surface  -  adjustable  tension  continuous  curvature surface gridding


       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-relax-
       ation_factor ] [ -: ] [ -bi[s][n] ] [ -f[i|o]colinfo ]


       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

               (1 - T) * L (L (z)) + T * L (z) = 0

       where T is a tension factor between 0 and 1, and L indicates the Lapla-
       cian  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 topog-
       raphy  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  mini-
       mum/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

       -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     xmin, xmax, ymin, and ymax specify the Region of  interest.  For
              geographic  regions,  these  limits  correspond  to  west, east,
              south, and north and you may specify them in decimal degrees  or
              in  [+-]dd:mm[][W|E|S|N]  format.  Append r if lower left
              and upper right map coordinates are given instead of  wesn.  The
              two  shorthands  -Rg  -Rd  stand  for  global  domain  (0/360 or
              -180/+180 in longitude respectively, with -90/+90 in  latitude).
              For  calendar time coordinates you may either give relative time
              (relative  to  the  selected  TIME_EPOCH  and  in  the  selected
              TIME_UNIT;  append  t  to  -JX|x),  or absolute time of the form
              [date]T[clock] (append T to -JX|x). At least  one  of  date  and
              clock must be present; the T is always required. The date string
              must be of the form [-]yyyy[-mm[-dd]]  (Gregorian  calendar)  or
              yyyy[-Www[-d]]  (ISO week calendar), while the clock string must
              be of the form hh:mm:ss[.xxx]. The use of delimiters  and  their
              type  and  positions must be as indicated (however, input/output
              and plotting formats are flexible).


       -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

       -C     Convergence  limit.  Iteration is assumed to have converged when
              the maximum absolute change in any grid value is less than  con-
              vergence_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  .gmtdefaults4 file. If used, GMT
              default is 1 header record. Use -Hi if only  input  data  should
              have  header  records  [Default will write out header records if
              the input data have them].  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 val-
              ues, 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   conver-
              gence_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  sup-
              presses  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 sur-
              face with free edges, i.e. a natural bicubic spline.  Use -Tten-
              sion_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 cur-
              vature 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  iter-
              ates  the  equations exactly, and will always assure stable con-
              vergence. 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  and/or output. [Default is (longitude,latitude)].  Append
              i to select input only or o  to  select  output  only.  [Default
              affects both].

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

       -f     Special  formatting  of  input  and output columns (time or geo-
              graphical data) Specify i(nput) or  o(utput)  [Default  is  both
              input  and output].  Give one or more columns (or column ranges)
              separated by commas.  Append T (Absolute calendar time), t (time
              relative  to  chosen TIME_EPOCH), x (longitude), y (latitude), g
              (geographic coordinate), or f (floating point) to each column or
              column range item.


       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 .gmtdefaults4 file  prior  to
       running  blockm*,  or choose binary input and/or output using single or
       double precision storage.


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


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

GMT4.0                            1 Oct 2004                        SURFACE(l)

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