Provided by: gmt-common_5.4.5+dfsg-1_all bug

NAME

       surface - Grid table data using adjustable tension continuous curvature splines

SYNOPSIS

       surface [ table ]  -Goutputfile.nc
        -Iincrement
        -Rregion  [   -Aaspect_ratio  ]  [  -Cconvergence_limit[%] ] [  -Lllower ] [ -Luupper ] [
       -Nmax_iterations ] [   -Q  ]  [   -Ssearch_radius[m|s]  ]  [   -T[i|b]tension_factor  ]  [
       -V[level]  ]  [   -Zover-relaxation_factor  ]  [  -aflags  ] [ -bibinary ] [ -dinodata ] [
       -eregexp ] [ -fflags ] [ -hheaders ] [ -iflags ] [ -r ] [ -:[i|o] ]

       Note: No space is allowed between the option flag and the associated arguments.

DESCRIPTION

       surface reads randomly-spaced (x,y,z) triples from standard input [or table] and  produces
       a binary grid file 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 grid with values, or simply
       be  the  minimum/maximum input data values. Natural boundary conditions are applied at the
       edges, except for geographic data with 360-degree range where we apply  periodic  boundary
       conditions in the longitude direction.

REQUIRED ARGUMENTS

       -Goutputfile.nc
              Output  file  name.  Output  is  a binary 2-D .nc file. Note that the smallest grid
              dimension must be at least 4.

       -Ixinc[unit][+e|n][/yinc[unit][+e|n]]
              x_inc [and optionally y_inc] is the  grid  spacing.  Optionally,  append  a  suffix
              modifier. Geographical (degrees) coordinates: Append m to indicate arc minutes or s
              to indicate arc seconds. If one of the units e,  f,  k,  M,  n  or  u  is  appended
              instead,  the  increment  is assumed to be given in meter, foot, km, Mile, nautical
              mile or US survey foot, respectively, and  will  be  converted  to  the  equivalent
              degrees  longitude  at the middle latitude of the region (the conversion depends on
              PROJ_ELLIPSOID). If y_inc is given but set to 0 it will be reset  equal  to  x_inc;
              otherwise  it  will  be  converted  to  degrees latitude. All coordinates: If +e is
              appended then the corresponding max x (east) or y (north) may be slightly  adjusted
              to  fit  exactly  the  given  increment  [by  default the increment may be adjusted
              slightly to fit the given domain]. Finally, instead of giving an increment you  may
              specify  the  number  of  nodes  desired  by  appending  +n to the supplied integer
              argument; the increment is then recalculated from  the  number  of  nodes  and  the
              domain.  The  resulting  increment  value  depends  on  whether you have selected a
              gridline-registered or pixel-registered grid;  see  App-file-formats  for  details.
              Note:  if -Rgrdfile is used then the grid spacing has already been initialized; use
              -I to override the values.

       -Rxmin/xmax/ymin/ymax[+r][+uunit] (more ...)
              Specify the region of interest.

OPTIONAL ARGUMENTS

       table  One or more ASCII (or binary, see -bi[ncols][type]) data table  file(s)  holding  a
              number of data columns. If no tables are given then we read from standard input.

       -Aaspect_ratio
              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.]

       -Cconvergence_limit[%]
              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).  Alternatively,  give  limit in percentage of rms deviation by appending %.
              [Default is scaled to 1e-4 of the root-mean-square deviation of  the  data  from  a
              best-fit  (least-squares)  plane.].   This  is  the  final convergence limit at the
              desired grid spacing; for intermediate (coarser) grids  the  effective  convergence
              limit is divided by the grid spacing multiplier.

       -Lllower and -Luupper
              Impose limits on the output solution. llower sets the lower bound. lower can be the
              name of a grid file 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 grid file with upper bound values, a fixed  value,  d  to  set  to
              maximum  input  value, or u for unconstrained [Default]. Grid files used to set the
              limits may contain NaNs. In the presence of NaNs, the limit of a node  masked  with
              NaN is unconstrained.

       -Nmax_iterations
              Number  of  iterations.  Iteration  will cease when convergence_limit is reached or
              when number of iterations reaches max_iterations.   This  is  the  final  iteration
              limit  at  the desired grid spacing; for intermediate (coarser) grids the effective
              iteration limit is scaled by the grid spacing multiplier.  [Default is 500.]

       -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.

       -Ssearch_radius[m|s]
              Search radius. Enter search_radius in same units as x,y data; append m to  indicate
              arc  minutes  or  s for arc seconds. 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[i|b]tension_factor
              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  -Titension_factor to set interior
              tension, and -Tbtension_factor to set boundary tension. If you do not prepend i  or
              b,  both  will  be  set  to  the  same  value.  [Default = 0 for both gives minimum
              curvature solution.]

       -V[level] (more ...)
              Select verbosity level [c]. -V3 will report the convergence after  each  iteration;
              -V will report only after each regional grid is converged.

       -Zover-relaxation_factor
              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.]

       -acol=name[...] (more ...)
              Set aspatial column associations col=name.

       -bi[ncols][t] (more ...)
              Select native binary input. [Default is 3 input columns].

       -dinodata (more ...)
              Replace input columns that equal nodata with NaN.

       -e[~]"pattern" | -e[~]/regexp/[i] (more ...)
              Only accept data records that match the given pattern.

       -f[i|o]colinfo (more ...)
              Specify data types of input and/or output columns.

       -h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
              Skip or produce header record(s). Not used with binary data.

       -icols[+l][+sscale][+ooffset][,...] (more ...)
              Select input columns and transformations (0 is first column).

       -r (more ...)
              Set pixel node registration [gridline].

       -:[i|o] (more ...)
              Swap 1st and 2nd column on input and/or output.

       -^ or just -
              Print a short message about the syntax of the command, then exits (NOTE: on Windows
              just use -).

       -+ or just +
              Print  an  extensive  usage  (help)  message,  including  the  explanation  of  any
              module-specific option (but not the GMT common options), then exits.

       -? or no arguments
              Print  a  complete  usage (help) message, including the explanation of all options,
              then exits.

GRID VALUES PRECISION

       Regardless of the precision of the input data, GMT programs that create  grid  files  will
       internally hold the grids in 4-byte floating point arrays. This is done to conserve memory
       and furthermore most if not all real data  can  be  stored  using  4-byte  floating  point
       values.  Data  with  higher  precision  (i.e.,  double  precision  values)  will lose that
       precision once GMT operates on the grid  or  writes  out  new  grids.  To  limit  loss  of
       precision  when  processing  data you should always consider normalizing the data prior to
       processing.

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.nc, and monitoring each iteration, try:

              gmt surface hawaii_5x5.xyg -R198/208/18/25 -I5m -Ghawaii_grd.nc -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 these decimators 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. You may specify more decimal places by editing
       the parameter FORMAT_FLOAT_OUT in your gmt.conf file prior to running  the  decimators  or
       choose binary input and/or output using single or double precision storage.

       Note   that   only  gridline  registration  is  possible  with  surface.  If  you  need  a
       pixel-registered grid you can resample a gridline registered grid using grdsample -T.

SEE ALSO

       blockmean, blockmedian, blockmode,  gmt,  grdcut,  grdsample,  greenspline,  nearneighbor,
       triangulate, sphtriangulate

REFERENCES

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

COPYRIGHT

       2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe