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       surface - adjustable tension continuous curvature surface gridding algorithm


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


       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.

              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.


       -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     Without any modifier, this option indicates that x is longitude and may be periodic
              in 360 degrees.  With optional arguments it  will  instead  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)].  Applies to geographic coordinates only.

       -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].


       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


       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.


       blockmean(1gmt),   blockmedian(1gmt),   blockmode(1gmt),   gmt(1gmt),  nearneighbor(1gmt),


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

                                            1 Jan 2004                                 SURFACE(l)