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.