bound
               values, a fixed value, d to set to minimum input value, or u for
               unconstrained [Default].  uupper sets the upper bound and can be
               the name of a grdfile with upper bound values, a fixed value, d
               to set to maximum input value, or u for unconstrained [Default].

          -N   Number of iterations.  Iteration will cease when
               convergence_limit is reached or when number of iterations reaches
               max_iterations. [Default is 250.]

          -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
               grdsample or grdcut on the output of surface.

          -S   Search radius.  Enter search_radius in same units as x,y data;
               append m 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.]

          -T   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
               -Ttension_factori to set interior tension, and -Ttension_factorb
               to set boundary tension.  If you do not append i or b, both will
               be set to the same value.  [Default = 0 for both gives minimum
               curvature solution.]

          -V   Selects verbose mode, which will send progress reports to stderr
               [Default runs "silently"].  -Vl will report the convergence after
               each iteration;  -V will report only after each regional grid is
               converged.

          -Z   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.]

          -:   Toggles between (longitude,latitude) and (latitude,longitude)
               input/output.  [Default is (longitude,latitude)].

          -bi  Selects binary input.  Append s for single precision [Default is
               double].  Append n for the number of columns in the binary
               file(s).  [Default is 3 input columns].

## 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.grd, and
          monitoring each iteration, try:

          surface hawaii_5x5.xyg -R198/208/18/25 -I5m -Ghawaii_grd.grd -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 blockmean, blockmedian, or blockmode
          first.  If you did run blockm* 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 blockm*.  You may specify more decimal
          places by editing the parameter D_FORMAT in your .gmtdefaults file
          prior to running blockm*, or choose binary input and/or output using
          single or double precision storage.

## SEE ALSO

          blockmean, blockmedian, blockmode, gmt, nearneighbor, triangulate

## REFERENCES

          Smith, W. H. F, and P. Wessel, 1990, Gridding with continuous
          curvature splines in tension, Geophysics, 55, 293-305.