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 ] [ -Lllower ]
[ - Luupper ] [ - Nmax_iterations ] [ - Q ] [ -
Ssearch_radius[m] ] [ -Ttension_factor[ib] ] [ -V[l] ] [ -
Zover-relaxation_factor ] [ -: ] [ -b[d] ]
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 pack-
ages. 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 or blockmedian 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 con-
verged 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 itera-
tions 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 sug-
gested 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 flat-
ten 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 solu-
tion.]
-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 con-
vergence, 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)]
-b Selects binary input mode [Default is ASCII]. Append
d to indicate double precision [Default is single].
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 or block-
median first. If you did run blockmean/median 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 blockmean/median. You may specify more decimal places by
editing the parameter D_FORMAT in your .gmtdefaults file
prior to running blockmean/median, or choose binary input
and/or output using single or double precision storage.
SEE ALSO
blockmean, blockmedian, gmt, nearneighbor, triangulate
REFERENCES
Wessel, P., and W. H. F. Smith, 1995, The Generic Mapping
Tools (GMT) version 3.0 Technical Reference & Cookbook,
SOEST/NOAA.
Wessel, P., and W. H. F. Smith, 1995, New Version of the
Generic Mapping Tools Released, EOS Trans. AGU, 76, p. 329.
Wessel, P., and W. H. F. Smith, 1995, New Version of the
Generic Mapping Tools Released,
http://www.agu.org/eos_elec/95154e.html, Copyright 1995 by
the American Geophysical Union.
Wessel, P., and W. H. F. Smith, 1991, Free Software Helps
Map and Display Data, EOS Trans. AGU, 72, p. 441.
Smith, W. H. F, and P. Wessel, 1990, Gridding with continu-
ous curvature splines in tension, Geophysics, 55, 293-305.